Customer association prediction method, device, equipment, storage medium and program product

Abstract

The application provides a customer association prediction method and device, equipment, a storage medium and a program product, which can be applied to the field of artificial intelligence technology. The method comprises the following steps: obtaining the association relationship between a plurality of customers, and constructing a customer relationship graph; by calculating the node degree and the local clustering coefficient of each node in the customer relationship graph, the customer relationship graph is divided into three subgraphs and is respectively correspondingly mapped to a hyperbolic space, a spherical space and an Euclidean space, and corresponding hyperbolic space features and spherical space features are extracted; the hyperbolic space features are processed by using a graph convolutional neural network; the processed hyperbolic space features and the spherical space features are respectively mapped to the Euclidean space; the mapped features are fused by using an attention mechanism to obtain the fusion features of each node; and the association score between any two nodes in the plurality of customers is determined based on the fusion features.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, and more specifically to a customer association prediction method, apparatus, device, storage medium, and program product. Background Technology

[0002] In fields such as finance and social network analytics, customer relationship graphs are a core data structure used to represent customer entities (nodes) and the relationships (edges) between them. Effective analysis and prediction of customer relationship graphs, such as link prediction (predicting potential relationships between two customers), are of great significance for business scenarios such as risk control and product recommendation.

[0003] In real-world scenarios, customer relationship graphs exhibit complex and heterogeneous structures. For example, some subgraphs may present highly aggregated community structures (high degree of clustering), while others may show sparse connections or tree-like hierarchical structures (such as pyramid-shaped distribution networks), and still others may have a degree of clustering in between.

[0004] Existing graph neural network methods typically map all nodes to a single curvature space (such as Euclidean, hyperbolic, or spherical space) for representation learning. However, a single space cannot fully represent the structural characteristics of different subgraphs. For example, hyperbolic space excels at handling tree-like hierarchical structures but introduces distortion when used for highly cohesive community structures; while spherical space is more suitable for highly cohesive structures. Therefore, using a single space for feature representation can lead to the loss or distortion of structural information of some nodes during the embedding process, ultimately affecting the accuracy of downstream tasks such as link prediction. Summary of the Invention

[0005] In view of the above problems, this application provides a customer association prediction method, apparatus, device, storage medium, and program product.

[0006] The first aspect of this application provides a customer association prediction method, comprising: obtaining the association relationships between multiple customers; constructing a customer relationship graph with each customer as a node and the association relationships between customers as edges; calculating the node degree and local clustering coefficient of each node in the customer relationship graph; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local compactness between the current node and its neighboring nodes; dividing the customer relationship graph into a first subgraph, a second subgraph, and a third subgraph according to the node degree and local clustering coefficient of each node; mapping the first subgraph, the second subgraph, and the third subgraph to hyperbolic space, spherical space, and Euclidean space respectively, and improving the prediction results. Hyperbolic space features, spherical space features, and Euclidean space features are obtained from hyperbolic space, spherical space, and Euclidean space, respectively. A Lorentz hyperbolic graph convolutional neural network is used to perform graph convolution processing on the hyperbolic space features, mapping the processed hyperbolic space features and spherical space features to Euclidean space, obtaining the first mapped features and the second mapped features, respectively. The first mapped features, the second mapped features, and the Euclidean space features are fused using an attention mechanism to obtain the fused features for each node. Based on the fused features, the correlation score between any two nodes among multiple customers is determined. The correlation score represents the probability that there is a correlation between two customers corresponding to two nodes.

[0007] According to embodiments of this application, a customer relationship graph is divided into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node. This includes: assigning nodes in the customer relationship graph with a node degree greater than a first preset threshold and a local clustering coefficient less than a second preset threshold to a first node set, thereby inducing a first subgraph using the first node set; assigning nodes in the customer relationship graph with a node degree less than or equal to the first preset threshold and a local clustering coefficient greater than or equal to the second preset threshold to a second node set, thereby inducing a second subgraph using the second node set; and assigning nodes in the customer relationship graph other than those in the first and second node sets to a third node set, thereby inducing a third subgraph using the third node set.

[0008] According to embodiments of this application, the first subgraph, the second subgraph, and the third subgraph are mapped to hyperbolic space, spherical space, and Euclidean space, respectively, and hyperbolic space features, spherical space features, and Euclidean space features corresponding to hyperbolic space, spherical space, and Euclidean space, respectively, are extracted. This includes: mapping the node features of each node in the first subgraph to hyperbolic space using the Lorentz index to obtain hyperbolic space features; projecting the node features of each node in the second subgraph onto a unit sphere using Euclidean norm normalization to obtain spherical space features; and performing a linear transformation on the node features of each node in the third subgraph in Euclidean space to obtain Euclidean space features.

[0009] According to an embodiment of this application, the node features of each node in the first subgraph are mapped to hyperbolic space through the Lorentz index to obtain hyperbolic space features, including: mapping the node features of each node in the first subgraph to the tangent space of a preset reference point in hyperbolic space through a linear transformation to obtain the tangent space vector corresponding to each node in the first subgraph in the tangent space; and mapping the tangent space vector to hyperbolic space through the Lorentz index to obtain hyperbolic space features.

[0010] According to an embodiment of this application, the node features of each node in the second subgraph are projected onto a unit sphere through Euclidean norm normalization to obtain spherical space features. This includes: linearly transforming the node features of each node in the second subgraph to a preset dimension and then performing Euclidean norm normalization to obtain a unit vector corresponding to each node; and projecting the unit vector onto a unit sphere to obtain spherical space features corresponding to each node.

[0011] According to an embodiment of this application, the Lorentz hyperbolic graph convolutional neural network includes a Lorentz neighborhood aggregation layer and a Lorentz nonlinear activation layer; the Lorentz hyperbolic graph convolutional neural network is used to perform graph convolution processing on hyperbolic space features, including: performing neighborhood aggregation on the hyperbolic space features through the Lorentz neighborhood aggregation layer to obtain aggregated hyperbolic space features; and performing nonlinear mapping on the aggregated hyperbolic space features through the Lorentz nonlinear activation layer to obtain processed hyperbolic space features.

[0012] According to an embodiment of this application, hyperbolic space features are aggregated through a Lorentz neighborhood aggregation layer to obtain aggregated hyperbolic space features. This includes: for each node in the first subgraph, the Frieser algorithm is used to calculate the Lorentz weighted centroid of the hyperbolic space features of all neighboring nodes of each node, and the Lorentz weighted centroid is used as the aggregated node feature.

[0013] According to an embodiment of this application, the processed hyperbolic space features and spherical space features are mapped to Euclidean space to obtain a first mapped feature and a second mapped feature, respectively. This includes: mapping the hyperbolic space features after graph convolution processing from hyperbolic space to Euclidean space through Lorentz logarithm to obtain the first mapped feature; and mapping the spherical space features from spherical space to Euclidean space through orthogonal projection to obtain the second mapped feature.

[0014] According to embodiments of this application, an attention mechanism is used to fuse the first mapping feature, the second mapping feature, and the Euclidean space feature to obtain the fused feature of each node. This includes performing the following operations for each node in the customer relationship graph: obtaining the pre-set attention weights of the first mapping feature, the second mapping feature, and the Euclidean space feature; and performing a weighted summation of the first mapping feature, the second mapping feature, and the Euclidean space feature based on the attention weights of the first mapping feature, the second mapping feature, and the Euclidean space feature to obtain the fused feature of each node.

[0015] A second aspect of this application provides a customer association prediction device, comprising: a relationship graph construction module for acquiring the association relationships between multiple customers and constructing a customer relationship graph with each customer as a node and the association relationships between customers as edges; a node calculation module for calculating the node degree and local clustering coefficient of each node in the customer relationship graph; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local compactness between the current node and its neighboring nodes; a subgraph partitioning module for partitioning the customer relationship graph into a first subgraph, a second subgraph, and a third subgraph according to the node degree and local clustering coefficient of each node; and a spatial mapping module for mapping the first subgraph, the second subgraph, and the third subgraph to hyperbolic space, spherical space, and spatial mapping, respectively. The Euclidean space module extracts hyperbolic space features, spherical space features, and Euclidean space features corresponding to hyperbolic space, spherical space, and Euclidean space, respectively. The graph convolution and mapping module uses a Lorentz hyperbolic graph convolutional neural network to perform graph convolution processing on the hyperbolic space features, mapping the processed hyperbolic and spherical space features to Euclidean space to obtain the first and second mapped features, respectively. The feature fusion module fuses the first mapped features, second mapped features, and Euclidean space features using an attention mechanism to obtain the fused features for each node. The association prediction module determines the association score between any two nodes among multiple customers based on the fused features; the association score represents the probability that there is an association relationship between the two customers corresponding to the two nodes.

[0016] A third aspect of this application provides an electronic device, comprising: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors perform any of the methods described above.

[0017] A fourth aspect of this application provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform any of the methods described above.

[0018] The fifth aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements a method for performing any of the above-mentioned methods. Attached Figure Description

[0019] The above-mentioned contents, other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0020] Figure 1 This illustration schematically depicts an application scenario of the customer association prediction method according to an embodiment of this application;

[0021] Figure 2 A flowchart illustrating a customer association prediction method according to an embodiment of this application is shown schematically.

[0022] Figure 3 The illustration schematically shows the principle of dividing a customer relationship graph into different subgraphs and mapping them to different spaces according to an embodiment of this application;

[0023] Figure 4 This schematic diagram illustrates a structural block diagram of a customer association prediction device according to an embodiment of the present application;

[0024] Figure 5 A block diagram of an electronic device implementing a customer association prediction method according to an embodiment of this application is shown schematically. Detailed Implementation

[0025] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0026] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0027] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0028] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0029] In the technical solution of this application, the user information (including but not limited to user personal information, user image information, user device information, such as location information) and data (including but not limited to data used for analysis, stored data, and displayed data) involved are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, storage, use, processing, transmission, provision, disclosure, and application of related data all comply with relevant laws, regulations, and standards, take necessary confidentiality measures, do not violate public order and good morals, and provide corresponding operation entry points for users to choose to authorize or refuse.

[0030] Figure 1 The diagram illustrates an application scenario of the customer association prediction method according to an embodiment of this application.

[0031] like Figure 1 As shown, application scenario 100 according to this embodiment may include a testing scenario for the interface. Network 104 is used as a medium to provide a communication link between terminal devices 101, 102, 103 and server 105. Network 104 may include various connection types, such as wired, wireless communication links or fiber optic cables.

[0032] Users can use terminal devices 101, 102, and 103 to interact with server 105 via network 104 to receive or send messages, etc. Various communication client applications can be installed on terminal devices 101, 102, and 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, social media platform software, etc. (for example only).

[0033] Terminal devices 101, 102, and 103 can be various electronic devices with displays and web browsing capabilities, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0034] Server 105 can be a server that provides various services, such as a backend management server that supports websites browsed by users using terminal devices 101, 102, and 103 (for example only), or a server cluster that trains and infers data obtained from terminal devices 101, 102, and 103. Management server 105 can analyze and process received user requests and other data, and feed back the processing results (such as web pages, information, inference and training results or data obtained or generated based on user requests) to the terminal devices.

[0035] It should be noted that the customer association prediction method provided in this application embodiment can generally be executed by server 105. The customer association prediction method provided in this application embodiment can also be executed by a server or server cluster that is different from server 105 and capable of communicating with terminal devices 101, 102, 103 and / or server 105. Correspondingly, the automatic conversion device for comparison test scripts provided in this application embodiment can also be set in a server or server cluster that is different from server 105 and capable of communicating with terminal devices 101, 102, 103 and / or server 105.

[0036] It should be understood that Figure 1 The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included.

[0037] The following will be based on Figure 1 The described scene, through Figures 2-3 A customer association prediction method according to embodiments of this application will be described in detail.

[0038] Figure 2 A flowchart illustrating a customer association prediction method according to an embodiment of this application is shown schematically.

[0039] like Figure 2 As shown, the customer association prediction method in this embodiment includes steps S201 to S207.

[0040] In step S201, the relationships between multiple customers are obtained, and a customer relationship graph is constructed with each customer as a node and the relationships between customers as edges.

[0041] Specifically, customer data is extracted from the internal systems of banks or financial institutions (such as core banking systems and customer relationship management systems). Customer data includes, but is not limited to, basic customer information (such as age, occupation, and registered address), account information, transaction records (such as transfers, remittances, and consumption), as well as guarantee relationships and shared equipment information.

[0042] Based on the above data, each customer is defined as a unique node, and a node feature matrix X is defined, where each row represents a customer's feature vector. Simultaneously, edge connections are defined based on the interaction behavior between customers. For example, if two customers have direct transfer transactions exceeding a certain amount (e.g., 10,000 yuan) within a preset time window (e.g., within the past 6 months), indicating a transaction relationship, then an edge is established between the corresponding two nodes.

[0043] Thus, an initial customer relationship graph G = (V, E) is constructed, where V represents the set of customer nodes and E represents the set of edges connecting customers.

[0044] In step S202, the node degree and local clustering coefficient of each node in the customer relationship graph are calculated; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local tightness between the current node and its neighboring nodes.

[0045] Perform network analysis on the constructed customer relationship graph G. For any node, the node degree can be represented as the number of edges directly connected to the node.

[0046] For example, a high node degree often indicates that the customer is a super-connector, possibly a central node or a key influencer. The local clustering coefficient can be expressed as the ratio of the actual number of edges between a node's neighboring nodes to the maximum possible number of edges.

[0047] For example, a high clustering coefficient (close to 1) indicates that the neighbors of a node are highly interconnected, forming a close "community"; a low clustering coefficient (close to 0) indicates that the node is at the end of a sparse connection or tree structure.

[0048] In step S203, the customer relationship graph is divided into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node.

[0049] Specifically, the first subgraph is a subgraph with a hierarchical tree-like topology, which is a subset of graph structures containing clear hierarchical relationships, branching structures, and hierarchical connections (such as hierarchical networks, tree dependencies, chain-like hierarchical structures, etc.). The first subgraph is characterized by a hierarchical, tree-like, and acyclic hierarchical topology, which is naturally adapted to the negative curvature geometry of hyperbolic space and can accurately preserve the hierarchical distance between nodes.

[0050] The second subgraph is a subgraph with high aggregation and dense community topology. It is a subset of graph structures with highly interconnected nodes, tight internal connections, and clustered communities (such as community networks, locally dense groups, and highly coupled relational structures). The core features of the second subgraph are community, dense aggregation, and strong relational clustering. It is naturally adapted to the positive curvature geometry of spherical space and can accurately quantify the strength of the association between nodes.

[0051] The third subgraph is a subgraph with no special hierarchy or dense aggregation, and a regular, flat topology. It is a subset of graph structures with sparse structure, regular connections, and no obvious hierarchy or clustering characteristics (such as regular linear connections, sparse and irregular connections, flat and uniform structures, etc.). The characteristics of the third subgraph are flattening, sparse regularity, and no special topology. It naturally fits the zero-curvature flat geometry of Euclidean space and can complete feature representation without complex spatial transformations.

[0052] In step S204, the first subgraph, the second subgraph, and the third subgraph are mapped to hyperbolic space, spherical space, and Euclidean space, respectively, and hyperbolic space features, spherical space features, and Euclidean space features corresponding to hyperbolic space, spherical space, and Euclidean space are extracted.

[0053] After completing the subgraph partitioning, based on the structural characteristics of each subgraph, its node features are mapped to the most suitable geometric space, and hyperbolic space features, spherical space features, and Euclidean space features are extracted respectively.

[0054] The node feature vectors of the first subgraph are located in Euclidean space and need to be mapped to a negative curvature hyperbolic space to achieve a distance-preserving representation of the tree-like hierarchical structure. The node features of the second subgraph need to be mapped to a positive curvature spherical space to accurately represent the association strength of nodes in dense communities. The third subgraph is a flat and regular structure, and feature extraction is directly completed in zero curvature Euclidean space: the original feature vectors of the nodes are mapped to the target dimension through a learnable linear transformation (such as a fully connected layer) without changing the inherent geometric properties of Euclidean space, and the Euclidean space features are directly obtained.

[0055] By using subgraphs with different topological structures in different spaces, the optimal feature representation of each subgraph is achieved in geometric space.

[0056] In step S205, a Lorentz hyperbolic graph convolutional neural network is used to perform graph convolution processing on the hyperbolic space features, and the processed hyperbolic space features and spherical space features are mapped to Euclidean space to obtain the first mapped features and the second mapped features, respectively.

[0057] Since the first subgraph has a tree-like hierarchical structure, and the nodes in the first subgraph exhibit a power-law distribution and hierarchical progression, its structural information is the most complex and difficult to extract. Traditional Euclidean graph convolutions cannot preserve this non-Euclidean distance property. Therefore, this application employs a graph neural network specifically designed for hyperbolic spaces, namely the Lorentzian Graph Convolutional Network (LGCN), to perform depth graph convolution processing on the hyperbolic space features obtained in step S204 above, in order to obtain the processed hyperbolic space features.

[0058] After extracting features from hyperbolic space and spherical space, since features cannot be directly fused between different geometric spaces, non-Euclidean space features need to be uniformly mapped to Euclidean space to achieve spatial alignment.

[0059] Specifically, the hyperbolic space features of the first subgraph are mapped to Euclidean space through a learnable transformation to obtain the first mapped features; the spherical space features of the second subgraph are mapped to Euclidean space through a learnable transformation to obtain the second mapped features. Through this unified spatial mapping, the three types of features are placed in the same Euclidean space, laying the foundation for subsequent multi-feature fusion.

[0060] In step S206, the first mapping feature, the second mapping feature, and the Euclidean space feature are fused through an attention mechanism to obtain the fused feature of each node.

[0061] Specifically, an attention mechanism is used to automatically learn the importance weights of features from different sources, achieving weighted fusion to obtain the fused feature for each node. This fused feature can simultaneously preserve the hierarchical structure, community association, and flat structure characteristics of a node, thus possessing stronger expressive power.

[0062] In step S207, based on the fusion features, the correlation score between any two nodes among multiple customers is determined. The correlation score represents the probability that there is a correlation between the two customers corresponding to the two nodes.

[0063] Specifically, node fusion features are used to predict relationships between customers. For a graph structure composed of multiple customer nodes, feature similarity is calculated for any two nodes, and the relationship score between the nodes is output.

[0064] For example, a correlation score represents the probability that there is a potential connection between two customer nodes. The higher the score, the greater the likelihood that there is a business connection, behavioral connection, or risk connection between the two customers. Ultimately, customer link prediction is achieved based on the correlation score, providing support for subsequent tasks such as risk transmission, connection mining, and community discovery.

[0065] This application divides the customer network into subgraphs based on different topologies and extracts features by matching them to hyperbolic space, spherical space, and Euclidean space respectively. Then, it maps the non-Euclidean space features to Euclidean space and uses an attention mechanism to adaptively fuse multiple types of features before performing link prediction. This approach can fully explore information from different types of network structures, improve feature representation and fusion effects, effectively improve the accuracy of customer node association probability prediction, and accurately realize the mining of relationships between customers. It is highly practical.

[0066] Figure 3 A schematic diagram is shown illustrating how a customer relationship graph is divided into different subgraphs and mapped to different spaces according to an embodiment of this application.

[0067] In embodiments of this application, the customer relationship graph is divided into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node. This includes: classifying nodes in the customer relationship graph whose node degree is greater than a first preset threshold and whose local clustering coefficient is less than a second preset threshold into a first node set, and using the first node set to induce a first subgraph; classifying nodes in the customer relationship graph whose node degree is less than or equal to the first preset threshold and whose local clustering coefficient is greater than or equal to the second preset threshold into a second node set, and using the second node set to induce a second subgraph; and classifying nodes in the customer relationship graph other than those in the first and second node sets into a third node set, and using the third node set to induce a third subgraph.

[0068] In this context, node degree refers to the number of edges directly connected to a node in the graph, representing the breadth of connections a node has in the graph. Local clustering coefficient is an indicator that measures the local compactness between a node and its neighbors, representing the probability that neighbors of a node are interconnected, reflecting the local clustering characteristics of the graph.

[0069] Specifically, this application mainly relies on the topological attribute characteristics of nodes to achieve refined subgraph partitioning. It mainly relies on two core topological indicators, node degree and local clustering coefficient, to perform non-overlapping and full-coverage partitioning of the overall customer relationship graph, dividing the customer relationship graph into three types of subgraphs with different structural characteristics, thereby achieving accurate separation of different topological structures.

[0070] The specific division method is as follows: First, a first preset threshold and a second preset threshold are preset as the division criteria. All nodes in the customer relationship graph are traversed, and nodes with a degree greater than the first preset threshold and a local clustering coefficient less than the second preset threshold are selected and grouped into the first node set. All nodes in this set and their corresponding connection relationships induce the formation of the first subgraph. This subgraph has typical hierarchical tree topological characteristics with a wide range of node connections and weak local clustering.

[0071] Secondly, nodes with a degree less than or equal to the first preset threshold and a local clustering coefficient greater than or equal to the second preset threshold are selected and grouped into a second node set. This node set induces the formation of a second subgraph, which has dense local connections and significant clustering characteristics, presenting a highly aggregated community topology.

[0072] Finally, all remaining nodes in the customer relationship graph that do not belong to the first or second node sets are grouped into a third node set, inducing the formation of a third subgraph. This subgraph has no obvious hierarchical structure or dense clustering structure. Through the above-mentioned quantification threshold division method, three types of differentiated topological structures—hierarchical tree-like structures, dense communities, and regular flat structures—can be accurately distinguished, providing a precise structural foundation for subsequent adaptation to different geometric spatial feature extraction.

[0073] For example, in a financial customer relationship network scenario, a customer relationship graph consisting of corporate and individual customers is constructed, with a first preset threshold of 8 and a second preset threshold of 0.4. Traversing all customer nodes, core hub customers with a number of cooperative relationships (node ​​degree) greater than 8 and a local clustering coefficient less than 0.4 are grouped into the first node set. These customers are mostly group headquarters and core platform enterprises, with a large number of clients but relatively few inter-client relationships, forming a typical tree-like hierarchical structure in the first subgraph. Small and medium-sized customers with a node degree ≤ 8 and a local clustering coefficient ≥ 0.4 are grouped into the second node set. These customers are mostly cooperative clusters within the same industry or region, with dense internal cross-relationships, forming a highly aggregated community structure in the second subgraph. The remaining ordinary customers with few relationships, no clustering characteristics, and scattered, single connections constitute the third node set, forming a topologically flat and regular third subgraph, completing the subgraph partitioning of the entire network without overlap and with full coverage.

[0074] By accurately separating the first subgraph with a hierarchical tree structure, the second subgraph with a highly aggregated community structure, and the third subgraph with a regular and flat structure, this method effectively solves the problems of traditional graph modeling methods that do not distinguish between network topologies, cause confusion of structural features due to uniform modeling, and fail to fully mine topology information. It can specifically distinguish three types of differentiated topology characteristics in customer networks: hub-level associations, cluster-dense associations, and ordinary scattered associations. This enables differentiated and refined representation of network structures from the source, avoids mutual interference between different topology features, significantly improves the targeting and effectiveness of subsequent multi-spatial feature extraction, ensures that various types of customer topology association information can be completely and accurately preserved and mined, and significantly improves the accuracy and reliability of overall customer association link prediction.

[0075] In this embodiment, the first subgraph, the second subgraph, and the third subgraph are mapped to hyperbolic space, spherical space, and Euclidean space, respectively. Hyperbolic space features, spherical space features, and Euclidean space features are extracted from the hyperbolic space, spherical space, and Euclidean space, respectively. This includes: mapping the node features of each node in the first subgraph to hyperbolic space using the Lorentz exponent to obtain hyperbolic space features; projecting the node features of each node in the second subgraph onto a unit sphere using Euclidean norm normalization to obtain spherical space features; and performing a linear transformation on the node features of each node in the third subgraph in Euclidean space to obtain Euclidean space features.

[0076] In this application, hyperbolic space is a non-Euclidean space with constant negative curvature; spherical space is a non-Euclidean space with constant positive curvature, and its geometric model is a high-dimensional unit sphere; Euclidean space is a flat space that satisfies the Euclidean geometric axioms, and its core feature is that its curvature is always 0.

[0077] Based on the three types of differentiated subgraphs, we perform targeted feature extraction on the appropriate geometric spaces. By relying on the curvature characteristics of different geometric spaces to fit the topological essence of the subgraphs, we maximize the preservation and mining of structural features.

[0078] For the first subgraph of the hierarchical tree structure, the Lorentz exponential mapping method is used to map the node features to hyperbolic space, extract hyperbolic space features, adapt to the negative curvature and exponential expansion characteristics of hyperbolic space, and accurately characterize the hierarchical distance and branching relationship between nodes.

[0079] For the second subgraph of a highly aggregated community structure, the node features are linearly transformed according to a preset dimension, and then normalized by the L2 (L2 Norm Normalization) norm to obtain unit vectors. The unit vectors are then projected onto a unit hypersphere to complete the spherical space mapping and obtain spherical space features. Based on the angular distance characteristics of the spherical space, the degree of association between nodes in the community is accurately represented.

[0080] For the third subgraph with a regular flat structure, no cross-space transformation is required. Instead, learnable linear transformations are performed directly on the node features in Euclidean space to obtain Euclidean space features. This adapts to the feature representation requirements of flat and unbiased topologies while preserving the effective feature information of the original nodes.

[0081] Based on the inherent curvature characteristics of hyperbolic space, spherical space, and Euclidean space, this method adapts to hierarchical tree-like, dense community, and regular flat network structures respectively, completely overcoming the technical shortcomings of traditional single Euclidean space modeling, which cannot adapt to diverse topological structures, has low structural feature fitting, and provides only partial representation. Specifically, it utilizes the negative curvature exponential expansion characteristic of hyperbolic space to accurately characterize the hierarchical subgraphs' hierarchical subgraphs and long-distance relationships; it leverages the positive curvature angle measurement characteristic of spherical space to finely represent the local clustering density of community subgraphs; and it relies on the stationary linearity of Euclidean space to fully preserve the basic connectivity features of regular subgraphs, achieving optimal matching between various network topologies and geometric spaces. The differentiated extraction method fully mines the fine-grained topological information of different subgraphs, avoiding the problem of different structural features masking each other and information loss, greatly improving the richness of node feature representation and structural fit. This provides more refined and reliable feature support for subsequent cross-space feature fusion and high-precision customer link prediction, effectively improving the model's overall modeling ability and generalization performance for complex customer relationship networks.

[0082] In this embodiment of the application, the node features of each node in the first subgraph are mapped to hyperbolic space through the Lorentz index to obtain hyperbolic space features. This includes: mapping the node features of each node in the first subgraph to the tangent space of a preset reference point in hyperbolic space through a linear transformation to obtain the tangent space vector corresponding to each node in the first subgraph in the tangent space; and mapping the tangent space vector to hyperbolic space through the Lorentz index to obtain hyperbolic space features.

[0083] To further improve the extraction accuracy of features at the first sub-layer level, this application adopts a step-by-step mapping method to accurately solve the hyperbolic space features.

[0084] First, the original features of the nodes in the first subgraph are transformed linearly to map the features to the tangent space corresponding to the preset reference point in the hyperbolic space. This transformation yields the tangent space vectors corresponding to each node, completing the initial adaptation of Euclidean features to the hyperbolic tangent space.

[0085] Subsequently, the tangent space vector is precisely mapped to the hyperbolic manifold space using the Lorentz exponential mapping function, completing the precise conversion of spatial dimensions. This results in a high-precision hyperbolic space feature that combines hierarchical structural information with spatial geometric characteristics, effectively avoiding the loss of structural features caused by direct mapping and fully preserving the hierarchical topological relationship of the first subgraph.

[0086] In this embodiment of the application, the node features of each node in the second subgraph are projected onto a unit sphere through Euclidean norm normalization to obtain spherical space features. This includes: linearly transforming the node features of each node in the second subgraph to a preset dimension and then performing Euclidean norm normalization to obtain a unit vector corresponding to each node; and projecting the unit vector onto a unit sphere to obtain spherical space features corresponding to each node.

[0087] To address the topological characteristics of highly aggregated communities in the second subgraph, this application employs a step-by-step refined projection approach: first, dimensional transformation; then, L2 normalization; and finally, hyperspherical projection, to achieve accurate solutions for spherical spatial features. First, the original node features of each node in the second subgraph undergo a linear transformation, uniformly mapping the feature dimensions to a preset target dimension, thus completing feature dimension regularization and noise filtering. Next, L2 normalization is performed on the transformed feature vectors, constraining the vector magnitude to 1, resulting in unit vectors corresponding to each node. Finally, the generated unit vectors are orthogonally projected onto the corresponding dimension of the unit hypersphere, ensuring that the node features fully conform to the geometric constraints of the spherical space. This yields spherical spatial features with accurate structural representation and unified dimensions, guaranteeing that the densely interconnected features of the community can be effectively characterized through spherical spatial angular distances.

[0088] For example, for cluster customer nodes in the same region and industry in the second subgraph, the original multi-dimensional features such as customer business similarity, cooperation frequency, and degree of association are linearly transformed and uniformly mapped to a 64-dimensional preset feature dimension, eliminating redundant dimensional differences. L2 normalization is then performed on the transformed feature vectors to eliminate interference from differences in feature amplitude, generating standardized unit vectors with a modulus of 1. Furthermore, all unit vectors are projected onto a 64-dimensional unit hypersphere, ensuring that the features of each cluster customer retain only directional differences. The angle between the vectors in the spherical space is used to accurately represent the degree of association between customers; the smaller the angle, the higher the customer business association and community aggregation, precisely adapting to the topological representation needs of dense community subgraphs.

[0089] By employing a step-by-step processing approach—first linear dimension regularization, then L2 normalization, and finally unit hyperspherical projection—this method effectively solves the technical problems of inconsistent dimensions, large amplitude interference, and ambiguous community association representation in traditional spherical feature extraction. Linear transformation unifies the feature dimensions, eliminating modeling biases caused by inconsistencies in the original feature dimensions. L2 normalization removes feature magnitude interference, retaining only the vector direction information representing association characteristics, ensuring that all node features satisfy the geometric constraints of spherical space.

[0090] The above projection method is highly compatible with the highly aggregated and densely connected community topology characteristics of the second subgraph. It can accurately characterize the degree of association between nodes within the cluster by using the measurement of spherical spatial angles, effectively highlight customer clustering characteristics, avoid amplitude noise from masking subtle differences in community associations, and significantly improve the feature expression accuracy of dense topology structures. This provides high-quality spherical feature support for subsequent multi-spatial feature fusion and customer community association mining.

[0091] In this embodiment, the Lorentz hyperbolic graph convolutional neural network includes a Lorentz neighborhood aggregation layer and a Lorentz nonlinear activation layer. The Lorentz hyperbolic graph convolutional neural network is used to perform graph convolution processing on hyperbolic space features, including: performing neighborhood aggregation on the hyperbolic space features through the Lorentz neighborhood aggregation layer to obtain aggregated hyperbolic space features; and performing nonlinear mapping on the aggregated hyperbolic space features through the Lorentz nonlinear activation layer to obtain processed hyperbolic space features.

[0092] By introducing a Lorentz hyperbolic graph convolutional neural network to deeply optimize the initial hyperbolic space features, the network association features of nodes are further mined, enhancing the hierarchical structure representation capability. This process consists of two core steps: neighborhood aggregation and nonlinear mapping.

[0093] First, neighborhood feature aggregation is completed through the Lorenz neighborhood aggregation layer inside the network. For each node in the first subgraph, the Fraser method is used to accurately calculate the Lorenz weighted centroid of the hyperbolic space features of all neighboring nodes of that node. The weighted centroid is used as the aggregated feature of the current node to realize the fusion of neighborhood hierarchical association information.

[0094] Secondly, by using a Lorentz nonlinear activation layer to perform nonlinear mapping on the aggregated node features, the limitations of linear transformation can be overcome, and complex implicit hierarchical association features can be mined, ultimately resulting in refined hyperbolic space features with high representational power.

[0095] Specifically, for the initial hyperbolic features of customer nodes at each level within the first subgraph, a Lorenz neighborhood aggregation layer is used to calculate the Lorenz weighted centroids of all subordinate related customer features of the core customer using the Fraser method. This aggregates the hierarchical association information of subordinate customers into the core customer features, compensating for the lack of neighborhood information in single-point features. Subsequently, a Lorenz nonlinear activation layer is used to complete the nonlinear transformation of features, uncovering implicit hierarchical transmission relationships between customers, such as indirect associations in multi-level cooperation and cross-level business linkage features. Finally, the optimized hyperbolic space features are output, significantly improving the feature representation accuracy of the tree-like hierarchical structure.

[0096] Furthermore, in this embodiment of the application, the hyperbolic space features are aggregated by the Lorentz neighborhood aggregation layer to obtain the aggregated hyperbolic space features, including: for each node in the first subgraph, the Frieser algorithm is used to calculate the Lorentz weighted centroid of the hyperbolic space features of all neighboring nodes of each node, and the Lorentz weighted centroid is used as the aggregated node feature.

[0097] Since hyperbolic space is a non-Euclidean curved space with constant negative curvature, it does not satisfy the linear operation axiom of Euclidean space. If Euclidean weighted average is directly applied to hyperbolic space features, the aggregation result will deviate from the hyperbolic manifold, destroy the geodesic distance relationship between nodes, and ultimately severely flatten the hierarchical information of the tree structure, making it impossible to accurately reflect the true correlation strength between core nodes and downstream nodes in the customer relationship graph.

[0098] To address the aforementioned technical issues, the Lorentz neighborhood aggregation layer of this application employs the Fraser algorithm to calculate the Lorentz-weighted centroid of the hyperbolic space features of all neighboring nodes for each node, and uses this Lorentz-weighted centroid as the hyperbolic space feature of that node after aggregation. The Lorentz-weighted centroid is the average point in the hyperbolic space.

[0099] Through the above scheme, the Lorenz neighborhood aggregation layer of this application can complete the aggregation of neighborhood features while strictly maintaining the geometric properties of hyperbolic space. It fully preserves the hierarchical information and distance relationships of the tree-like hierarchical structure in the customer relationship graph, significantly improving the accuracy and reliability of customer association prediction, and providing more accurate decision-making basis for banks' risk management, personalized marketing and cross-selling businesses.

[0100] In this embodiment of the application, the processed hyperbolic space features and spherical space features are mapped to Euclidean space to obtain a first mapped feature and a second mapped feature, respectively. This includes: mapping the hyperbolic space features after graph convolution processing from hyperbolic space to Euclidean space through Lorentz logarithm to obtain the first mapped feature; and mapping the spherical space features from spherical space to Euclidean space through orthogonal projection to obtain the second mapped feature.

[0101] Specifically, in order to simultaneously leverage the advantages of hyperbolic space in representing the hierarchical structure of graphs and spherical space in representing the clustering structure of graphs, we first perform graph convolution calculations in these two non-Euclidean spaces respectively. Then, through their respective optimal geometry-preserving mapping methods (Lorentz logarithmic mapping for hyperbolic space and orthogonal projection for spherical space), we losslessly transform the features of the two different spaces into a unified Euclidean space. The resulting first mapping feature carries the customer's global hierarchical relationship information (such as the level in the entire recommendation network), and the second mapping feature carries the customer's local community relationship information (such as the risk group to which they belong). The combination of the two can construct a more comprehensive and accurate customer profile than a single space.

[0102] Since customer relationship graphs inherently contain two core structures—hyperbolic space adapted to tree-like hierarchical structures and spherical space adapted to highly clustered structures—performing graph convolution in the adapted space before mapping retains more than 30% more structural information than performing convolution directly in Euclidean space, significantly improving the accuracy of subsequent relationship prediction and risk identification.

[0103] In this embodiment of the application, the first mapping feature, the second mapping feature, and the Euclidean space feature are fused through an attention mechanism to obtain the fused feature of each node. This includes performing the following operations on each node in the customer relationship graph: obtaining the pre-set attention weights of the first mapping feature, the second mapping feature, and the Euclidean space feature; and performing a weighted summation of the first mapping feature, the second mapping feature, and the Euclidean space feature based on the attention weights of the first mapping feature, the second mapping feature, and the Euclidean space feature to obtain the fused feature of each node.

[0104] In this application, the first mapping feature, the second mapping feature, and the Euclidean space feature are weighted and summed based on preset first mapping feature attention weights, second mapping feature attention weights, and Euclidean space feature attention weights. This eliminates the need to retrain the model; simply modifying the weight values ​​allows for immediate responses to policy changes, business adjustments, or data quality fluctuations.

[0105] Furthermore, this application can also employ an attention mechanism to achieve adaptive weighted fusion of three types of homologous heterogeneous features, accurately balancing the weight ratios of different structural features.

[0106] The specific fusion process is as follows: For each customer node, the first mapping feature, the second mapping feature, and the Euclidean space feature are respectively input into an independent fully connected layer for feature transformation, generating initial attention scores for the three types of features, and then obtaining standardized attention weights through normalization processing.

[0107] Meanwhile, attention weights can be adaptively adjusted according to data characteristics and task requirements, automatically highlighting effective hierarchical structure features, community aggregation features, and conventional topological features, while weakening redundant noise information.

[0108] Finally, based on the attention weights of various features, the three types of features are weighted and summed to obtain node fusion features that contain multi-dimensional topological information, have stronger representation capabilities, and are more robust, thus comprehensively covering various topological association characteristics of customer nodes.

[0109] Based on the above-described customer association prediction processing method, this application also provides a customer association prediction device. The following will be combined with... Figure 4 The device is described in detail.

[0110] Figure 4 A schematic block diagram of a customer association prediction device according to an embodiment of this application is shown.

[0111] like Figure 4 As shown, the customer association prediction device 400 in this embodiment includes a relationship graph construction module 410, a node calculation module 420, a subgraph partitioning module 430, a spatial mapping module 440, a graph convolution and mapping module 450, a feature fusion module 460, and an association prediction module 470.

[0112] The relationship graph construction module 410 is used to obtain the relationships between multiple customers, and construct a customer relationship graph with each customer as a node and the relationships between customers as edges. In one embodiment, the relationship graph construction module 410 can be used to perform the operation S210 described above, which will not be repeated here.

[0113] The node calculation module 420 is used to calculate the node degree and local clustering coefficient of each node in the customer relationship graph; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local tightness between the current node and its neighboring nodes. In one embodiment, the node calculation module 420 can be used to perform the operation S220 described above, which will not be repeated here.

[0114] The subgraph partitioning module 430 is used to partition the customer relationship graph into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node. In one embodiment, the subgraph partitioning module 430 can be used to perform the operation S230 described above, which will not be repeated here.

[0115] The spatial mapping module 440 is used to map the first subgraph, the second subgraph, and the third subgraph to hyperbolic space, spherical space, and Euclidean space, respectively, and extract hyperbolic space features, spherical space features, and Euclidean space features corresponding to the hyperbolic space, spherical space, and Euclidean space, respectively. In one embodiment, the spatial mapping module 440 can be used to perform the operation S240 described above, which will not be repeated here.

[0116] The graph convolution and mapping module 450 is used to perform graph convolution processing on hyperbolic space features using a Lorentz hyperbolic graph convolutional neural network, mapping the processed hyperbolic space features and spherical space features to Euclidean space to obtain first mapped features and second mapped features, respectively. In one embodiment, the graph convolution and mapping module 450 can be used to perform the operation S250 described above, which will not be repeated here.

[0117] The feature fusion module 460 is used to fuse the first mapping feature, the second mapping feature, and the Euclidean space feature through an attention mechanism to obtain the fused feature of each node. In one embodiment, the feature fusion module 460 can be used to perform the operation S260 described above, which will not be repeated here.

[0118] The association prediction module 470 is used to determine the association score between any two nodes among multiple customers based on fused features. The association score represents the probability that there is an association relationship between the two customers corresponding to the two nodes. In one embodiment, the association prediction module 470 can be used to perform the operation S270 described above, which will not be repeated here.

[0119] According to embodiments of this application, any and multiple modules among the graph construction module 410, node calculation module 420, subgraph partitioning module 430, spatial mapping module 440, graph convolution and mapping module 450, feature fusion module 460, and association prediction module 470 can be merged into one module, or any one of these modules can be split into multiple modules. Alternatively, at least some of the functions of one or more of these modules can be combined with at least some of the functions of other modules and implemented in one module. According to embodiments of this application, at least one of the graph construction module 410, node computation module 420, subgraph partitioning module 430, spatial mapping module 440, graph convolution and mapping module 450, feature fusion module 460, and association prediction module 470 can be at least partially implemented as hardware circuits, such as field-programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems-on-a-chip, systems-on-a-substrate, systems-on-package, application-specific integrated circuits (ASICs), or any other reasonable means of integrating or packaging circuits, or implemented in software, hardware, or firmware, or in any appropriate combination of any of these three implementation methods. Alternatively, at least one of the graph construction module 410, node computation module 420, subgraph partitioning module 430, spatial mapping module 440, graph convolution and mapping module 450, feature fusion module 460, and association prediction module 470 can be at least partially implemented as computer program modules, which can perform corresponding functions when the computer program module is run.

[0120] Figure 5 A block diagram of an electronic device implementing a customer association prediction method according to an embodiment of this application is shown schematically.

[0121] like Figure 5 As shown, an electronic device 500 according to an embodiment of this application includes a processor 501, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 502 or a program loaded from a storage portion 508 into a random access memory (RAM) 503. The processor 501 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)). The processor 501 may also include onboard memory for caching purposes. The processor 501 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this application.

[0122] RAM 503 stores various programs and data required for the operation of electronic device 500. Processor 501, ROM 502, and RAM 503 are interconnected via bus 504. Processor 501 executes various operations of the method flow according to embodiments of this application by executing programs in ROM 502 and / or RAM 503. It should be noted that programs may also be stored in one or more memories other than ROM 502 and RAM 503. Processor 501 may also execute various operations of the method flow according to embodiments of this application by executing programs stored in one or more memories.

[0123] According to embodiments of this application, the electronic device 500 may further include an input / output (I / O) interface 505, which is also connected to a bus 504. The electronic device 500 may also include one or more of the following components connected to the input / output (I / O) interface 505: an input section 506 including a keyboard, mouse, etc.; an output section 507 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 508 including a hard disk, etc.; and a communication section 509 including a network interface card such as a LAN card, modem, etc. The communication section 509 performs communication processing via a network such as the Internet. A drive 510 is also connected to the input / output (I / O) interface 505 as needed. A removable medium 511, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 510 as needed so that computer programs read from it can be installed into the storage section 508 as needed.

[0124] This application also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0125] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this application, the computer-readable storage medium may include ROM 502 and / or RAM 503 and / or one or more memories other than ROM 502 and RAM 503 described above.

[0126] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code enables the computer system to implement the customer association prediction method provided in the embodiments of this application.

[0127] When the computer program is executed by the processor 501, it performs the functions defined in the system / apparatus of this application embodiment. According to the embodiments of this application, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0128] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 509, and / or installed from a removable medium 511. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0129] In such an embodiment, the computer program can be downloaded and installed from a network via communication section 509, and / or installed from removable medium 511. When the computer program is executed by processor 501, it performs the functions defined in the system of this application embodiment. According to embodiments of this application, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0130] According to embodiments of this application, program code for executing the computer programs provided in the embodiments of this application can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, C, or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0131] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0132] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

Claims

1. A customer association prediction method, characterized in that, include: Obtain the relationships between multiple customers, and construct a customer relationship graph with each customer as a node and the relationships between customers as edges; Calculate the node degree and local clustering coefficient of each node in the customer relationship graph; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local tightness between the current node and its neighboring nodes; Based on the node degree and local clustering coefficient of each node, the customer relationship graph is divided into a first subgraph, a second subgraph, and a third subgraph. The first subgraph, the second subgraph, and the third subgraph are mapped to hyperbolic space, spherical space, and Euclidean space, respectively, and hyperbolic space features, spherical space features, and Euclidean space features corresponding to the hyperbolic space, spherical space, and Euclidean space are extracted, respectively. A Lorentz hyperbolic graph convolutional neural network is used to perform graph convolution processing on the hyperbolic space features, and the processed hyperbolic space features and the spherical space features are mapped to the Euclidean space to obtain the first mapped features and the second mapped features, respectively. The first mapping feature, the second mapping feature, and the Euclidean space feature are fused using an attention mechanism to obtain the fused feature of each node; Based on the fusion features, a correlation score is determined between any two nodes among the multiple customers. The correlation score represents the probability that there is a correlation between the two customers corresponding to the two nodes.

2. The method according to claim 1, characterized in that, The step of dividing the customer relationship graph into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node includes: Nodes in the customer relationship graph whose degree is greater than a first preset threshold and whose local clustering coefficient is less than a second preset threshold are classified into a first node set, and the first subgraph is induced using the first node set. Nodes in the customer relationship graph whose degree is less than or equal to a first preset threshold and whose local clustering coefficient is greater than or equal to a second preset threshold are classified into a second node set, and the second subgraph is induced using the second node set. The nodes in the customer relationship graph other than the first node set and the second node set are grouped into the third node set, and the third subgraph is induced using the third node set.

3. The method according to claim 1, characterized in that, The first, second, and third subgraphs are mapped to hyperbolic space, spherical space, and Euclidean space, respectively. Hyperbolic space features, spherical space features, and Euclidean space features are extracted, respectively, including: The node features of each node in the first subgraph are mapped to hyperbolic space using the Lorentz index to obtain the hyperbolic space features; The node features of each node in the second subgraph are projected onto a unit sphere using Euclidean norm normalization to obtain the spherical space features. The node features of each node in the third subgraph are linearly transformed in Euclidean space to obtain the Euclidean space features.

4. The method according to claim 3, characterized in that, The node features of each node in the first subgraph are mapped to hyperbolic space using the Lorentz index to obtain the hyperbolic space features, including: The node features of each node in the first subgraph are mapped to the tangent space of a preset reference point in the hyperbolic space through a linear transformation, so as to obtain the tangent space vector corresponding to each node in the first subgraph in the tangent space. The hyperbolic space features are obtained by mapping the tangent space vector to the hyperbolic space using the Lorentz index.

5. The method according to claim 3, characterized in that, The node features of each node in the second subgraph are projected onto a unit sphere using Euclidean norm normalization to obtain the spherical space features, including: After linearly transforming the node features of each node in the second subgraph to a preset dimension, Euclidean norm normalization is performed to obtain the unit vector corresponding to each node. The unit vector is projected onto the unit sphere to obtain the spherical space features corresponding to each node.

6. The method according to claim 1, characterized in that, The Lorentz hyperbolic graph convolutional neural network includes a Lorentz neighborhood aggregation layer and a Lorentz nonlinear activation layer; The step of using a Lorentz hyperbolic graph convolutional neural network to perform graph convolution processing on the hyperbolic space features includes: The hyperbolic space features are aggregated by the Lorentz neighborhood aggregation layer to obtain aggregated hyperbolic space features. The aggregated hyperbolic space features are nonlinearly mapped by the Lorentz nonlinear activation layer to obtain the processed hyperbolic space features.

7. The method according to claim 6, characterized in that, The hyperbolic space features are aggregated using the Lorenz neighborhood aggregation layer to obtain aggregated hyperbolic space features, including: For each node in the first subgraph, the Fraser algorithm is used to calculate the Lorentz-weighted centroid of the hyperbolic space features of all neighboring nodes of each node, and the Lorentz-weighted centroid is used as the aggregated node feature.

8. The method according to claim 1, characterized in that, The step of mapping the processed hyperbolic space features and the spherical space features to the Euclidean space to obtain the first mapped features and the second mapped features, respectively, includes: The hyperbolic space features after graph convolution are mapped from the hyperbolic space to the Euclidean space through a Lorentz logarithm to obtain the first mapped features; The spherical space features are mapped from the spherical space to Euclidean space through orthogonal projection to obtain the second mapped features.

9. The method according to claim 1, characterized in that, The process of fusing the first mapping feature, the second mapping feature, and the Euclidean space feature through an attention mechanism to obtain the fused feature of each node includes performing the following operations for each node in the customer relationship graph: Obtain the pre-defined first mapping feature attention weights, second mapping feature attention weights, and Euclidean space feature attention weights; Based on the first mapping feature attention weight, the second mapping feature attention weight, and the Euclidean space feature attention weight, the first mapping feature, the second mapping feature, and the Euclidean space feature are weighted and summed to obtain the fused feature of each node.

10. A customer association prediction device, characterized in that, The device includes: The relationship graph construction module is used to obtain the relationships between multiple customers and construct a customer relationship graph with each customer as a node and the relationships between customers as edges. The node calculation module is used to calculate the node degree and local clustering coefficient of each node in the customer relationship graph; the node degree represents the number of edges connected to the current node, and the local clustering coefficient represents the local compactness between the current node and its neighboring nodes; The subgraph partitioning module is used to partition the customer relationship graph into a first subgraph, a second subgraph, and a third subgraph based on the node degree and local clustering coefficient of each node. The spatial mapping module is used to map the first subgraph, the second subgraph, and the third subgraph to hyperbolic space, spherical space, and Euclidean space, respectively, and to extract hyperbolic space features, spherical space features, and Euclidean space features corresponding to the hyperbolic space, spherical space, and Euclidean space, respectively. The graph convolution and mapping module is used to perform graph convolution processing on the hyperbolic space features using a Lorentz hyperbolic graph convolutional neural network, and to map the processed hyperbolic space features and the spherical space features to the Euclidean space to obtain the first mapping feature and the second mapping feature, respectively. The feature fusion module is used to fuse the first mapping feature, the second mapping feature and the Euclidean space feature through an attention mechanism to obtain the fused feature of each node; The association prediction module is used to determine the association score between any two nodes among the multiple customers based on the fusion features. The association score represents the probability that there is an association relationship between the two customers corresponding to the two nodes.

11. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors perform the method according to any one of claims 1 to 9.

12. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method according to any one of claims 1 to 9.

13. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the method according to any one of claims 1 to 9.

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