Systems, methods, and computer program products for determining impact of nodes of graph on graph neural network

Abstract

Systems, methods, and computer program products are provided for determining the impact of nodes of a graph on a graph neural network (GNN). The method includes receiving a data set including graph data associated with a graph. The method may also include selecting a target node of a plurality of nodes based on the graph data; and determining target node data associated with the target node and target edge data associated with the target node. The method may also include removing the target node data and the target edge data from the dataset to provide a target graph dataset; determining an influence metric of the target node on a GNN based on the target graph data set, wherein the GNN is trained using the data set; and performing an action based on the measure of impact of the target node on the GNN.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 410,553 filed on September 27, 2022, the disclosure of which is incorporated herein by reference in its entirety. Technical Field

[0003] The present disclosure relates generally to graph neural networks (GNNs), and in some non-limiting embodiments or aspects, to systems, methods, and computer program products for determining the influence of nodes of a graph on a GNN. Background Art

[0004] Some machine learning models, such as neural networks (e.g., convolutional neural networks), may receive an input data set including data points for training. After training the neural network, each data point in the training data set may have a different effect on a neural network generated based on the training neural network (e.g., a trained neural network). In some cases, the input data set (e.g., training data set) designed for the neural network may be independent and identically distributed. Such an input data set can be used to determine the effect (e.g., influence) of each data point of the input data set on a graph neural network (GNN).

[0005] GNNs are designed to receive graph data (e.g., graph data representing a graph), including node data and edge data. However, the graph data received by the GNN may not be independent and / or identically distributed. Therefore, it may be more difficult to determine the effect of data points of the graph data on one or more GNNs. In some cases, one or more GNNs may be relatively large and / or may require a relatively large amount of computing resources (e.g., processor resources, memory resources, etc.) to train and use. In addition, one or more GNNs may receive a relatively large amount of data for training (e.g., an input data set including graph data) and / or may require a large amount of memory space during training. Determining the effect (e.g., an influence metric) of each data point of the graph data in the input data set may require retraining one or more GNNs for each data point of the graph data for which the effect of the data point is to be determined. In addition, training one or more GNNs using one or more GNNs and generating outputs (e.g., predictions) may not accurately determine the effect of data points of the graph data on one or more GNNs. Summary of the invention

[0006] It is therefore an object of the present disclosure to provide systems, methods, and computer program products for determining the influence of nodes of a graph on a graph neural network (GNN).

[0007] According to some non-limiting embodiments or aspects, a computer-implemented method for determining the impact of a node of a graph on a GNN is provided. In some non-limiting embodiments or aspects, the method may include receiving, using at least one processor, a data set including graph data associated with a graph, the graph data including node data associated with multiple nodes of the graph and edge data associated with multiple edges of the graph. In some non-limiting embodiments or aspects, the method may include selecting, using at least one processor, a target node among the multiple nodes based on the graph data. In some non-limiting embodiments or aspects, the method may include determining, using at least one processor, target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data including the target node data, and the edge data of the graph data including the target edge data, wherein the target node may be associated with one or more target edges among the multiple edges, the one or more target edges including one or more edges connected to the target node in the graph. In some non-limiting embodiments or aspects, the method may include using at least one processor to remove the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed. In some non-limiting embodiments or aspects, the method may include using at least one processor to determine an influence measure of the target node on the GNN based on the target graph data set, wherein the GNN is trained using the data set. In some non-limiting embodiments or aspects, the method may include using the at least one processor to detect anomalies in the GNN based on the influence measure of the target node on the GNN.

[0008] In some non-limiting embodiments or aspects, the method may further include training an initial GNN based on the data set to provide the GNN.

[0009] In some non-limiting embodiments or aspects, determining the influence metric of the target node on the GNN based on the target graph dataset may include: determining a set of first model parameters of the GNN based on the dataset; determining a set of modified model parameters of the GNN based on the target graph dataset; and determining the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0010] In some non-limiting embodiments or aspects, determining the influence metric of the target node on the GNN based on the target graph dataset may include: determining a first influence metric of the target node on the GNN, wherein the first influence metric may be associated with a property of the target node with respect to the topology of the graph; determining a second influence metric of the target node on the GNN, wherein the second influence metric may be associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric may be associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determining the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0011] In some non-limiting embodiments or aspects, determining the first influence metric of the target node on the GNN may include determining the first influence metric of the target node on the GNN based on a Hessian matrix.

[0012] In some non-limiting embodiments or aspects, determining the second influence metric of the target node on the GNN may include determining the second influence metric of the target node on the GNN based on a Hessian matrix.

[0013] In some non-limiting embodiments or aspects, determining the third influence metric of the target node on the GNN may include determining the third influence metric of the target node on the GNN based on a Hessian matrix.

[0014] In some non-limiting embodiments or aspects, detecting the anomaly in the GNN based on the influence metric of the target node on the GNN may include: determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detecting whether the fairness metric of the GNN meets a predetermined threshold.

[0015] In some non-limiting embodiments or aspects, removing the target node data and the target edge data from the data set may include removing the target node and the one or more target edges from the graph.

[0016] According to non-limiting embodiments or aspects, a system is provided, comprising: at least one processor, the at least one processor being programmed or configured to receive a data set including graph data associated with a graph, the graph data including node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph. In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to select a target node among the plurality of nodes based on the graph data. In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to determine target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data including the target node data, and the edge data of the graph data including the target edge data, the target node may be associated with one or more target edges among the plurality of edges, the one or more target edges including one or more edges connected to the target node in the graph. In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to remove the target node data and the target edge data from the data set to provide a target graph data set, the target graph data set including the data set with the target node data and the target edge data removed. In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to determine an influence metric of the target node on a GNN based on the target graph dataset, the GNN being trained using the dataset. In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to detect anomalies in the GNN based on the influence metric of the target node on the GNN.

[0017] In some non-limiting embodiments or aspects, the at least one processor may be programmed or configured to train an initial GNN based on the data set to provide the GNN.

[0018] In a non-limiting embodiment or aspect, when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor can be programmed or configured to: determine a set of first model parameters of the GNN based on the dataset; determine a set of modified model parameters of the GNN based on the target graph dataset; and determine the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0019] In a non-limiting embodiment or aspect, when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor may be programmed or configured to: determine a first influence metric of the target node on the GNN, the first influence metric may be associated with a property of the target node with respect to the topology of the graph; determine a second influence metric of the target node on the GNN, the second influence metric may be associated with a feature of the target node; determine a third influence metric of the target node on the GNN, the third influence metric may be associated with the target graph dataset; combine the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determine the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0020] In a non-limiting embodiment or aspect, when determining the first influence metric of the target node on the GNN, the at least one processor may be programmed or configured to: determine the first influence metric of the target node on the GNN based on a Hessian matrix.

[0021] In a non-limiting embodiment or aspect, when determining the second influence metric of the target node on the GNN, the at least one processor may be programmed or configured to: determine the second influence metric of the target node on the GNN based on a Hessian matrix.

[0022] In a non-limiting embodiment or aspect, when determining the third influence metric of the target node on the GNN, the at least one processor may be programmed or configured to determine the third influence metric of the target node on the GNN based on a Hessian matrix.

[0023] In a non-limiting embodiment or aspect, when the anomaly in the GNN is detected based on the influence metric of the target node on the GNN, the at least one processor may be programmed or configured to: determine a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detect whether the fairness metric of the GNN satisfies a predetermined threshold.

[0024] In a non-limiting embodiment or aspect, wherein when the target node data and the target edge data are removed from the data set, the at least one processor may be programmed or configured to: remove the target node and the one or more target edges from the graph.

[0025] According to non-limiting embodiments or aspects, a computer program product is provided, comprising at least one non-transitory computer-readable medium, the at least one non-transitory computer-readable medium comprising one or more instructions, the one or more instructions, when executed by at least one processor, cause the at least one processor to receive a data set including graph data associated with a graph, the graph data comprising node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph. In some non-limiting embodiments or aspects, the one or more instructions may also cause the at least one processor to select a target node from the plurality of nodes based on the graph data. In some non-limiting embodiments or aspects, the one or more instructions may also cause the at least one processor to determine target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data comprising the target node data, and the edge data of the graph data comprising the target edge data, the target node may be associated with one or more target edges of the plurality of edges, the one or more target edges comprising one or more edges connected to the target node in the graph. In some non-limiting embodiments or aspects, the one or more instructions may also cause the at least one processor to remove the target node data and the target edge data from the data set to provide a target graph data set, the target graph data set comprising the data set with the target node data and the target edge data removed. In some non-limiting embodiments or aspects, the one or more instructions may also cause the at least one processor to determine a measure of influence of the target node on the GNN based on the target graph data set, the GNN being trained using the data set. In some non-limiting embodiments or aspects, the one or more instructions may also cause the at least one processor to detect anomalies in the GNN based on the measure of influence of the target node on the GNN.

[0026] In a non-limiting embodiment or aspect, the one or more instructions may also cause the at least one processor to: train an initial graph neural network based on the data set to provide the GNN.

[0027] In a non-limiting embodiment or aspect, when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions may cause the at least one processor to: determine a set of first model parameters of the GNN based on the dataset; determine a set of modified model parameters of the GNN based on the target graph dataset; and determine the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0028] In a non-limiting embodiment or aspect, when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions may cause the at least one processor to: determine a first influence metric of the target node on the GNN, wherein the first influence metric may be associated with a property of the target node with respect to the topology of the graph; determine a second influence metric of the target node on the GNN, wherein the second influence metric may be associated with a feature of the target node; determine a third influence metric of the target node on the GNN, wherein the third influence metric may be associated with the target graph dataset; combine the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determine the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0029] In a non-limiting embodiment or aspect, when determining the first influence metric of the target node on the GNN, the one or more instructions may cause the at least one processor to: determine the first influence metric of the target node on the GNN based on the Hessian matrix.

[0030] In a non-limiting embodiment or aspect, when determining the second influence metric of the target node on the GNN, the one or more instructions may cause the at least one processor to: determine the second influence metric of the target node on the GNN based on the Hessian matrix.

[0031] In a non-limiting embodiment or aspect, when determining the third influence metric of the target node on the GNN, the one or more instructions may cause the at least one processor to determine the third influence metric of the target node on the GNN based on the Hessian matrix.

[0032] In a non-limiting embodiment or aspect, when the anomaly in the GNN is detected based on the influence metric of the target node on the GNN, the one or more instructions may cause the at least one processor to: determine a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detect whether the fairness metric of the GNN satisfies a predetermined threshold.

[0033] In a non-limiting embodiment or aspect, wherein when the target node data and the target edge data are removed from the data set, the one or more instructions may cause the at least one processor to: remove the target node and the one or more target edges from the graph.

[0034] Other non-limiting embodiments or aspects are set forth in the following numbered clauses:

[0035] Clause 1: A computer-implemented method, comprising: receiving, using at least one processor, a data set including graph data associated with a graph, the graph data including node data associated with multiple nodes of the graph and edge data associated with multiple edges of the graph; selecting, using at least one processor, a target node among the multiple nodes based on the graph data; determining, using at least one processor, target node data associated with the target node and target edge data associated with the target node based on the graph data, wherein the node data of the graph data includes the target node data, and the edge data of the graph data includes the target edge data, wherein the target node is associated with one or more target edges among the multiple edges, wherein the one or more target edges include one or more edges connected to the target node in the graph; removing, using at least one processor, the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed; determining, using at least one processor, an influence measure of the target node on a graph neural network (GNN) based on the target graph data set, wherein the GNN is trained using the data set; and detecting anomalies in the GNN based on the influence measure of the target node on the GNN.

[0036] Clause 2: The computer-implemented method of clause 1, further comprising: training an initial GNN based on the data set to provide the GNN.

[0037] Clause 3: A computer-implemented method according to clause 1 or 2, wherein determining the influence metric of the target node on the GNN based on the target graph dataset comprises: determining a set of first model parameters of the GNN based on the dataset; determining a set of modified model parameters of the GNN based on the target graph dataset; and determining the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0038] Clause 4: A computer-implemented method according to any one of clauses 1 to 3, wherein determining the influence metric of the target node on the GNN based on the target graph dataset comprises: determining a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to the topology of the graph; determining a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determining the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0039] Clause 5: A computer-implemented method according to any one of clauses 1 to 4, wherein determining the first influence metric of the target node on the GNN comprises determining the first influence metric of the target node on the GNN based on a Hessian matrix.

[0040] Clause 6: A computer-implemented method according to any one of clauses 1 to 5, wherein determining the second influence metric of the target node on the GNN comprises determining the second influence metric of the target node on the GNN based on a Hessian matrix.

[0041] Clause 7: A computer-implemented method according to any one of clauses 1 to 6, wherein determining the third influence metric of the target node on the GNN comprises determining the third influence metric of the target node on the GNN based on a Hessian matrix.

[0042] Clause 8: A computer-implemented method according to any one of clauses 1 to 7, wherein detecting the anomaly in the GNN based on the influence metric of the target node on the GNN comprises: determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detecting whether the fairness metric of the GNN satisfies a predetermined threshold.

[0043] Clause 9: The computer-implemented method of any one of clauses 1 to 8, wherein removing the target node data and the target edge data from the data set comprises removing the target node and the one or more target edges from the graph.

[0044] Clause 10: A system comprising: at least one processor, the at least one processor being programmed or configured to: receive a data set comprising graph data associated with a graph, the graph data comprising node data associated with multiple nodes of the graph and edge data associated with multiple edges of the graph; select a target node among the multiple nodes based on the graph data; determine target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data comprising the target node data, and the edge data of the graph data comprising the target edge data, wherein the target node is associated with one or more target edges among the multiple edges, the one or more target edges comprising one or more edges connected to the target node in the graph; remove the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set comprises the data set with the target node data and the target edge data removed; determine an influence metric of the target node on a graph neural network (GNN) based on the target graph data set, wherein the GNN is trained using the data set; and detect anomalies in the GNN based on the influence metric of the target node on the GNN.

[0045] Clause 11: The system of clause 10, wherein the at least one processor is further programmed or configured to: train an initial GNN based on the data set to provide the GNN.

[0046] Clause 12: A system according to clause 10 or 11, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor is programmed or configured to: determine a set of first model parameters of the GNN based on the dataset; determine a set of modified model parameters of the GNN based on the target graph dataset; and determine the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0047] Clause 13: A system according to any one of clauses 10 to 12, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor is programmed or configured to: determine a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to the topology of the graph; determine a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determine a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combine the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determine the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0048] Clause 14: A system according to any one of clauses 10 to 13, wherein when determining the first influence measure of the target node on the GNN, the at least one processor is programmed or configured to: determine the first influence measure of the target node on the GNN based on the Hessian matrix.

[0049] Clause 15: A system according to any one of clauses 10 to 14, wherein when determining the second influence metric of the target node on the GNN, the at least one processor is programmed or configured to: determine the second influence metric of the target node on the GNN based on the Hessian matrix.

[0050] Clause 16: A system according to any one of clauses 10 to 15, wherein when determining the third influence metric of the target node on the GNN, the at least one processor is programmed or configured to: determine the third influence metric of the target node on the GNN based on the Hessian matrix.

[0051] Clause 17: A system according to any one of clauses 10 to 16, wherein when the anomaly in the GNN is detected based on the influence metric of the target node on the GNN, the at least one processor is programmed or configured to: determine a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detect whether the fairness metric of the GNN meets a predetermined threshold.

[0052] Clause 18: A system according to any one of clauses 10 to 17, wherein when the target node data and the target edge data are removed from the data set, the at least one processor is programmed or configured to: remove the target node and the one or more target edges from the graph.

[0053] Clause 19: A computer program product comprising at least one non-transitory computer-readable medium, the at least one non-transitory computer-readable medium comprising one or more instructions that, when executed by at least one processor, cause the at least one processor to: receive a data set comprising graph data associated with a graph, the graph data comprising node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph; select a target node from the plurality of nodes based on the graph data; determine target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data comprising the target node data, and the graph data comprising the target node data; The edge data of the data includes the target edge data, wherein the target node is associated with one or more target edges of the multiple edges, and the one or more target edges include one or more edges connected to the target node in the graph; removing the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed; determining an influence measure of the target node on a graph neural network (GNN) based on the target graph data set, wherein the GNN is trained using the data set; and detecting anomalies in the GNN based on the influence measure of the target node on the GNN.

[0054] Clause 20: The computer program product of clause 19, wherein the one or more instructions further cause the at least one processor to: train an initial GNN based on the data set to provide the GNN.

[0055] Clause 21: A computer program product according to clause 19 or 20, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions cause the at least one processor to: determine a set of first model parameters of the GNN based on the dataset; determine a set of modified model parameters of the GNN based on the target graph dataset; and determine the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0056] Clause 22: A computer program product according to any one of clauses 19 to 21, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions cause the at least one processor to: determine a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to the topology of the graph; determine a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determine a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combine the first influence metric, the second influence metric and the third influence metric to provide an influence matrix; and determine the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0057] Clause 23: A computer program product according to any one of clauses 19 to 22, wherein when determining the first influence measure of the target node on the GNN, the one or more instructions cause the at least one processor to: determine the first influence measure of the target node on the GNN based on the Hessian matrix.

[0058] Clause 24: A computer program product according to any one of clauses 19 to 23, wherein when determining the second influence measure of the target node on the GNN, the one or more instructions cause the at least one processor to: determine the second influence measure of the target node on the GNN based on the Hessian matrix.

[0059] Clause 25: A computer program product according to any one of clauses 19 to 24, wherein when determining the third influence metric of the target node on the GNN, the one or more instructions cause the at least one processor to: determine the third influence metric of the target node on the GNN based on a Hessian matrix.

[0060] Clause 26: A computer program product according to any one of clauses 19 to 25, wherein when the anomaly in the GNN is detected based on the impact metric of the target node on the GNN, the one or more instructions cause the at least one processor to: determine a fairness metric of the GNN based on the impact metric of the target node on the GNN; and detect whether the fairness metric of the GNN satisfies a predetermined threshold.

[0061] Clause 27: A computer program product according to any one of clauses 19 to 26, wherein when the target node data and the target edge data are removed from the data set, the one or more instructions cause the at least one processor to: remove the target node and the one or more target edges from the graph.

[0062] These and other features and characteristics of the present disclosure, as well as methods of operation and functions of the related structural elements and combinations of parts and economies of manufacture, will become more apparent when considering the following description and appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for illustration and description purposes only and are not intended as a definition of the limits of the disclosed subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Additional advantages and details are explained in more detail below with reference to non-limiting exemplary embodiments shown in the schematic drawings, in which:

[0064] Figure 1 is a schematic diagram of an example environment in which the apparatus, systems and / or methods described herein may be implemented according to the principles of the present disclosure;

[0065] Figure 2 According to some non-limiting embodiments or aspects Figure 1 schematic diagrams of example components of one or more devices;

[0066] Figure 3 is a flowchart of a process for determining the influence of a node of a graph on a graph neural network (GNN) according to some non-limiting embodiments or aspects; and

[0067] Figures 4A-4M is a diagram of a non-limiting embodiment or aspect of an implementation of a process for determining the influence of a node of a graph on a GNN according to some non-limiting embodiments or aspects. DETAILED DESCRIPTION

[0068] For the purposes of the following description, the terms "end," "upper," "lower," "right," "left," "vertical," "horizontal," "top," "bottom," "lateral," "longitudinal," and their derivatives shall relate to the orientation of the embodiments in the accompanying drawings. However, it shall be understood that the embodiments may employ various alternative variations and step sequences, except where expressly specified to the contrary. It shall also be understood that the specific devices and processes illustrated in the accompanying drawings and described in the following specification are merely exemplary embodiments or aspects of the disclosed subject matter. Accordingly, specific dimensions and other physical characteristics relating to the embodiments or aspects disclosed herein shall not be considered limiting.

[0069] The aspects, parts, elements, structures, actions, steps, functions, instructions, etc. used herein should not be understood as critical or necessary unless explicitly described as such. Moreover, as used herein, the article "one" is intended to include one or more items, and can be used interchangeably with "one or more" and "at least one". In addition, as used herein, the term "group" is intended to include one or more items (e.g., related items, unrelated items, a combination of related items and unrelated items, etc.), and can be used interchangeably with "one or more" or "at least one". In the case of wishing only one item, the term "one" or similar language is used. Moreover, as used herein, the term "having" and / or its analogs are intended to be open terms. In addition, unless otherwise explicitly stated, the phrase "based on" is intended to mean "based at least in part on".

[0070] As used herein, the term "acquirer institution" may refer to an entity that is licensed and / or approved by a transaction service provider to initiate transactions (e.g., payment transactions) using a payment device associated with the transaction service provider. Transactions that may be initiated by an acquirer institution may include payment transactions (e.g., purchases, original letter of credit transactions (OCTs), account funding transactions (AFTs), and / or the like). In some non-limiting embodiments or aspects, the acquirer institution may be a financial institution, such as a bank. As used herein, the term "acquirer system" may refer to one or more computing devices operated by or on behalf of an acquirer institution, such as a server computer executing one or more software applications.

[0071] As used herein, the term "communication" may refer to the reception, acceptance, transmission, transmission, provision and / or the like of data (e.g., information, signals, messages, instructions, commands and / or the like). A unit (e.g., a device, a system, a component of a device or system, a combination thereof, etc.) communicating with another unit means that the unit is able to directly or indirectly receive information from the other unit and / or send information to the other unit. This may refer to a direct or indirect connection (e.g., a direct communication connection, an indirect communication connection and / or the like) that is wired and / or wireless in nature. In addition, although the information sent may be modified, processed, relayed and / or routed between the first unit and the second unit, the two units may also communicate with each other. For example, even if the first unit passively receives information and does not actively send information to the second unit, the first unit may communicate with the second unit. As another example, if at least one intermediate unit processes the information received from the first unit and transmits the processed information to the second unit, the first unit may communicate with the second unit.

[0072] As used herein, the term "computing device" may refer to one or more electronic devices configured to process data. In some examples, a computing device may include the necessary components for receiving, processing, and outputting data, such as a processor, a display, a memory, an input device, a network interface, etc. The computing device may be a mobile device. As an example, a mobile device may include a cellular phone (e.g., a smartphone or a standard cellular phone), a portable computer, a wearable device (e.g., a watch, glasses, lenses, clothing, etc.), a personal digital assistant (PDA), and / or other similar devices. A computing device may also be a desktop computer or other form of non-mobile computer.

[0073] As used herein, the term "issuer institution" may refer to one or more entities, such as a bank, that provide accounts to customers to conduct transactions (e.g., payment transactions), such as initiating credit and / or debit payments. For example, an issuer institution may provide customers with account identifiers, such as a primary account number (PAN), that uniquely identify one or more accounts associated with the customer. The account identifier may be implemented on a portable financial device, such as a physical financial instrument (e.g., a payment card), and / or may be electronic and used for electronic payments. The term "issuer system" refers to one or more computer devices operated by or on behalf of an issuer institution, such as a server computer executing one or more software applications. For example, an issuer system may include one or more authorization servers for authorizing transactions.

[0074] As used herein, the term "merchant" may refer to a person or entity that provides goods and / or services, or access to goods and / or services, to a customer based on a transaction, such as a payment transaction. The term "merchant" or "merchant system" may also refer to one or more computer systems operated by or on behalf of a merchant, such as a server computer that executes one or more software applications.

[0075] As used herein, the terms "client" and "client device" may refer to one or more client-side devices or systems (e.g., remote from a transaction service provider) used to initiate or facilitate a transaction (e.g., a payment transaction). As an example, a "client device" may refer to one or more point-of-sale (POS) devices used by a merchant, one or more acquirer host computers used by an acquirer, one or more mobile devices used by a user, and the like. In some non-limiting embodiments or aspects, a client device may be an electronic device configured to communicate with one or more networks and initiate or facilitate a transaction. For example, a client device may include one or more computers, portable computers, laptop computers, tablet computers, mobile devices, cellular phones, wearable devices (e.g., watches, glasses, lenses, clothing, etc.), PDAs, and the like. In addition, a "client" may also refer to an entity (e.g., a merchant, an acquirer, etc.) that owns, utilizes, and / or operates a client device for initiating a transaction (e.g., for initiating a transaction with a transaction service provider).

[0076] As used herein, the term "server" may refer to or include one or more computing devices operated by or facilitating communications and processing by multiple parties in a network environment such as the Internet, but it should be understood that communications may be facilitated through one or more public or private network environments, and that there may be various other arrangements. In addition, multiple computing devices (e.g., servers, POS devices, mobile devices, etc.) that communicate directly or indirectly in a network environment may constitute a "system." As used herein, references to "servers" or "processors" may refer to previously described servers and / or processors, different servers and / or processors, and / or combinations of servers and / or processors that are stated to implement previous steps or functions. For example, as used in the specification and claims, a first server and / or first processor stated to perform a first step or function may refer to the same or different servers and / or processors stated to perform a second step or function.

[0077] As used herein, the term "transaction service provider" may refer to an entity that receives transaction authorization requests from merchants or other entities and, in some cases, provides payment assurance through an agreement between the transaction service provider and an issuer organization. For example, a transaction service provider may include, for example The term "transaction processing system" may refer to one or more computer systems operated by or on behalf of a transaction service provider, such as a transaction processing server that executes one or more software applications. A transaction processing server may include one or more processors and, in some non-limiting embodiments or aspects, may be operated by or on behalf of a transaction service provider.

[0078] Non-limiting embodiments or aspects of the disclosed subject matter relate to systems, methods, and computer program products for determining the impact of data on a graph neural network (GNN), including but not limited to determining the impact of a node of a graph on the GNN. Non-limiting embodiments or aspects of the disclosed subject matter may receive a data set including graph data associated with a graph. The graph data may include node data associated with multiple nodes of the graph and edge data associated with multiple edges of the graph. The non-limiting embodiments or aspects may select a target node from the multiple nodes based on the graph data. The non-limiting embodiments or aspects may determine target node data associated with the target node and target edge data associated with the target node based on the graph data. The node data of the graph data may include target node data, and the edge data of the graph data may include target edge data. The target node may be associated with one or more target edges of the multiple edges. The one or more target edges may include one or more edges connected to the target node in the graph. The non-limiting embodiments or aspects may remove the target node data and the target edge data from the data set to provide a target graph data set. The target graph data set may include a data set with the target node data and the target edge data removed. The non-limiting embodiments or aspects may determine an impact metric of the target node on the GNN (e.g., a trained GNN) based on the target graph data set. The GNN may be trained using a data set. A non-limiting embodiment or aspect may detect anomalies in the GNN based on an influence metric of a target node on the GNN.

[0079] Non-limiting embodiments or aspects may train an initial GNN based on a data set to provide a GNN.

[0080] In some non-limiting embodiments or aspects, determining the influence metric of the target node on the GNN based on the target graph dataset may include: determining a set of first model parameters of the GNN based on the dataset; determining a set of modified model parameters of the GNN based on the target graph dataset; and determining the difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0081] In some non-limiting embodiments or aspects, determining the influence metric of the target node on the GNN based on the target graph dataset may include: determining a first influence metric of the target node on the GNN, wherein the first influence metric may be associated with a property of the target node with respect to the topology of the graph; determining a second influence metric of the target node on the GNN, wherein the second influence metric may be associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric may be associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; and determining the influence metric of the target node on the GNN based on a loss function and the influence matrix.

[0082] In some non-limiting embodiments or aspects, determining the first influence metric of the target node on the GNN may include determining the first influence metric of the target node on the GNN based on a Hessian matrix.

[0083] In some non-limiting embodiments or aspects, determining the second influence metric of the target node on the GNN may include determining the second influence metric of the target node on the GNN based on a Hessian matrix.

[0084] In some non-limiting embodiments or aspects, determining the third influence metric of the target node on the GNN may include determining the third influence metric of the target node on the GNN based on a Hessian matrix.

[0085] In some non-limiting embodiments or aspects, detecting the anomaly in the GNN based on the influence metric of the target node on the GNN may include: determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; and detecting whether the fairness metric of the GNN meets a predetermined threshold.

[0086] In some non-limiting embodiments or aspects, removing the target node data and the target edge data from the data set may include removing the target node and the one or more target edges from the graph.

[0087] In this way, non-limiting embodiments or aspects of the disclosed subject matter can determine the impact of a node of a graph on a GNN (e.g., a trained GNN) without having to retrain the GNN using a dataset and / or a target graph dataset. For example, non-limiting embodiments or aspects of the disclosed subject matter can determine the impact (e.g., impact metric) that a training data instance (e.g., nodes and edges, etc.) may have on an output (e.g., prediction) of the GNN. Different impacts (e.g., different impact metrics) can be determined for different data instances based on the inputs (e.g., test inputs, production inputs) to the GNN that produce the output. For example, each of a plurality of training data instances can each have a different impact on the GNN, such that when the input is provided to the GNN, the GNN can produce (e.g., generate) different outputs. The difference in the output of the GNN can be related to the impact of the training data instance.

[0088] The non-limiting embodiments or aspects do not require retraining the GNN using the target graph dataset in order to determine the influence of the node on the GNN. In this way, the non-limiting embodiments or aspects can reduce the amount of resources required to determine the influence metric of the node of the graph on the GNN.

[0089] Non-limiting embodiments or aspects of the disclosed subject matter may determine the impact of a node of a graph on a GNN to provide insights (e.g., data) into the graph and / or GNN. For example, non-limiting embodiments or aspects may be used to analyze the strength of a GNN against manipulation of a graph and / or GNN (e.g., a graph attack). In this way, non-limiting embodiments or aspects may improve the robustness of a GNN against attacks. As another example, non-limiting embodiments or aspects may be used to analyze the output of a GNN based on node data (e.g., target node data) of a data set to obtain different impact metrics. Non-limiting embodiments or aspects may improve the training and / or accuracy of a GNN by analyzing the output of a GNN (e.g., prediction) and determining which nodes (e.g., target nodes) have the greatest impact on the output of the GNN.

[0090] In this way, non-limiting embodiments or aspects can improve the fairness and / or quality of predictions by GNNs (e.g., node classification). Therefore, non-limiting embodiments or aspects of the disclosed subject matter can improve the training and / or use of GNNs without the need to retrain the GNNs based on multiple data sets. In this way, non-limiting embodiments or aspects of the disclosed subject matter can reduce the overall time and / or resources required to train GNNs.

[0091] Reference now Figure 1 , Figure 1 1 is a diagram of an example environment 100 in which the apparatus, systems, and / or methods described herein may be implemented. Figure 1As shown, environment 100 includes a GNN influencing system 102, a transaction service provider system 104, a user device 106, and a communication network 108. The GNN influencing system 102, the transaction service provider system 104, and / or the user device 106 may be interconnected (e.g., connected to communicate) via a wired connection, a wireless connection, or a combination of a wired connection and a wireless connection.

[0092] The GNN influence system 102 may include a computing device, such as a server (e.g., a single server), a server group, and / or other similar devices. In some non-limiting embodiments or aspects, the GNN influence system 102 may include a processor and / or memory, as described herein. In some non-limiting embodiments or aspects, the GNN influence system 102 may include one or more software instructions (e.g., one or more software applications) executed on a server (e.g., a single server), a server group, a computing device (e.g., a single computing device), a computing device group, and / or other similar devices. In some non-limiting embodiments or aspects, the GNN influence system 102 may be configured to communicate with the transaction service provider system 104 and / or the user device 106 via the communication network 108. In some non-limiting embodiments or aspects, the GNN influence system 102 may communicate with the transaction service provider system 104 and / or the user device 106, so that the GNN influence system 102 is separated from the transaction service provider system 104 and / or the user device 106. In some non-limiting embodiments or aspects, the transaction service provider system 104 and / or the user device 106 may be implemented by (eg, may be a part of) the GNN influence system 102 .

[0093] In some non-limiting embodiments or aspects, the GNN influence system 102 can be associated with a transaction service provider system, as described herein. Additionally or alternatively, the GNN influence system 102 can generate (e.g., train, validate, retrain, etc.), store and / or implement one or more machine learning models (e.g., operate one or more machine learning models, provide input to one or more machine learning models, and / or provide output from one or more machine learning models, etc.). In some non-limiting embodiments or aspects, the GNN influence system 102 can communicate with a data storage device, which can be local or remote to the GNN influence system 102. In some non-limiting embodiments or aspects, the GNN influence system 102 can be capable of receiving information from the data storage device, storing information in the data storage device, sending information to the data storage device, and / or searching for information stored in the data storage device.

[0094] The transaction service provider system 104 may include one or more devices configured to communicate with the GNN influence system 102 and / or the user device 106 via the communication network 108. For example, the transaction service provider system 104 may include a computing device, such as a server, a server group, and / or other similar devices. In some non-limiting embodiments or aspects, the transaction service provider system 104 may be associated with a transaction service provider system, as discussed herein. In some non-limiting embodiments or aspects, the GNN influence system 102 may be a component of the transaction service provider system 104.

[0095] The user device 106 may include a computing device configured to communicate with the GNN influence system 102 and / or the transaction service provider system 104 via the communication network 108. For example, the user device 106 may include a computing device such as a desktop computer, a portable computer (e.g., a tablet computer, a laptop computer, etc.), a mobile device (e.g., a cellular phone, a smartphone, a personal digital assistant, a wearable device, etc.), and / or other similar devices. In some non-limiting embodiments or aspects, the user device 106 may be associated with a user (e.g., an individual operating the user device 106).

[0096] The communication network 108 may include one or more wired and / or wireless networks. For example, the communication network 108 may include a cellular network (e.g., a long term evolution (LTE) network, a third generation (3G) network, a fourth generation (4G) network, a fifth generation (5G) network, a code division multiple access (CDMA) network, etc.), a public land mobile network (PLMN), a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a telephone network (e.g., a public switched telephone network (PSTN)), etc.), a private network, an ad hoc network, an intranet, the Internet, a fiber-based network, a cloud computing network, etc., and / or a combination of some or all of these or other types of networks.

[0097] Figure 1 The number and arrangement of the systems and devices shown in the FIG. are provided as examples. Figure 1 There may be additional systems and / or devices, fewer systems and / or devices, different systems and / or devices, and / or systems and / or devices arranged in a different manner than the systems and / or devices shown in the drawings. Furthermore, a single system and / or device may be implemented Figure 1 Two or more systems or devices shown in Figure 1 The single system or device shown in the figure may be implemented as multiple distributed systems or devices. In addition or alternatively, a group of systems (e.g., one or more systems) or a group of devices (e.g., one or more devices) of the system 100 can perform one or more functions described as being performed by another group of systems or another group of devices of the system 100.

[0098] Reference now Figure 2 , Figure 2 200. The apparatus 200 may correspond to the GNN influencing system 102 (e.g., one or more apparatuses of the GNN influencing system 102), the transaction service provider system 104 (e.g., one or more apparatuses of the transaction service provider system 104), and / or the user apparatus 106. In some non-limiting embodiments or aspects, the GNN influencing system 102, the transaction service provider system 104, and / or the user apparatus 106 may include at least one apparatus 200 or at least one component of the apparatus 200. Figure 2 As shown, apparatus 200 may include a bus 202 , a processor 204 , a memory 206 , a storage component 208 , an input component 210 , an output component 212 , and a communication interface 214 .

[0099] The bus 202 may include components that permit communication between components of the device 200. In some non-limiting embodiments, the processor 204 may be implemented in hardware, software, or a combination of hardware and software. For example, the processor 204 may include a processor (e.g., a central processing unit (CPU), a graphics processing unit (GPU), an accelerated processing unit (APU), etc.), a microprocessor, a digital signal processor (DSP), and / or any processing component that can be programmed to perform a function (e.g., a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), etc.). The memory 206 may include a random access memory (RAM), a read-only memory (ROM), and / or another type of dynamic or static memory (e.g., flash memory, magnetic memory, optical memory, etc.) that stores information and / or instructions for use by the processor 204.

[0100] The storage component 208 may store information and / or software related to the operation and use of the device 200. For example, the storage component 208 may include a hard disk (e.g., a magnetic disk, an optical disk, a magneto-optical disk, a solid-state disk, etc.), a compact disk (CD), a digital versatile disk (DVD), a floppy disk, a cassette, a magnetic tape, and / or another type of computer-readable medium, and a corresponding drive.

[0101] Input components 210 may include components that permit device 200 to receive information, such as via user input (e.g., a touch screen display, a keyboard, a keypad, a mouse, buttons, switches, a microphone, etc.). Additionally or alternatively, input components 210 may include sensors for sensing information (e.g., a global positioning system (GPS) component, an accelerometer, a gyroscope, an actuator, etc.). Output components 212 may include components that provide output information from device 200 (e.g., a display, a speaker, one or more light emitting diodes (LEDs), etc.).

[0102] The communication interface 214 may include a transceiver-type component (e.g., a transceiver, a separate receiver and transmitter, etc.) that enables the device 200 to communicate with other devices, for example, via a wired connection, a wireless connection, or a combination of a wired connection and a wireless connection. The communication interface 214 may permit the device 200 to receive information from another device and / or provide information to another device. For example, the communication interface 214 may include an Ethernet interface, an optical interface, a coaxial interface, an infrared interface, a radio frequency (RF) interface, a universal serial bus (USB) interface, Interface, cellular network interface, etc.

[0103] The device 200 can perform one or more processes described herein. The device 200 can perform these processes based on the processor 204 executing software instructions stored by a computer-readable medium such as the memory 206 and / or the storage component 208. Computer-readable media (e.g., non-transitory computer-readable media) are defined herein as non-transitory memory devices. Non-transitory memory devices include memory space located within a single physical storage device or memory space spread across multiple physical storage devices.

[0104] The software instructions may be read into the memory 206 and / or storage component 208 from another computer-readable medium or from another device via the communication interface 214. When executed, the software instructions stored in the memory 206 and / or storage component 208 may cause the processor 204 to perform one or more processes described herein. Additionally or alternatively, hard-wired circuitry may be used in place of or in combination with software instructions to perform one or more processes described herein. Therefore, the embodiments described herein are not limited to any specific combination of hardware circuitry and software.

[0105] Figure 2 The number and arrangement of components shown in FIG. 2 are provided as examples. In some non-limiting embodiments or aspects, the device 200 may include additional components, fewer components, different components, or components in a manner similar to that of FIG. Figure 2 Additionally or alternatively, one set of components (eg, one or more components) of the apparatus 200 may perform one or more functions described as being performed by another set of components of the apparatus 200.

[0106] Reference now Figure 3 , Figure 3Flowchart of a non-limiting embodiment or aspect of a process 300 for determining the influence of a node of a graph on a GNN. In some non-limiting embodiments or aspects, one or more of the steps of the process 300 may be performed (e.g., completely, partially, etc.) by the GNN influence system 102 (e.g., one or more devices of the GNN influence system 102). In some non-limiting embodiments or aspects, one or more of the steps of the process 300 may be performed (e.g., completely, partially, etc.) by another device or group of devices that is separate from or includes the GNN influence system 102 (e.g., one or more devices of the GNN influence system 102), the transaction service provider system 104 (e.g., one or more devices of the transaction service provider system 104), and / or the user device 106.

[0107] like Figure 3 As shown, at step 302, process 300 may include receiving a data set associated with a graph. For example, the GNN influence system 102 may receive a data set including graph data associated with the graph. In some non-limiting embodiments or aspects, the graph may include multiple nodes and / or multiple edges. In some non-limiting embodiments or aspects, each of the multiple edges of the graph may connect one of the multiple nodes of the graph to another node of the multiple nodes of the graph. In some non-limiting embodiments or aspects, the graph data may include node data associated with multiple nodes of the graph and / or edge data associated with multiple edges of the graph.

[0108] In some non-limiting embodiments or aspects, the GNN influence system 102 may receive a data set including a group of multiple data instances associated with multiple features. For example, the GNN influence system 102 may receive a data set including a group of multiple data instances associated with multiple features (e.g., a group of individuals, such as account holders, users associated with an account, etc.). In some non-limiting embodiments or aspects, the multiple data instances may represent multiple transactions (e.g., electronic payment transactions) conducted by the group. In some non-limiting embodiments or aspects, the GNN influence system 102 may receive the data set from the transaction service provider system 104 and / or the user device 106.

[0109] In some non-limiting embodiments or aspects, each data instance may include transaction data associated with a transaction. In some non-limiting embodiments or aspects, the transaction data may include a plurality of transaction parameters associated with an electronic payment transaction. In some non-limiting embodiments or aspects, a plurality of features may represent a plurality of transaction parameters. In some non-limiting embodiments or aspects, the plurality of transaction parameters may include electronic wallet card data associated with an electronic card (e.g., an electronic credit card, an electronic debit card, an electronic membership card, etc.), decision data associated with a decision (e.g., a decision to approve or deny a transaction authorization request), authorization data associated with an authorization response (e.g., an approved spending limit, an approved transaction value, etc.), a PAN, an authorization code (e.g., a personal identification number (PIN)), etc.), data associated with a transaction amount (e.g., an approved limit, a transaction value, etc.), data associated with a transaction date and time, data associated with a currency conversion rate, data associated with a merchant type (e.g., a merchant category code indicating a type of merchandise such as groceries, fuel, etc.), data associated with an acquirer country, data associated with an identifier of a country associated with the PAN, data associated with a response code, data associated with a merchant identifier (e.g., a merchant name, a merchant location, etc.), data associated with a currency type corresponding to funds stored in association with the PAN, and the like.

[0110] In some non-limiting embodiments or aspects, each of the plurality of nodes may be associated with one of the plurality of entities, such as an account holder or a merchant. In some non-limiting embodiments or aspects, each of the plurality of edges may be associated with a relationship, such as a transaction between two of the plurality of entities. For example, a first node may be connected to a second node via an edge. The first node may be associated with a first entity, and the second node may be associated with a second entity. The edge connecting the first node and the second node may represent a relationship (e.g., a transaction) between the first entity and the second entity.

[0111] In some non-limiting embodiments or aspects, the GNN impact system 102 may include a machine learning model. The machine learning model may include a GNN machine learning model configured to provide an output including a prediction. For example, the GNN impact system 102 may train a GNN to provide an output including a prediction of whether a node of a graph is an anomaly, whether a node of a graph indicates damage or label noise within a data set, and / or whether a training strategy of the GNN is a fair training strategy. For example, the GNN impact system 102 may train an initial GNN based on a data set to provide a GNN (e.g., a trained GNN). In some non-limiting embodiments or aspects, training the initial GNN may include generating an initial GNN, training the initial GNN based on a data set, and / or retraining the initial GNN based on a data set. In some non-limiting embodiments or aspects, the GNN may include one or more layers. For example, the GNN may include an input layer, one or more hidden layers, and / or an output layer.

[0112] In some non-limiting embodiments or aspects, the GNN can output a prediction (e.g., a confidence score) based on receiving a data set as input. In some non-limiting embodiments or aspects, the GNN can be trained to perform one or more tasks. For example, the GNN can classify a node among multiple nodes.

[0113] like Figure 3 As shown, at step 304, the process 300 may include selecting a target node from the graph. For example, the GNN influencing system 102 may select the target node from the plurality of nodes from the graph. In some non-limiting embodiments or aspects, the GNN influencing system 102 may select the target node based on graph data (e.g., node data associated with a plurality of nodes of the graph and / or edge data associated with a plurality of edges of the graph).

[0114] In some non-limiting embodiments or aspects, the GNN influencing system 102 may randomly select a target node. For example, the GNN influencing system 102 may randomly (e.g., based on a random number generator) select one of the multiple nodes as the target node.

[0115] In some non-limiting embodiments or aspects, the GNN influence system 102 may select a target node based on criteria (e.g., data associated with a graph topology of a graph, such as data associated with a plurality of nodes and / or data associated with a plurality of edges, adjacency data, such as data associated with adjacent nodes and / or data associated with adjacent edges of a given node, etc.). In some non-limiting embodiments or aspects, the GNN influence system 102 may select a target node from all of the plurality of nodes. In some non-limiting embodiments or aspects, the GNN influence system 102 may select a target node from all of the plurality of nodes in order.

[0116] like Figure 3 As shown, at step 306, process 300 may include determining target node data and target edge data associated with the target node. For example, the GNN influence system 102 may determine the target node data associated with the target node and the target edge data associated with the target node based on the graph data. In some non-limiting embodiments or aspects, the node data of the graph data may include the target node data, and the edge data of the graph data may include the target edge data.

[0117] In some non-limiting embodiments or aspects, the target node can be associated with one or more target edges in a plurality of edges. In some non-limiting embodiments or aspects, one or more target edges can include one or more edges connected to the target node in the figure. In some non-limiting embodiments or aspects, the target node can be connected to another node in a plurality of nodes via the target edge. In some non-limiting embodiments or aspects, the edge in a plurality of edges connected to the target node can be the target edge.

[0118] In some non-limiting embodiments or aspects, the node connected to the target node by an edge among the plurality of nodes may be an adjacent node. In some non-limiting embodiments or aspects, the target edge may be an edge adjacent to the target node (e.g., an adjacent edge of the target node).

[0119] like Figure 3 As shown, at step 308, process 300 may include removing target node data and target edge data from the data set. For example, the GNN influence system 102 may remove (e.g., delete) the target node data and target edge data from the data set to provide a target graph data set. In some non-limiting embodiments or aspects, the target graph data set may include a data set with the target node data and target edge data removed (e.g., the target graph data set does not include the target node data and / or target edge data). In some non-limiting embodiments or aspects, the GNN influence system 102 may remove the target node data and target edge data from the data set by removing the target node and one or more target edges from the graph.

[0120] In some non-limiting embodiments or aspects, the GNN influence system 102 may store the target graph dataset in a database (not shown). The GNN influence system 102 may include a database. In some non-limiting embodiments or aspects, the database may be external to the GNN influence system 102. In some non-limiting embodiments or aspects, the database may include multiple target graph datasets.

[0121] like Figure 3As shown, at step 310, process 300 may include determining an influence metric of the target node on the GNN. For example, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the data set and / or the target graph data set. In some non-limiting embodiments or aspects, the data set may be used to train the GNN (e.g., the GNN has been previously trained, etc.).

[0122] In some non-limiting embodiments or aspects, when determining an influence metric of a target node on a GNN based on a target graph dataset, the GNN influence system 102 may determine a set of first model parameters of the GNN based on the dataset. In some non-limiting embodiments or aspects, the GNN influence system 102 may provide a first prediction of the GNN based on the set of first model parameters.

[0123] In some non-limiting embodiments or aspects, when determining the influence metric of the target node on the GNN based on the target graph dataset, the GNN influence system 102 may determine a set of modified model parameters of the GNN based on the target graph dataset. In some non-limiting embodiments or aspects, the GNN influence system 102 may provide a second prediction of the GNN based on the set of modified model parameters.

[0124] In some non-limiting embodiments or aspects, when determining the set of modified model parameters based on the target graph dataset, the GNN influence system 102 may retrieve the target graph dataset stored in a database. For example, the GNN influence system 102 may retrieve the target graph dataset from the database and input the target graph dataset into the GNN.

[0125] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine an influence metric of the target node on the GNN based on the set of first model parameters, the set of modified model parameters, and / or a combination thereof. For example, when determining an influence metric of the target node on the GNN based on the target graph dataset, the GNN influence system 102 may determine a difference between a first prediction of the GNN based on the set of first model parameters and a second prediction of the GNN based on the set of modified model parameters.

[0126] In some non-limiting embodiments or aspects, the data set may include training data samples {(x_1, y_1), [(x]_2, y_2) ... (x_n, y_n)}, where n represents the number of training data samples. In some non-limiting embodiments or aspects, the set of first model parameters may be determined based on the following equation, where l(x, y, θ) is the loss function of the GNN, where x i is the node data associated with node i, and where y i is the edge data associated with node i:

[0127]

[0128] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the set of modified model parameters based on the following equation, where j represents the target node, and where Model parameters representing the target graph dataset (i.e., the dataset with the target node data and target edge data removed):

[0129]

[0130] In some non-limiting embodiments or aspects, the GNN influence system 102 may approximate the parameter change of a data point by calculating the parameter change of a target node j, where the target node j is weighted by ∈ based on the following equation:

[0131]

[0132] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine a first influence metric of the target node on the GNN, a second influence metric of the target node on the GNN, and / or a third influence metric of the target node on the GNN.

[0133] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph data set by determining a first influence metric of the target node on the GNN. In some non-limiting embodiments or aspects, the first influence metric may be associated with a property of the target node with respect to the topology of the graph (e.g., the degree of the graph, the length of the edges in the graph, the arrangement of the nodes in the graph, the presence of clusters of nodes in the graph, etc.). In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the first influence metric of the target node on the GNN by determining the first influence metric of the target node on the GNN based on a Hessian matrix.

[0134] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by determining a second influence metric of the target node on the GNN. In some non-limiting embodiments or aspects, the second influence metric may be associated with features of the target node (e.g., features embedded in the target node, such as the type of entity represented by the node (person, account, etc.), the size of the node (e.g., representing the amount of accounts represented by the node, etc.). In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by determining the second influence metric of the target node on the GNN based on the Hessian matrix.

[0135] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by determining a third influence metric of the target node on the GNN. In some non-limiting embodiments or aspects, the third influence metric may be associated with the target graph dataset (e.g., associated with a target graph including the target graph dataset, wherein the third influence metric is related to the topology of the target graph). In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by determining the third influence metric of the target node on the GNN based on the Hessian matrix.

[0136] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix. In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the target graph dataset by determining the influence metric of the target node on the GNN based on the loss function and the influence matrix.

[0137] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine an influence metric of a target node on a GNN based on a first influence metric, a second influence metric, a third influence metric, an influence matrix, a loss function, and / or any combination thereof.

[0138] In some non-limiting embodiments or aspects, the Hessian matrix H θ It can be a block matrix of second-order partial derivatives of a scalar-valued function, which describes the local part of the scalar-valued function. In some non-limiting embodiments or aspects, the Hessian matrix can be determined based on the following equation:

[0139]

[0140] In some non-limiting embodiments or aspects, the effect of increasing the weight of the target node j (eg, adding additional weight to the target node) on a set of first model parameters may be determined based on the following equation: The impact of is the inverse of the Hessian matrix:

[0141]

[0142] In some non-limiting embodiments or aspects, removing the target node data and the target edge data associated with the target node j can be done by increasing the weight of the Hessian matrix equation by has the same effect.

[0143] In some non-limiting embodiments or aspects, removing the target node data and the target edge data associated with the target node j may cause parameter changes that may be linearly approximated without the need to retrain the GNN. For example, after removing the target node data and the target edge data associated with the target node j, the GNN influencing system 102 may approximate the set of modified model parameters based on the following equations:

[0144]

[0145] In some non-limiting embodiments or aspects, the change in model predictions can be determined to measure how increasing the weight of target node j changes the predictions based on a test data set. For example, for test data sample z test =(x test ,y test ), the loss function is l(z test ) 2 , the effect of increasing the weight of target node j on test data sample z can be determined based on the following equation: test The impact of the loss:

[0146]

[0147] like Figure 3 As shown, at step 312, the process 300 may include performing an action on the GNN based on the influence metric. For example, the GNN influence system 102 may detect anomalies in the GNN based on the influence metric of the target node on the GNN. In some non-limiting embodiments or aspects, the GNN influence system 102 may detect anomalies in the GNN based on the influence metric of the target node on the GNN, by determining the fairness metric of the GNN based on the influence metric of the target node on the GNN. In some non-limiting embodiments or aspects, the GNN influence system 102 may detect anomalies in the GNN based on the influence metric of the target node on the GNN by detecting whether the fairness metric of the GNN satisfies a threshold (e.g., a predetermined threshold). Some non-limiting embodiments or aspects are described herein in conjunction with a threshold (e.g., a predetermined threshold). As used herein, satisfying a threshold may refer to a value greater than a threshold, more than a threshold, higher than a threshold, greater than or equal to a threshold, less than a threshold, less than a threshold, lower than a threshold, less than or equal to a threshold, equal to a threshold, and the like.

[0148] In some non-limiting embodiments or aspects, the GNN influence system 102 can detect anomalies based on adversarial graph defenses. In some non-limiting embodiments or aspects, the GNN influence system 102 can detect anomalies based on graph topology of a graph. For example, the GNN influence system 102 can detect anomalies based on corruption or label noise associated with the topology of the graph.

[0149] In some non-limiting embodiments or aspects, the GNN influence system 102 may refine the data set based on the fairness metric of the GNN. For example, the GNN influence system 102 may reweight the node data associated with the target node or reweight the edge data associated with the target node based on the fairness metric of the GNN to improve the performance of the GNN.

[0150] Reference now Figures 4A-4M , Figures 4A-4M 4 is a diagram of a non-limiting example or aspect of an implementation of a process 400 (e.g., process 300) for determining the influence of a node of a graph on a GNN. Figures 4A-4M As shown, embodiment 400 may include steps of a process (e.g., the same or similar process as process 300) performed by the GNN influence system 102. In some non-limiting embodiments or aspects, one or more of the steps of process 400 may be performed (e.g., completely, partially, etc.) by another device or device group that is separate from or includes the GNN influence system 102 (one or more devices of the GNN influence system 102), such as the transaction service provider system 104 (e.g., one or more devices of the transaction service provider system 104), and / or the user device 106.

[0151] like Figure 4A As shown in the figure 402, the GNN influencing system 102 can receive a data set. For example, the GNN influencing system 102 can receive a data set including graph data G=(X, A) associated with a graph 440, where X represents multiple node features and A represents a graph topology.

[0152] In some non-limiting embodiments or aspects, the graph data may include a label y, where y is a ground truth label A∈{0,1} nxn , where n represents the number of nodes, and where d represents the size of the input features. The graph data can consist solely of a training dataset S train and / or test dataset S test In some non-limiting embodiments or aspects, the training data set S train The test data set S may include sample j and / or a target node associated with sample j. test A test node t may be included.

[0153] In some non-limiting embodiments or aspects, graph 440 may include a plurality of nodes 442 and / or a plurality of edges 444. Each edge 444 of the plurality of edges may connect a node 442 of the plurality of nodes with another node 442 of the plurality of nodes.

[0154] The graph data associated with the graph 440 may include node data associated with a plurality of nodes of the graph 440 (eg, x1, x2, ..., x n ) and / or edge data associated with multiple edges of the graph 440 (e.g., y1, y2, ... y n ).

[0155] like Figure 4B As shown in the figure 404 in FIG. 1 , the GNN influencing system 102 can train the GNN. For example, the GNN influencing system 102 can be based on a data set (e.g., a training data set S train ) trains the initial GNN to provide the GNN. In some non-limiting embodiments or aspects, training the initial GNN may include generating the initial GNN, train Train the initial GNN and / or based on the training dataset S train Retrain the initial GNN. In some non-limiting embodiments or aspects, the GNN may include an input layer, one or more hidden layers, and / or an output layer (not shown). In some non-limiting embodiments or aspects, the GNN may integrate features of multiple nodes and / or the topology of the graph 440.

[0156] In some non-limiting embodiments or aspects, the GNN can be trained to perform one or more tasks. For example, the GNN can be trained to classify a node among multiple nodes. In some non-limiting embodiments or aspects, the GNN can provide enhanced fairness in node classification.

[0157] In some non-limiting embodiments or aspects, the GNN can be trained by a leave-one-out (LOO) training process, in which a dataset S train Remove a sample from the .

[0158] In some non-limiting embodiments or aspects, empirical risk minimization (ERM) may be used to train the GNN.

[0159] like Figure 4C As shown in the figure 406 in the figure, the GNN influence system 102 can select a target node. For example, the GNN influence system 102 can select a target node 446 from the plurality of nodes 442 of the graph 440. In some non-limiting embodiments or aspects, the target node 446 can be associated with the sample j. In some non-limiting embodiments or aspects, the target node 446 can be a test node t.

[0160] like Figure 4DAs shown, target node 446 can be associated with one or more target edges 448 in plurality of edges 444. In some non-limiting embodiments or aspects, one or more target edges 448 can include one or more edges connected to target node 446 in graph 440. In some non-limiting embodiments or aspects, target node 446 can be connected to one or more other nodes in plurality of nodes 442 via target edge 448.

[0161] like Figure 4D As shown in the figure 408 in FIG. 1 , the GNN influence system 102 can determine the target node data and the target edge data associated with the target node. For example, the GNN influence system 102 can determine the target node data (e.g., x ) associated with the target node 446 based on the graph data. i ) and target edge data associated with target node 446 and / or target edge 448 (e.g., t i ).

[0162] like Figure 4E As shown in the reference numeral 410 in FIG, the GNN influencing system 102 may determine a set of first model parameters based on the data set. For example, the GNN influencing system 102 may determine a set of first model parameters of the GNN based on the data set.

[0163] In some non-limiting embodiments or aspects, the GNN may be a prediction model whose parameters θ∈Θ map the input X∈X to the output space The dataset can include training data samples {(x1,y1),(x2,y2)…(x n ,y n )}, where n represents the number of training data samples.

[0164] In some non-limiting embodiments or aspects, the GNN may include a loss function l(x, y, θ), which may be twice differentiable in and convex in θ. In some non-limiting embodiments or aspects, the ERM may be used to train model parameters. The loss function for node classification may depend on multiple node features X, graph topology A, and / or ground truth table y. In some non-limiting embodiments or aspects, the loss function for node i may be defined by the following equation, where l(.,.) represents the cross entropy loss function and the GNN i (θ,X,A) represents the prediction of the i-th node of the given graph data:

[0165] L(θ|X,A,y i )=l(GNN i (θ,X,A),y i )

[0166] In some non-limiting embodiments or aspects, the set of first model parameters may be determined based on the following equation:

[0167]

[0168] like Figure 4F As shown in the figure at 412 in FIG. 1 , the GNN influencing system 102 can remove the target node data and the target edge data to provide a target graph dataset. For example, the GNN influencing system 102 can remove the target node data x associated with the target node 446 from the dataset. i and the target edge data y associated with the target edge 448 i To provide a target graph dataset. The target graph dataset may include removing the target node data x i and target edge data y i of the dataset.

[0169] In some non-limiting embodiments or aspects, when target node data and / or target edge data are removed from the data set, the GNN influence system 102 may remove the target nodes 446 and / or target edges 448 from the graph 440 to provide a target graph 450 .

[0170] like Figure 4G As shown in the reference numeral 414 in , the GNN influencing system 102 can determine a set of modified model parameters based on the target graph dataset. For example, the GNN influencing system 102 can determine a set of modified model parameters of the GNN based on the target graph dataset.

[0171] In some non-limiting embodiments or aspects, the first set of model parameters may be based on a training data set S train Remove the target node (for example, node j∈S train )'s node topology and / or removal loss contributions.

[0172] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the set of modified model parameters based on the following equation, where j represents a sample associated with the target node, and where represents the model parameters of the target graph dataset, and where A j Represents the influence matrix after removing all edges connected to the target node:

[0173]

[0174] In some non-limiting embodiments or aspects, the test loss function for testing node t may be defined by the following equation:

[0175]

[0176] In some non-limiting embodiments or aspects, at node j∈S train The node topology and loss contribution of the training dataset S train In the case where the GNN influence system 102 is removed, the GNN influence system 102 can use the test loss function to predict the test node t∈S based on the following equation test :

[0177]

[0178] like Figure 4H As shown at reference numeral 416 in , the GNN influence system 102 can determine a difference between a first prediction based on a first set of model parameters and a second prediction based on a modified set of model parameters.

[0179] In some non-limiting embodiments or aspects, the GNN influencing system 102 may determine the first prediction based on inputting the data set into the GNN and receiving the first prediction as a first output of the GNN.

[0180] In some non-limiting embodiments or aspects, the GNN influencing system 102 may determine the second prediction based on inputting the target graph dataset into the GNN and receiving the second prediction as a second output of the GNN.

[0181] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine modified model parameters by providing a continuous change of node topology and loss contribution via perturbations of the node topology and increasing the weights of the loss function for sample j by n and ∈, respectively. For example, the modified model parameters of the target node j with perturbations n and ∈ may be based on the following equation:

[0182]

[0183] In some non-limiting embodiments or aspects, a modified adjacency matrix having m rows and n columns may be based on the following equation:

[0184]

[0185] like Fig. 4I As shown in the figure at 418, the GNN influence system 102 can determine the influence metric of the target node on the GNN. For example, the GNN influence system 102 can determine the influence metric of the target node 446 on the GNN based on the target graph dataset, where the GNN is trained using the dataset (e.g., before removing the target node data and / or the target edge data).

[0186] In some non-limiting embodiments or aspects, the influence metric of the target node can be tracked in the forward and / or backward propagation by gradient access relative to the topology of the target graph 450 and the parameters of the GNN. For example, the influence metric of the target node can include the node topological influence of the target node during the forward propagation and / or the node prediction contribution to the training loss during the backward propagation. In some non-limiting embodiments or aspects, a closed-form solution can be derived to approximate the influence metric of the target node.

[0187] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine a first influence metric, a second influence metric, and / or a third influence metric.

[0188] In some non-limiting embodiments or aspects, the first influence metric may be associated with a property of the target node 446 with respect to the topology of the graph 440. In some non-limiting embodiments or aspects, determining the first influence metric of the target node 446 on the GNN may include determining the first influence metric of the target node 446 on the GNN based on a Hessian matrix.

[0189] In some non-limiting embodiments or aspects, the impact metric may include: a first impact metric; a second impact metric; and / or a third impact metric. The first impact metric may be based on topological impact (TI), which represents the effect of removing only the node topology of the target node (e.g., sample j). The second impact metric may be based on loss weight impact (LWI), which represents the effect of simultaneously removing the node topology and loss weight of the target node. The third impact metric may be based on interaction impact (II). TI may measure the topological impact of the target node 446 in the forward propagation. LWI may represent the original impact function in the data set. II may occur during the removal of both the topological and predicted contributions in the loss function.

[0190] In some non-limiting embodiments or aspects, the first influence metric may be associated with a property of the target node 446 with respect to the topology of the graph 440. In some non-limiting embodiments or aspects, determining the first influence metric of the target node 446 on the GNN may include determining the first influence metric of the target node 446 on the GNN based on a Hessian matrix.

[0191] In some non-limiting embodiments or aspects, the second influence metric may be associated with one or more features of the target node 446. In some non-limiting embodiments or aspects, determining the second influence metric of the target node 446 on the GNN may include determining the second influence metric of the target node 446 on the GNN based on a Hessian matrix.

[0192] In some non-limiting embodiments or aspects, the third influence metric may be associated with the target graph dataset. In some non-limiting embodiments or aspects, determining the third influence metric of the target node 446 on the GNN may include determining the third influence metric of the target node 446 on the GNN based on the Hessian matrix.

[0193] In some non-limiting embodiments or aspects, based on the modified model parameters For node j, perturb the node topology with n and increase the weight of the loss function by ∈ to obtain the optimal model parameter difference, which is defined as It can be based on the following equation, where represents the topological influence, where represents the weight influence, and Indicates interactive effects:

[0194]

[0195] In some non-limiting embodiments or aspects, the Hessian matrix H θ It can be a block matrix of second-order partial derivatives of a scalar-valued function, which describes the local part of the scalar-valued function. In some non-limiting embodiments or aspects, the Hessian matrix can be positive definite. In some non-limiting embodiments or aspects, the Hessian matrix can be determined based on the following equation:

[0196]

[0197] In some non-limiting embodiments or aspects, the GNN influence system 102 may use random estimation to estimate the influence of the target node on the GNN. For example, the GNN influence system 102 may determine the first-order Taylor expansion of the Hessian matrix based on the following equation:

[0198]

[0199] In some non-limiting embodiments or aspects, the GNN influence system 102 may replace the Hessian matrix with a gradient based on the following equation:

[0200]

[0201] In some non-limiting embodiments or aspects, the GNN influence system 102 may approximate the inverse of the Hessian matrix based on the following equation:

[0202]

[0203] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the first influence (eg, topological influence) based on the following equation: ):

[0204]

[0205] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the second influence (e.g., weighted influence) based on the following equation: ):

[0206]

[0207] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the third influence (e.g., the interaction influence) based on the following equation: ):

[0208]

[0209] In some non-limiting embodiments or aspects, simultaneously removing the node topology and the loss weight can be combined with increasing the weight of sample j by n=1 and using The perturbation samples j are the same or similar. In some non-limiting embodiments or aspects, the parameter changes can be linearly approximated without retraining the model based on the following equation:

[0210]

[0211] In some non-limiting embodiments or aspects, given a model parameter perturbation, the GNN influencing system 102 may be based on the loss function for testing node t To determine the test node t∈S test The difference between a first prediction based on a first set of model parameters and a second prediction based on a modified set of model parameters.

[0212] In some non-limiting embodiments or aspects, the GNN influence system 102 may determine the model prediction change for the test node t via the chain rule based on the following equation:

[0213]

[0214] like Figure 4J As shown in the reference numeral 420 in , the GNN influence system 102 may provide an influence matrix. For example, the GNN influence system 102 may combine (e.g., add, concatenate, average, etc.) the first influence metric, the second influence metric, and / or the third influence metric to provide an influence matrix.

[0215] In some non-limiting embodiments or aspects, the influence matrix can be based on the following equation, where the influence matrix can be calculated by train {i}Set n j = 0 to separate the topology of nodes i∈S train The gradient is:

[0216]

[0217] like Figure 4K As shown in the reference numeral 422 in FIG, the GNN influence system 102 may determine the influence metric of the target node on the GNN. For example, the GNN influence system 102 may determine the influence metric of the target node on the GNN based on the influence matrix and the loss function.

[0218] like Figure 4L As shown in the reference numeral 424 in FIG, the GNN influence system 102 can determine the fairness metric of the GNN. For example, the GNN influence system 102 can determine the fairness metric of the GNN based on population equality and / or equal opportunity.

[0219] In some non-limiting embodiments or aspects, population equality Δ may be determined based on the following equation: DP , where y represents the ground truth label, and where Represents the predicted label:

[0220]

[0221] In some non-limiting embodiments or aspects, the equal opportunity Δ may be determined based on the following equation: EO , where y represents the ground truth label, and where Represents the predicted label:

[0222]

[0223] like Figure 4M As shown in the reference numeral 426 in FIG, the GNN influence system 102 can detect anomalies. For example, the GNN influence system 102 can detect anomalies in the GNN based on the influence metric of the target node.

[0224] In some non-limiting embodiments or aspects, when an anomaly in the GNN is detected, the GNN impact system 102 may determine the fairness metric of the GNN based on the impact metric of the target node on the GNN. In some non-limiting embodiments or aspects, when an anomaly in the GNN is detected, the GNN impact system 102 may detect whether the value of the fairness metric of the GNN meets a predetermined threshold. For example, the GNN impact system 102 may compare the value of the fairness metric of the GNN with a predetermined threshold to determine whether the value of the fairness metric of the GNN meets the predetermined threshold. If the GNN impact system 102 determines that the fairness metric of the GNN meets the predetermined threshold, the GNN impact system 102 may detect the anomaly and / or perform an action based on the detection of the anomaly. If the GNN impact system 102 determines that the fairness metric of the GNN does not meet the predetermined threshold, the GNN impact system 102 may determine that the anomaly has not been detected and / or the process may end.

[0225] In some non-limiting embodiments or aspects, detecting anomalies may include detecting fraud. For example, the GNN influence system 102 may detect a fraudulent transaction based on a fairness metric satisfying a predetermined threshold. In some non-limiting embodiments or aspects, the GNN influence system 102 may perform an action on the GNN based on detecting anomalies, such as sending an alert, a notification, etc.

[0226] Although the embodiments have been described in detail for the purpose of illustration, it should be understood that such details are used for that purpose only, and the present disclosure is not limited to the disclosed embodiments or aspects, but on the contrary, is intended to cover modifications and equivalent arrangements within the spirit and scope of the appended claims. For example, it should be understood that the present disclosure contemplates that, to the extent possible, one or more features of any embodiment or aspect can be combined with one or more features of any other embodiment or aspect.

Claims

1. A computer-implemented method comprising: receiving, with at least one processor, a data set comprising graph data associated with a graph, the graph data comprising node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph; selecting, using at least one processor, a target node from among the plurality of nodes based on the graph data; determining, using at least one processor, target node data associated with the target node and target edge data associated with the target node based on the graph data, the node data of the graph data including the target node data, and the edge data of the graph data including the target edge data, wherein the target node is associated with one or more target edges of the plurality of edges, the one or more target edges including one or more edges connected to the target node in the graph; removing the target node data and the target edge data from the data set using at least one processor to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed; determining, using at least one processor, an influence metric of the target node on a graph neural network (GNN) based on the target graph dataset, wherein the GNN is trained using the dataset; as well as The at least one processor is used to detect anomalies in the GNN based on the impact metric of the target node on the GNN.

2. The computer-implemented method of claim 1 , further comprising: An initial GNN is trained based on the dataset to provide the GNN.

3. The computer-implemented method of claim 1 , wherein determining the influence metric of the target node on the GNN based on the target graph dataset comprises: Determining a set of first model parameters of the GNN based on the data set; Determining a set of modified model parameters of the GNN based on the target graph dataset; as well as A difference between a first prediction of the GNN based on the first set of model parameters and a second prediction of the GNN based on the modified set of model parameters is determined.

4. The computer-implemented method of claim 1 , wherein determining the influence metric of the target node on the GNN based on the target graph dataset comprises: determining a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to a topology of the graph; Determining a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; as well as The influence metric of the target node on the GNN is determined based on the loss function and the influence matrix.

5. The computer-implemented method of claim 4, wherein determining the first influence metric of the target node on the GNN comprises determining the first influence metric of the target node on the GNN based on a Hessian matrix.

6. The computer-implemented method of claim 4, wherein determining the second influence metric of the target node on the GNN comprises determining the second influence metric of the target node on the GNN based on a Hessian matrix.

7. The computer-implemented method of claim 4, wherein determining the third influence metric of the target node on the GNN comprises determining the third influence metric of the target node on the GNN based on a Hessian matrix.

8. The computer-implemented method of claim 1 , wherein detecting the anomaly in the GNN based on the influence metric of the target node on the GNN comprises: Determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; as well as Detecting whether the fairness metric of the GNN satisfies a predetermined threshold. 9 . The computer-implemented method of claim 1 , wherein removing the target node data and the target edge data from the data set comprises removing the target node and the one or more target edges from the graph.

10. A system comprising: at least one processor programmed or configured to: receiving a data set comprising graph data associated with a graph, the graph data comprising node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph; selecting a target node from among the plurality of nodes based on the graph data; determining, based on the graph data, target node data associated with the target node and target edge data associated with the target node, the node data of the graph data including the target node data, and the edge data of the graph data including the target edge data, wherein the target node is associated with one or more target edges of the plurality of edges, the one or more target edges including one or more edges connected to the target node in the graph; removing the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed; Determining an influence metric of the target node on a graph neural network (GNN) based on the target graph dataset, wherein the GNN is trained using the dataset; as well as Anomalies in the GNN are detected based on the influence metric of the target node on the GNN.

11. The system of claim 10, wherein the at least one processor is further programmed or configured to: An initial GNN is trained based on the dataset to provide the GNN.

12. The system of claim 10, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor is programmed or configured to: Determining a set of first model parameters of the GNN based on the data set; Determining a set of modified model parameters of the GNN based on the target graph dataset; as well as A difference between a first prediction of the GNN based on the first set of model parameters and a second prediction of the GNN based on the modified set of model parameters is determined.

13. The system of claim 10, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the at least one processor is programmed or configured to: determining a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to a topology of the graph; Determining a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; as well as The influence metric of the target node on the GNN is determined based on the loss function and the influence matrix.

14. The system of claim 13, wherein when determining the first influence metric of the target node on the GNN, the at least one processor is programmed or configured to: Determine the first influence metric of the target node on the GNN based on the Hessian matrix.

15. The system of claim 13, wherein when determining the second influence metric of the target node on the GNN, the at least one processor is programmed or configured to: Determine the second influence metric of the target node on the GNN based on the Hessian matrix.

16. The system of claim 13, wherein when determining the third influence metric of the target node on the GNN, the at least one processor is programmed or configured to: Determine the third influence metric of the target node on the GNN based on the Hessian matrix.

17. The system of claim 10, wherein when detecting the anomaly in the GNN based on the impact metric of the target node on the GNN, the at least one processor is programmed or configured to: Determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; and Detecting whether the fairness metric of the GNN satisfies a predetermined threshold.

18. The system of claim 10, wherein when removing the target node data and the target edge data from the data set, the at least one processor is programmed or configured to: The target node and the one or more target edges are removed from the graph.

19. A computer program product comprising at least one non-transitory computer readable medium, the at least one non-transitory computer readable medium comprising one or more instructions that, when executed by at least one processor, cause the at least one processor to: receiving a data set comprising graph data associated with a graph, the graph data comprising node data associated with a plurality of nodes of the graph and edge data associated with a plurality of edges of the graph; selecting a target node from among the plurality of nodes based on the graph data; determining, based on the graph data, target node data associated with the target node and target edge data associated with the target node, the node data of the graph data including the target node data, and the edge data of the graph data including the target edge data, wherein the target node is associated with one or more target edges of the plurality of edges, the one or more target edges including one or more edges connected to the target node in the graph; removing the target node data and the target edge data from the data set to provide a target graph data set, wherein the target graph data set includes the data set with the target node data and the target edge data removed; Determining an influence metric of the target node on a graph neural network (GNN) based on the target graph dataset, wherein the GNN is trained using the dataset; as well as Anomalies in the GNN are detected based on the influence metric of the target node on the GNN.

20. The computer program product of claim 19, wherein the one or more instructions further cause the at least one processor to: An initial GNN is trained based on the dataset to provide the GNN.

21. The computer program product of claim 19, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions cause the at least one processor to: Determining a set of first model parameters of the GNN based on the data set; Determining a set of modified model parameters of the GNN based on the target graph dataset; as well as A difference between a first prediction of the GNN based on the first set of model parameters and a second prediction of the GNN based on the modified set of model parameters is determined.

22. The computer program product of claim 19, wherein when determining the influence metric of the target node on the GNN based on the target graph dataset, the one or more instructions cause the at least one processor to: determining a first influence metric of the target node on the GNN, wherein the first influence metric is associated with a property of the target node with respect to a topology of the graph; Determining a second influence metric of the target node on the GNN, wherein the second influence metric is associated with a feature of the target node; determining a third influence metric of the target node on the GNN, wherein the third influence metric is associated with the target graph dataset; combining the first influence metric, the second influence metric, and the third influence metric to provide an influence matrix; as well as The influence metric of the target node on the GNN is determined based on the loss function and the influence matrix.

23. The computer program product of claim 22, wherein when determining the first influence metric of the target node on the GNN, the one or more instructions cause the at least one processor to: Determine the first influence metric of the target node on the GNN based on the Hessian matrix.

24. The computer program product of claim 22, wherein when determining the second influence metric of the target node on the GNN, the one or more instructions cause the at least one processor to: Determine the second influence metric of the target node on the GNN based on the Hessian matrix.

25. The computer program product of claim 22, wherein when determining the third influence metric of the target node on the GNN, the one or more instructions cause the at least one processor to: Determine the third influence metric of the target node on the GNN based on the Hessian matrix.

26. The computer program product of claim 19, wherein when detecting the anomaly in the GNN based on the impact metric of the target node on the GNN, the one or more instructions cause the at least one processor to: Determining a fairness metric of the GNN based on the influence metric of the target node on the GNN; and Detecting whether the fairness metric of the GNN satisfies a predetermined threshold.

27. The computer program product of claim 19, wherein when removing the target node data and the target edge data from the data set, the one or more instructions cause the at least one processor to: The target node and the one or more target edges are removed from the graph.

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