Artificial intelligence-based graph structure learning method and system, and graph-based data processing method and system using same

Abstract

The present invention relates to an artificial intelligence-based graph structure learning method and system, and a graph-based data processing method and system using same, and provides an artificial intelligence-based graph structure learning method and system, and a graph-based data processing method and system using same, which are capable of more effectively analyzing and learning graph data.

Description

Artificial intelligence-based graph structure learning method and system, and graph-based data processing method and system using the same

[0001] The present invention relates to an artificial intelligence-based graph structure learning method and system, and a graph-based data processing method and system using the same, and provides an artificial intelligence-based graph structure learning method and system capable of more effectively analyzing and learning graph data, and a graph-based data processing method and system using the same.

[0002] Recently, large-scale network graphs have been utilized as fundamental data structures in various application fields, including bioinformatics, drug discovery, social network analysis, recommendation systems, and financial transaction networks. Unlike regular grid structures in Euclidean space, these graph data possess a non-Euclidean structure and are utilized as data structures where the connections or interactions between nodes hold significant meaning. Such graph data plays a crucial role in diverse application areas, such as social network analysis, molecular structure analysis, recommendation systems, financial networks, and knowledge graphs. Accordingly, various graph neural network models have been studied to effectively reflect the characteristics of graph data and perform downstream tasks such as node classification, link prediction, and graph classification. Representative existing graph learning techniques include the Graph Convolutional Network (GCN), Graph Attention Network (GAT), and GraphSAGE.

[0003] These Graph Neural Network (GNN) models are based on a message passing method that aggregates information from adjacent nodes and updates the representation of each node accordingly. Furthermore, these models learn the structural characteristics of the graph by utilizing feature propagation based on similarity or adjacency between nodes.

[0004] However, these graph neural network models have limitations in that they fail to adequately reflect the structural complexity of graphs. For instance, most graph neural network models are trained based on fixed assumptions, such as homophilia (the assumption that interconnected nodes are similar), leading to significant performance degradation in graphs with more complex structures or in other tasks. Furthermore, as the diversity and heterogeneity of graph data increase, it becomes necessary to adaptively adjust the model's representation to match the unique structural characteristics or data distribution of each graph. However, existing graph neural network models rely on fixed aggregation methods and fixed structural biases (inductive bias), making it difficult to provide consistent performance across different types of graphs or tasks. To address this, research has been conducted on various graph neural network models incorporating manual biases specialized for specific tasks; however, this merely replaces one fixed assumption with another and fundamentally limits the generalization capabilities of graph neural network models.

[0005] Accordingly, there is a need for technology that can flexibly capture changes in the structural and node characteristics of graphs, be reliably applied to various graph types and tasks, and adaptively respond to the structural features of data.

[0006] The present invention aims to provide an artificial intelligence-based graph structure learning method and system capable of more effectively analyzing and learning graph data, and a graph-based data processing method and system using the same.

[0007] Furthermore, the present invention aims to provide an artificial intelligence-based graph structure learning method and system capable of flexibly capturing changes in the structural characteristics and node characteristics of a graph, and a graph-based data processing method and system using the same.

[0008] Furthermore, the present invention aims to provide an artificial intelligence-based graph structure learning method and system that can be stably applied to various types of graphs and various application fields, and a graph-based data processing method and system using the same.

[0009] To solve the problem described above, the artificial intelligence-based graph structure learning method according to the present invention, which is performed by a computer, may include the steps of: receiving at least one graph including at least one node and at least one edge; inputting the at least one graph into at least one artificial intelligence model to learn the structural characteristics of the at least one graph; performing a transformation according to a preset standard for each of the at least one node and the at least one edge included in the at least one graph in the at least one artificial intelligence model to learn the structural characteristics of the at least one graph structure; and training the artificial intelligence model to generate a reference structure of the at least one graph using the transformed at least one graph including the transformed at least one node and the transformed at least one edge.

[0010] In an embodiment, the previously set criterion includes at least one of a first criterion for performing a deformation for the at least one node and a second criterion for performing a deformation for the at least one edge, and in the step of performing the deformation, the deformation for the at least one node and the at least one edge can be performed using the first criterion and the second criterion.

[0011] In the embodiment, in the step of performing the deformation, a deformation of the at least one node may be performed according to the first criterion, and a deformation of the at least one edge may be performed according to the second criterion.

[0012] In an embodiment, the first criterion among the plurality of preset criteria is a criterion for performing a modification on the at least one node, and the step of performing the modification may include the step of performing a modification on the at least one node included in the at least one graph according to the first criterion.

[0013] In the embodiment, in the step of performing a deformation for the at least one node, a deformation can be performed in which the characteristic value of each of the at least one node has the same characteristic value according to the first criterion, by stepwise smoothing.

[0014] In an embodiment, the second criterion among the plurality of preset criteria is a criterion related to a preset probability for performing a deformation on the at least one edge, and the step of performing the deformation may include the step of performing a deformation on the at least one edge included in the at least one graph according to the second criterion.

[0015] In the embodiment, in the step of performing a deformation on the at least one edge, a structural deformation on the at least one edge included in the at least one graph can be performed according to the second criterion.

[0016] In the embodiment, in the step of performing a deformation on the at least one edge, according to the second criterion, it is determined whether to remove the at least one edge included in the at least one graph based on the preset probability, and according to the removal decision, at least some of the at least one edge may be removed.

[0017] In an embodiment, structural noise can be imparted to the at least one graph by removing at least a portion of the at least one edge according to the second criterion.

[0018] In an embodiment, in the training step, the artificial intelligence model can be trained to reconstruct the at least one graph having the reference structure using the at least one modified graph including the at least one modified node and the at least one modified edge according to each of the first criterion and the second criterion.

[0019] In the embodiment, in the training step, to reconstruct the at least one graph, at least one node representation for the modified at least one graph is generated, and the artificial intelligence model can be trained to reconstruct at least one of the modified at least one node and the modified at least one edge using the at least one node representation.

[0020] In an embodiment, the artificial intelligence model can be trained to perform reconstruction of at least one of the at least one node that has undergone transformation and at least one edge that has undergone transformation by using at least one graph of the previous transformation step.

[0021] In an embodiment, the artificial intelligence model can be trained to reconstruct the characteristic values ​​of each of the at least one node that has been stepwise smoothed to have the same characteristic value through reconstruction of the at least one node that has undergone the above modification.

[0022] In an embodiment, noise applied to the at least one graph can be removed through reconstruction of the at least one edge on which the deformation has been performed.

[0023] In an embodiment, the artificial intelligence model can be trained to reconstruct the at least one graph having the reference structure using at least one of the reconstructed at least one node and the reconstructed at least one edge.

[0024] A graph-based data processing method according to the present invention, performed by a computer, may include the steps of receiving at least one graph including at least one node and at least one edge, inputting the received at least one graph into a previously trained artificial intelligence model, and generating a processing result for the at least one graph using at least one of the at least one node and at least one edge included in the at least one graph in the artificial intelligence model.

[0025] An artificial intelligence-based graph structure learning system according to the present invention, comprising a memory configured to store executable instructions and one or more processors configured to perform operations by executing one or more instructions, receives at least one graph including at least one node and at least one edge, inputs the at least one graph to at least one artificial intelligence model to learn the structural characteristics of the at least one graph, and in the at least one artificial intelligence model, performs a transformation according to a preset standard for each of the at least one node and the at least one edge included in the at least one graph to learn the structural characteristics of the at least one graph structure, and can train the artificial intelligence model to generate a reference structure of the at least one graph using the transformed at least one graph including the at least one node and the at least one edge that has undergone the transformation.

[0026] A program according to the present invention is a program that is executed by one or more processes in an electronic device and can be stored on a computer-readable recording medium, and may include instructions for performing the steps of: receiving at least one graph including at least one node and at least one edge; inputting at least one graph into at least one artificial intelligence model to learn the structural characteristics of at least one graph; performing a transformation according to a preset standard for each of the at least one node and at least one edge included in the at least one graph in the at least one artificial intelligence model to learn the structural characteristics of the at least one graph structure; and training the artificial intelligence model to generate a reference structure of at least one graph using the transformed at least one graph including the at least one node and at least one edge that has undergone the transformation.

[0027] As described above, the artificial intelligence-based graph structure learning method and system according to the present invention, and the graph-based data processing method and system using the same, can learn the standard structure of a graph by deforming the nodes and edges constituting the graph according to certain criteria to apply noise, and by using the noise-applied graph. Through this, it is possible to learn a representation that more clearly reflects the structural characteristics of the graph and the relationships between nodes, stably reconstruct a meaningful structure even in graphs containing incomplete information or structural variations, and apply it to various environments without being dependent on a specific domain.

[0028] Furthermore, the AI-based graph structure learning method and system according to the present invention is configured to simultaneously restore node characteristic information and structural change information of the graph during the diffusion process, thereby enabling the learning of patterns meaningful for actual task performance within the graph. Accordingly, rather than simple structure restoration, it is possible to generate task-appropriate structural representations, which can demonstrate consistent performance in graph-based data processing tasks with different purposes, such as link prediction, node classification, and anomaly detection. In particular, it can address incompleteness that frequently occurs in real-world environments, such as the loss of some node information or uncertain measurement of some edges, thereby increasing applicability in actual service environments. Through this, the present invention can be reliably utilized in various industrial and real-world network environments where variations in graph data quality, measurement errors in sensor-based graphs, and arbitrary dynamic deformations exist.

[0029] Furthermore, the artificial intelligence-based graph structure learning method and system according to the present invention utilizes graph Laplacian-based low-pass filtering to prevent rapid loss of high-frequency components during the noise injection process and to preserve global structural information of the graph. Through this, the problem of indiscriminate signal destruction inherent in existing diffusion models is resolved, and learning can be performed while effectively maintaining the intrinsic topological characteristics and latent structural factors of the graph data.

[0030] Furthermore, the artificial intelligence-based graph structure learning method and system according to the present invention does not require manual design of the structure, thereby providing excellent universality and business efficiency without changing the model structure in various benchmark environments. Through this, the same model can be applied to various application services in actual industrial environments that differ in data conditions, graph structures, and business objectives, thereby simultaneously achieving operational benefits such as reduced maintenance costs, ease of system integration, and improved scalability.

[0031] FIG. 1 illustrates an example of a block diagram of a computing system in which the present invention can be implemented.

[0032] FIG. 2 illustrates an example of a block diagram of a computing device that may be included in a user computing device, a server computing system, and a training computing system, as an embodiment of a computing system in which the present invention can be implemented.

[0033] Figure 3 illustrates an example of a block diagram from another perspective of a computing device, which is one of the components of a computing system.

[0034] FIG. 4 is a conceptual diagram illustrating an artificial intelligence-based graph structure learning system according to the present invention.

[0035] FIG. 5 is a flowchart illustrating an artificial intelligence-based graph structure learning method according to the present invention.

[0036] FIG. 6 is a conceptual diagram illustrating an artificial intelligence-based graph structure learning method according to the present invention.

[0037] FIG. 7 is a conceptual diagram illustrating the graph noise application process according to the present invention.

[0038] FIG. 8 is a conceptual diagram illustrating the graph restoration process and the learning process according to the present invention.

[0039] FIGS. 9 and FIGS. 10 are formulas related to an artificial intelligence-based graph structure learning method according to the present invention.

[0040] FIGS. 11, FIGS. 12 and FIGS. 13 are drawings illustrating an embodiment according to the present invention.

[0041] FIG. 14 is a flowchart illustrating a graph-based data processing method according to the present invention.

[0042] Hereinafter, embodiments disclosed in this specification will be described in detail with reference to the attached drawings. Identical or similar components are assigned the same reference number regardless of the drawing symbols, and redundant descriptions thereof will be omitted. The suffixes "module" and "part" used for components in the following description are assigned or used interchangeably solely for the ease of drafting the specification and do not have distinct meanings or roles in themselves. Furthermore, in describing the embodiments disclosed in this specification, if it is determined that a detailed description of related prior art could obscure the essence of the embodiments disclosed in this specification, such detailed description will be omitted. Additionally, the attached drawings are intended only to facilitate understanding of the embodiments disclosed in this specification; the technical concept disclosed in this specification is not limited by the attached drawings, and it should be understood that they include all modifications, equivalents, and substitutions that fall within the spirit and technical scope of the present invention.

[0043] Terms including ordinal numbers, such as first, second, etc., may be used to describe various components, but said components are not limited by said terms. These terms are used solely for the purpose of distinguishing one component from another.

[0044] When it is stated that one component is "connected" or "connected" to another component, it should be understood that while it may be directly connected or connected to that other component, there may also be other components in between. On the other hand, when it is stated that one component is "directly connected" or "directly connected" to another component, it should be understood that there are no other components in between.

[0045] A singular expression includes a plural expression unless the context clearly indicates otherwise.

[0046] In this application, terms such as “comprising” or “having” are intended to specify the existence of the features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0047] Hereinafter, the present invention will be examined in more detail with reference to the attached drawings. FIG. 1 illustrates an example of a block diagram of a computing system in which the present invention can be implemented. FIG. 2 illustrates an example of a block diagram of a computing device that may be included in a user computing device, a server computing system, and a training computing system as an embodiment of a computing system in which the present invention can be implemented. FIG. 3 illustrates an example of a block diagram of a computing device from another perspective, which is one of the components of a computing system. FIG. 4 is a conceptual diagram for explaining an artificial intelligence-based graph structure learning system according to the present invention.

[0048] Meanwhile, FIG. 1 illustrates an example of a block diagram of a computing system in which the present invention can be implemented. In this regard, the artificial intelligence-based graph structure learning system according to the present invention can be implemented through a computing device described below and can perform data processing related to the artificial intelligence-based graph structure learning method.

[0049] Referring to FIG. 1, a computing system (10000) for performing the artificial intelligence-based graph structure learning method of the present invention may include at least one computing device. At this time, the at least one computing device may be a single processor or a multi-processor computing device.

[0050] The components of at least one computing device of the present invention may include various hardware components such as one or more processors, memory, other hardware, and a system bus (not shown) that connects various system components so that they can transmit and receive data to and from each other (e.g., telecommutatively connected, physically connected, electrically connected), and the components of at least one computing device are not limited thereto and may be very diverse.

[0051] Meanwhile, at least one computing device included in a computing system (10000) that performs an artificial intelligence-based graph structure learning method may be connected to communicate via a network (1070). For example, at least one computing device included in the computing system (10000) may be clustered or may be part of a local area network (LAN). Additionally, at least one computing device may be part of a wide area network (WAN) or connected to at least one of a client-server network and a peer-to-peer network within the cloud.

[0052] Meanwhile, when at least one computing device is used in at least one of a network environment and a cloud computing environment, the at least one computing device may be connected to at least one of a public and private network through a network interface or adapter. In one embodiment, other communication connection devices, such as a modem, may be used to establish communication through the network. The modem may be at least one of an internal modem and an external modem, and may be connected to a system bus through a network interface or a specific mechanism, etc. A wireless network component consisting of an interface and an antenna may be coupled to the network through a device such as an access point, a peer computer, etc. In the present invention, the method of connecting at least one computing device to communicate through the network (1070) is not limited, and it may be connected to communicate in a manner different from the described example.

[0053] Furthermore, other computer-type devices and / or systems not shown in FIG. 1 may also interact technically with at least one computing device or other system through one or more connections to the network (1070) via a network interface. Here, the network interface may include network interface equipment such as a physical network interface controller (NIC) or a virtual network interface (VIF).

[0054] The network (1070) of the present invention may include various forms such as the Internet, WLAN (Wireless LAN), Wi-Fi (Wireless-Fidelity), Wi-Fi (Wireless Fidelity) Direct, DLNA (Digital Living Network Alliance), WiBro (Wireless Broadband), WiMAX (World Interoperability for Microwave Access), HSDPA (High Speed ​​Downlink Packet Access), HSUPA (High Speed ​​Uplink Packet Access), LTE (Long Term Evolution), LTE-A (Long Term Evolution-Advanced), 5G (5th Generation Mobile Telecommunication), Bluetooth (Bluetooth™ RFID (Radio Frequency Identification), Infrared Data Association (IrDA), UWB (Ultra-Wideband), ZigBee, NFC (Near Field Communication), Wi-Fi Direct, Wireless USB (Wireless Universal Serial Bus), etc., and in the present invention, data transmission may be performed based on standard communication protocols such as TCP / IP, HTTP, SSL, etc.

[0055] A computing system (10000) that performs an artificial intelligence-based graph structure learning method according to the present invention may include at least one of a user computing device (1010), a training computing system (1050), and a server computing system (1030).

[0056] A user computing device (1010) according to the present invention may be understood as a computing device comprising at least one processor (1011) and a memory (1012) for performing an artificial intelligence-based graph structure learning method. For example, the user computing device (1010) may include at least one computing device among a smartphone, a smart TV, a laptop computer, a desktop computer, a digital broadcasting terminal, a PDA (personal digital assistants), a PMP (portable multimedia player), a navigation device, a slate PC, a tablet PC, an ultrabook, a wearable device (e.g., a smartwatch, a smart glass, and a head-mounted display).

[0057] At least one processor (1011) constituting the user computing device (1010) may include one or more general-purpose processors and / or one or more special-purpose processors. For example, at least one processor (1011) constituting the user computing device (1010) may be composed of at least one of a central processing unit (CPU), a graphics processing unit (GPU), a tensor processing unit (TPU), a neural network processing unit (NPU), an arithmetic logic unit (ALU), a floating-point arithmetic unit (FPU), an application integrated circuit, an application semiconductor (ASIC), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, and / or electrical units for performing other functions, or a plurality of electrically connected processors.

[0058] Furthermore, at least one processor (1011) may be configured to execute computer-readable instructions contained in memory (1012) and / or other instructions described herein.

[0059] The memory (1012) constituting the user computing system (1010) according to the present invention may include volatile memory, non-volatile memory, fixed media, removable media, magnetic media, optical media, semiconductor media and / or other types of physically durable storage media.

[0060] For example, the memory (1012) may include one or more non-transient / transient computer-readable storage media such as RAM, ROM, HDD (Hard Disk Drive), SSD (Solid State Disk), SSD (Silicon Disk Drive), EEPROM, EPROM, flash memory device, magnetic disk, and combinations thereof, and may include web storage of a server that performs the storage function of memory over the internet. This memory (1012) may store data and instructions necessary for the at least one processor (1011) to perform the operation of an application for learning an artificial intelligence-based graph structure.

[0061] A user computing device (1010) may include one or more user input components (1021) that detect user input. For example, the user input component (1021) may also be referred to as a user interface module. The user input component (1021) may include a touch screen, a computer mouse, a keyboard, a keypad, a touchpad, a trackball, a joystick, a voice recognition module, or other similar devices. However, the present invention does not limit the type of user input component (1021). In this case, the user input component (1021) in the present invention does not necessarily mean a hardware means, but can be understood as a channel for receiving input from a user. Meanwhile, the user of the present invention may refer to an automated agent, script, playback software, etc., that operates on behalf of one or more people.

[0062] A user can interact with a computing system (10000) including at least one computing device through input text, touch, voice, movement, computer vision, gestures and / or other forms of input / output using a user input component (1021). For example, the user input component (1021) may include one or more of a command line interface (CLI), a graphical user interface (GUI), a natural user interface (NUI), a voice command interface and / or other user interface (UI) representations.

[0063] Between the user input component (1021) and the user computing device (1010), one or more application programming interface (API) calls may be made based on user input received from the user interface and / or network.

[0064] Here, the expression "based on" may be interpreted to include cases where it is based on the use of a specific configuration, modified from, derived from, influenced by, dependent on, or otherwise derived from a specific configuration. In some embodiments, an API call may be configured for a specific API, which may be interpreted or converted into an API call configured for another API. Here, an API may refer to a defined interface or connection between computers or between computer programs.

[0065] In one embodiment, the user computing device (1010) may store at least one machine learning model (1020). For example, the user computing device (1010) may be various machine learning models, such as a plurality of neural networks (e.g., deep neural networks) that perform artificial intelligence-based graph structure learning by reflecting user input and preferences, or other types of machine learning models including non-linear models and / or linear models, and may be composed of a combination thereof.

[0066] According to an embodiment of the present invention, a user computing device (1010) may perform an artificial intelligence-based graph structure learning method using a local or / and external machine learning model (1020). Alternatively, the user computing device (1010) may perform at least one artificial intelligence-based graph structure learning method using a machine learning model (1040) provided by a server.

[0067] In addition, according to another embodiment of the present invention, a server computing system (1030) communicating with a user computing device (1010) can provide processing results related to an artificial intelligence-based graph to the user computing device (1010) on an application or / and the web in accordance with a user's request received through the user computing device (1010).

[0068] In addition, according to another embodiment of the present invention, at least a part of the user computing device (1010) and the server computing system (1030) are interconnected to perform an artificial intelligence-based graph structure learning method, thereby providing the user with processing results related to the graph.

[0069] Additionally, according to various embodiments of the present invention, a user computing device (1010) and / or a server computing system (1030) can learn machine learning models (1020, 1040) performed in an artificial intelligence-based graph structure learning method through interaction with a training computing system (1050) that is communicatedly connected via a network (1070). In this case, the training computing system (1050) may be a computing system separate from the server computing system (1030). Alternatively, in some embodiments, the training computing system (1050) may be part of the server computing system (1030) or part of the user computing device (1010).

[0070] Meanwhile, the server computing system (1030) may include at least one processor (1031) and memory (1032). Here, the processor (1031) may be composed of at least one or a plurality of electrically connected processors among a central processing unit (CPU), a graphics processing unit (GPU), a tensor processing unit (TPU), a neural network processing unit (NPU), an application integrated circuit, an application semiconductor (ASIC), an arithmetic logic unit (ALU), a floating-point arithmetic unit (FPU), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, and / or other electrical units for performing functions. For example, at least one processor (1031) may include a circuit and a transistor configured to execute instructions from memory (1032).

[0071] The memory (1032) constituting the server computing system (1030) according to the present invention may include volatile memory, non-volatile memory, fixed media, removable media, magnetic media, optical media, semiconductor media, and / or other types of physically durable storage media. For example, the memory (1032) may include one or more non-transient / transient computer-readable storage media such as RAM, ROM, HDD (Hard Disk Drive), SSD (Solid State Disk), SSD (Silicon Disk Drive), EEPROM, EPROM, flash memory device, magnetic disk, etc., and combinations thereof, and may include web storage of a server that performs the storage function of memory over the internet. Additionally, the server computing system (1030) may further include a data storage (data store). For example, the data storage may be composed of at least one of a relational database, a NoSQL database, a data warehouse, and a local file system.

[0072] In the memory (1032) constituting the server computing system (1030) according to the present invention, data and instructions necessary for the at least one processor (1031) to perform the operation of an application for artificial intelligence-based graph structure learning may be stored.

[0073] In one embodiment, the server computing system (1030) may be composed of a single device or a plurality of computing devices, and these may be configured to operate according to a sequential or parallel computing architecture. Additionally, a distributed processing system may be configured with a plurality of networked devices.

[0074] Meanwhile, the training computing system (1050) may include at least one processor (1051) and memory (1052). The model trainer (1060) is a logical component that executes the training of at least one machine learning model (1020, 1040) and may be implemented in the form of hardware, firmware, or software. For example, the model trainer (1060) may be executed by the processor (1051) after loading training data (1061) stored in a storage device into memory (1052). For example, the model trainer (1060) may be configured to execute one or more operations (e.g., model training, model reconstruction, model validation, model testing) on ​​at least one machine learning model.

[0075] The machine learning model of the present invention may include at least one of a statistical model, an algorithm, a neural network (NN), a convolutional neural network (CNN), a generative neural network (GNN), a Word2Vec model, a Bag of Words model, a TF-IDF (document frequency-inverse document frequency) model, a GPT (Generative Pre-trained Transformer) model (or other autoregressive models), a PPO (Proximal Policy Optimization) model, a nearest neighbor model (e.g., a k-nearest neighbor model), a linear regression model, a K-means clustering model, a Q-learning model, a TD (Temporal Difference) model, a Deep Adversarial Network model, and all other types of models further described herein.

[0076] Specifically, the model trainer (1060) may execute operations to train a machine learning model, and said operations may include at least one of adding, removing, and modifying model parameters. At this time, the training of the machine learning model may be at least one of supervised learning, semi-supervised learning, and unsupervised learning. In one embodiment, the training of the machine learning model may include the step of repeatedly inputting training data (1061) based on epochs and repeatedly performing the machine learning model training process configured in this way. Here, an epoch may refer to a unit in which the entire set of training data (1061) undergoes forward and backpropagation processing once. In some implementations, different levels of training methods (e.g., supervised learning, semi-supervised learning, unsupervised learning) may be used for different epochs.

[0077] The training data (1061) of the present invention may include input data and / or data previously output from at least one machine learning model (e.g., recursive learning feedback).

[0078] At least one parameter of a machine learning model may include at least one of a seed value, a model node, a model layer, an algorithm, a function, connections between different machine learning models, connections between parameters, machine learning model constraints, and other digital components that influence the output of the machine learning model. In this case, model connections between different machine learning models may include or represent relationships between model parameters and / or models, which may be dependent or interdependent, hierarchical, and / or static or dynamic. The combinations and configurations of model parameters described herein may be too complex to be maintained or utilized by human cognitive abilities.

[0079] In the present invention, the machine learning parameters described according to the embodiments are not limited, and a single machine learning model may further include a plurality of model parameters.

[0080] Meanwhile, FIG. 2 illustrates an example of a block diagram of a computing device (1100) that may be included in a user computing device (1010), a server computing system (1030), and a training computing system (1050), as an embodiment of a computing system (10000) in which the present invention can be implemented.

[0081] As illustrated in FIG. 2, the computing device (1100) may include at least one application (e.g., Application 1 to Application N), and each of the at least one application may include a machine learning library and a model execution environment for performing a machine learning-based artificial intelligence-based graph structure learning method. The at least one application included in the computing device (1100) may communicate with the sensor, context manager, device state manager, or additional component(s) within the computing device (1100) via an Application Programming Interface (API). In one embodiment, the at least one application may interface with device components, such as receiving sensor data or state data or transmitting prediction results to an output device via a public or private API.

[0082] Meanwhile, FIG. 3 illustrates an example of a block diagram in another aspect of a computing device (1200), which is one of the components of a computing system (10000) that performs an artificial intelligence-based graph structure learning method according to an embodiment of the present invention.

[0083] A computing device (1200) according to the present invention may include at least one application (e.g., Application 1 to Application N), and at least one application may communicate with a central intelligence layer (1210). Each application may interact with a shared model within the central intelligence layer (1210) through an API (e.g., a common API).

[0084] The central intelligence layer (1210) includes one or more machine learning models and may share them among multiple applications or provide them independently to each. In one embodiment, the central intelligence layer (1210) may be integrated as part of an operating system or implemented as a separate logical layer.

[0085] Additionally, the central intelligence layer (1210) can communicate with the central device data layer (1220). The central device data layer (1220) can integrate and store data related to artificial intelligence-based graph structure learning stored within the computing device (1200) and provide this as input data necessary for training at least one target model. Each device component (e.g., sensor, state manager, etc.) can communicate with the central device data layer (1220) via a private API, etc.

[0086] The technology described in this specification may be composed of a single or multiple computing devices, and a machine learning model performing an artificial intelligence-based graph structure learning method may be executed sequentially or in parallel on one component or multiple distributed components. Data storage, machine learning models, and applications may be distributed and operated locally or over a network, and these configurations can be flexibly applied to various system architectures.

[0087] Meanwhile, the present invention relates to an artificial intelligence-based graph structure learning method and system, and a graph-based data processing method and system using the same. The artificial intelligence-based graph structure learning system according to the present invention may be a system in which at least one artificial intelligence model learns the structural characteristics of at least one graph.

[0088] Here, the graph according to the present invention is a data structure represented by a set of nodes and edges, and may include a network-type data representation for indicating mutual association, interaction, or connectivity. For example, the graph may be a structure for representing various forms of relational data, such as a social network, a molecular structure, a financial transaction network, a knowledge graph, or a user-item relationship graph within a recommendation system.

[0089] Here, a node according to the present invention is a component for representing a specific unit of information within a graph, and may be an element representing various types of objects, such as a person, user account, product, document, atom within a molecule, system state, event, or location information. Additionally, a node may include one or more pieces of information. For example, when a person is represented as a node, personal information such as name, age, occupation, and areas of interest may be included; when a product is represented as a node, price, category, and characteristic value may be included; and when a document or concept is represented as a node, information indicating the characteristics of the object, such as title, keywords, and embedding vectors, may be included.

[0090] In addition, an edge according to the present invention is a component for representing the relationship, connectivity, or interaction between nodes in a graph, and may be an element that expresses the degree of association between nodes or represents various forms of interaction occurring between nodes.

[0091] For example, in social networks, edges can represent friend or follow relationships between users; in molecular structures, edges can represent bonding relationships between atoms; and in financial networks, they can represent transaction information between accounts. In recommendation systems, interactions, clicks, and purchase history between a user and an item can be represented as edges.

[0092] In addition, the artificial intelligence-based graph structure learning system according to the present invention can learn the structural features of a graph by applying noise to at least one graph and performing a process of removing the noise.

[0093] Here, noise according to the present invention may refer to a deformation intentionally applied to a node or edge constituting a graph.

[0094] In addition, at least one artificial intelligence model mentioned in the present invention may include various models that can be utilized depending on various situations or purposes. For example, the artificial intelligence model of the present invention may include at least one of a machine learning (ML) model, a deep learning model, a deep neural network (DNN), a language model (LM), a large language model (LLM), a super-large foundation model, a generative artificial intelligence (Generative AI) model, a transformer-based model, a supervised learning (SL) model, a reinforcement learning (RL) model, a special purpose model (e.g., a time series forecasting model (e.g., ARIMA model, SARIMA model, etc.), a time series foundation model, a graph neural network (GNN), a multimodal model, a natural language processing (NLP) model, a computer vision model, a speech recognition / synthesis model, a recommendation system model, etc.).

[0095] In addition, the artificial intelligence-based graph structure learning method and system according to the present invention may also be referred to as a “graph structure learning system.”

[0096] Meanwhile, as illustrated in FIG. 4, the graph structure learning system (100) according to the present invention may be a system that trains an artificial intelligence model to generate a reference structure of a graph by applying noise to nodes and edges included in an input graph and removing the applied noise (10).

[0097] A graph structure learning system (100) according to the present invention may include at least one of an input unit (110), an output unit (120), a communication unit (130), a storage unit (140), an artificial intelligence model (150), a smoothing unit (160), an edge removal unit (161), a graph encoding unit (180), a feature decoder (181), a structure decoder (182), and a control unit (190). However, the components of the graph structure learning system (100) according to the present invention are not limited thereto and may further include various hardware components that perform the same or similar roles as the functions described in the present specification.

[0098] Although not illustrated, the graph structure learning system (100) according to the present invention may include one or more processors, and such processors may include one or more general-purpose processors and / or one or more special-purpose processors (e.g., digital signal processor, tensor processing unit (TPU), graphics processing unit (GPU), neural network processing unit (NPU), application integrated circuit, application semiconductor (ASIC), field programmable gate array (FPGA), quantum processing unit (or quantum processor, QPU), etc.). One or more processors may be configured to execute instructions, computer-readable instructions, and / or other instructions described herein that are stored (or included) in the storage unit (140). The data generation system and the control method thereof according to the present invention may perform data processing described below in cooperation with memory and at least one processor. The processor may perform a series of operations and data processing using data and information stored in memory. In this case, memory may be a component of the storage unit (140).

[0099] Meanwhile, the input unit (110) can be configured in various ways as a means of data input. For example, the input unit (110) can be configured to receive user input. The input unit (110) can be configured to receive user input from a user terminal (10). Here, “receiving input” may mean receiving an input signal (or selection signal) corresponding to the user’s input based on input made by the user through the input unit configuration provided in the user terminal (10).

[0100] Here, the user terminal may include at least one of a mobile phone, a smartphone, a notebook computer, a laptop computer, a slate PC, a tablet PC, an ultrabook, a desktop computer, a digital broadcasting terminal, a PDA (personal digital assistants), a PMP (portable multimedia player), a navigation device, and a wearable device (e.g., a smartwatch, a smart glass, a head-mounted display).

[0101] In addition, the input unit (110) in the present invention does not necessarily mean a hardware means, but can be understood as a channel for receiving input from a user.

[0102] The input unit (110) may also be referred to as a user interface module. The input unit (110) may include a touch screen, a computer mouse, a keyboard, a keypad, a touchpad, a trackball, a joystick, a voice recognition module, or other similar devices. However, the present invention does not limit the type of input unit (110).

[0103] Here, user input may include documents, text, images (or videos), voice, etc. In this case, the graph structure learning system (100) may further include a module that converts voice into text.

[0104] Next, the output unit (120) can output information through an output unit configuration (e.g., a display unit, a touch screen, a speaker, etc.) provided in a user terminal linked to the graph structure learning system (100) according to the present invention. For example, the output unit (120) can output at least one page linked to the graph structure learning system (100) according to the present invention to the display unit of the user terminal. In addition, the output unit (120) does not necessarily mean a hardware means, but can be understood as a channel for outputting results to a user.

[0105] Next, the communication unit (130) may be connected via a wireless or wired network to a user terminal, a server (e.g., a central server, an external server, etc.), a device, and at least one network, etc., to receive or transmit overall data and information necessary for the operation of the graph structure learning system (100) according to the present invention.

[0106] The communication unit (130) can support various communication methods depending on the communication standard of the communicating device.

[0107] For example, the communication unit (130) may be configured to communicate with a communication target using at least one of the following technologies: WLAN (Wireless LAN), Wi-Fi (Wireless-Fidelity), Wi-Fi (Wireless Fidelity) Direct, DLNA (Digital Living Network Alliance), WiBro (Wireless Broadband), WiMAX (World Interoperability for Microwave Access), HSDPA (High Speed ​​Downlink Packet Access), HSUPA (High Speed ​​Uplink Packet Access), LTE (Long Term Evolution), LTE-A (Long Term Evolution-Advanced), 5G (5th Generation Mobile Telecommunication), Bluetooth (Bluetooth™ RFID (Radio Frequency Identification), Infrared Communication (Infrared Data Association; IrDA), UWB (Ultra-Wideband), ZigBee, NFC (Near Field Communication), Wi-Fi Direct, and Wireless USB (Wireless Universal Serial Bus).

[0108] Next, the storage unit (140, or memory) serves to store various data related to the present invention and may include one or more non-transient computer-readable storage media that can be read and / or accessed by at least one of one or more processors.

[0109] One or more computer-readable storage media may include volatile and / or non-volatile storage components, such as optical, magnetic, organic, or other memory or disk storage devices. In some examples, the storage unit (140) may be implemented using a single physical device (e.g., one optical, magnetic, organic, or other memory or disk storage device), whereas in other examples, the storage unit (140) may be implemented using two or more physical devices.

[0110] The storage unit (140) may include computer-readable instructions and additional data. The storage unit (140) may include a storage necessary to perform at least some of the methods, scenarios, and techniques described herein and / or at least some of the functions of the device and network.

[0111] Furthermore, at least a portion of the storage unit (140) may be a cloud storage or a cloud server. At least a portion of the data corresponding to user input received from the input unit (110) and the training data may be stored in the storage unit (140).

[0112] Additionally, the storage unit (140) may store at least one data collected (or received) from various sources (e.g., a web corpus, a document corpus, a database (DB) website, an API, a server linked to the data generation system (100), a central server, an external server, cloud storage, a user terminal (10), a large dataset, etc.). For example, the storage unit (140) may store at least one document collected from at least one of the various sources (e.g., at least one and / or at least one or more documents (i.e., multiple documents) collected from a user terminal). In this case, the collected documents may include at least one and / or at least one document related to learning (or fields).

[0113] That is, the storage unit (140) is sufficient as a space where information necessary for the operation of the graph structure learning system (100) according to the present invention is stored, and it can be understood that there are no restrictions on the physical space.

[0114] Furthermore, the storage unit (140) can store a computer program including computer program instructions. Furthermore, the storage unit (140) can store a computer program including computer program instructions that control the operation of the graph structure learning system (100) or control the operation of the control unit (190) when loaded into the processor of the graph structure learning system (100).

[0115] Furthermore, the artificial intelligence model (150) can learn the structural characteristics of a graph by applying noise to at least one graph and restoring at least one graph with noise applied.

[0116] Furthermore, the smoothing unit (160) can perform smoothing processing that reflects the relationship structure between at least one node by performing stepwise transformation on the characteristic value of at least one node included in the graph according to a pre-set criterion. The smoothing unit (160) can perform a transformation that causes the characteristic value of a node to gradually become similar to the characteristics of a neighboring node, or a feature diffusion process that reflects the structural characteristics of the graph.

[0117] Furthermore, the edge removal unit (161) can perform structural modifications to maintain or remove edges according to a predefined probability or rule for at least one edge included in at least one graph.

[0118] The graph encoding unit (180) can restore at least one graph with noise based on the node and edge information of at least one graph with noise and generate a node representation for learning the structural characteristics of the graph.

[0119] The feature decoder (181) can restore the modified feature value of a node or reconstruct node feature information for constructing a reference structure based on the node representation provided from the graph encoding unit (180).

[0120] The structure decoder (182) can restore whether edges exist, connection relationships, or structural patterns of the graph based on the node representation provided from the graph encoding unit (180).

[0121] The smoothing unit (160), edge removal unit (161), graph encoding unit (180), feature decoder (181), and structure decoder (182) described in this specification may be implemented in a form integrated within the artificial intelligence model (150), or may be implemented as separate functional components separated from the artificial intelligence model (150). Furthermore, even if it is stated that the components perform a specific processing, this can be understood as the operation being performed by the artificial intelligence model (150). Therefore, each component described separately in this specification is merely a functional classification for convenience of explanation, and in actual implementation, it may be realized according to various implementation methods, such as the form in which the artificial intelligence model or various components operate.

[0122] Next, the control unit (190) can perform the role of controlling the overall operation of the graph structure learning system (100) related to the present invention. The control unit (180) can process signals, data, information, etc. that are input or output through the components of the graph structure learning system (100) described above, or perform a series of data processing to provide or process appropriate information and functions to the user. The control unit (180) can be physically implemented by the processor described above.

[0123] In the foregoing, a graph structure learning system (100) according to the present invention has been described, and it can operate to implement the graph structure learning method described below. FIG. 5 is a flowchart for explaining an artificial intelligence-based graph structure learning method according to the present invention. FIG. 6 is a conceptual diagram for explaining an artificial intelligence-based graph structure learning method according to the present invention. FIG. 7 is a conceptual diagram for explaining a graph noise assignment process according to the present invention. FIG. 8 is a conceptual diagram for explaining a graph restoration process and a learning process according to the present invention. FIG. 9 and FIG. 10 are formulas related to an artificial intelligence-based graph structure learning method according to the present invention. FIG. 11, FIG. 12, and FIG. 13 are drawings illustrating an embodiment according to the present invention. FIG. 14 is a flowchart for explaining a graph-based data processing method according to the present invention.

[0124] Meanwhile, in the present invention, a process of receiving at least one graph including at least one node and at least one edge may be performed (S510, see FIG. 5).

[0125] The control unit (190) can receive a graph. At this time, referring to FIGS. 6 and FIGS. 7, the received graph (710) may be a graph including nodes and edges.

[0126] Here, a graph including nodes and edges may mean a data structure comprising at least one (or multiple) nodes constituting the graph and at least one (or multiple) edges representing the connection relationships between each node.

[0127] Additionally, receiving a graph may mean the process of receiving a graph from at least one of an external system, a storage device, and a network, and the received graph may include cases where a single graph or multiple graphs are received.

[0128] In addition, a node according to the present invention is a component for representing a specific unit of information within a graph, and may be an element representing various types of objects, such as a person, user account, product, document, atom within a molecule, system state, event, location information, etc.

[0129] A node may contain one or more pieces of information. For example, if a person is represented as a node, personal information such as name, age, occupation, and interests may be included; if a product is represented as a node, price, category, and attribute values ​​may be included; and if a document or concept is represented as a node, information indicating the characteristics of the object, such as title, keywords, and embedding vectors, may be included.

[0130] In addition, an edge according to the present invention is a component for representing the relationship, connectivity, or interaction between nodes in a graph, and may be an element that expresses the degree of association between nodes or represents various forms of interaction occurring between nodes.

[0131] Meanwhile, in the present invention, a process of inputting at least one graph into at least one artificial intelligence model to learn the structural features of at least one graph may be performed (S520, see FIG. 5).

[0132] The control unit (190) can train an artificial intelligence model (150) to learn the structural features of a graph (710) using a graph (710) that includes at least one of the received nodes and edges.

[0133] Here, structural features may refer to features that represent the unique shape and relationships of the graph, such as the connection relationships between nodes included in the graph (710), the presence and weight of edges, the pattern of adjacency relationships of nodes, the topological shape of the entire graph, the hierarchical structure or the correlation structure.

[0134] In addition, learning the structural features of the graph (710) may mean that the artificial intelligence model (150) learns graph-specific structural information such as the connection relationships between nodes constituting the graph, the existence and connection patterns of edges, the neighborhood structure around the nodes, and the morphological and relational patterns of the entire graph so that it can internally express them.

[0135] The control unit (190) can input the received graph (710) into the artificial intelligence model (150) in order to train the artificial intelligence model (150) to learn the structural features of the graph (710).

[0136] Here, processing the received graph (170) as input to the artificial intelligence model (150) may mean converting data constituting the graph, such as node information, edge information, or node characteristic values ​​included in the graph, into a data form that the artificial intelligence model (150) can process and providing it to the learning process of the artificial intelligence model (150).

[0137] The artificial intelligence model (150) can learn the structural features of the graph using the input graph (710).

[0138] Meanwhile, in the present invention, a process may be performed to learn structural characteristics of at least one graph structure in at least one artificial intelligence model by performing a transformation according to a preset standard for each of at least one node and at least one edge included in at least one graph (S530, see FIG. 5).

[0139] The control unit (190) can use the artificial intelligence model (150) to perform a transformation according to a preset standard for each node and edge included in the graph so that the artificial intelligence model (150) learns structural features of the graph structure.

[0140] The artificial intelligence model (150) can perform transformations according to a pre-set standard for each node and edge included in the graph in order to learn the structural features of the input graph (710).

[0141] More specifically, the artificial intelligence model (150) can perform a transformation according to a preset standard for each node and edge included in the graph (710) using a smoothing unit (160) and an edge removal unit (161).

[0142] The artificial intelligence model (150) can input the received graph (710) into the smoothing unit (160) and the edge removal unit (161) to perform a transformation according to a preset standard for each node and edge included in the graph.

[0143] For convenience of explanation in this specification, the smoothing unit (160) and the edge removal unit (161) are described as each independently performing deformation of the graph (710); however, in actual implementation, the two components may be configured in a linked or integrated form so that node deformation and edge deformation can be performed in a processing flow that is substantially combined simultaneously or sequentially.

[0144] First, the smoothing unit (160) can perform a transformation (i.e., a feature diffusion process) on the nodes included in the input graph (710) according to the first criterion among the pre-set criteria.

[0145] Here, the first criterion is a criterion for performing a transformation on a node included in the graph (710), and the smoothing unit (160) can perform a transformation in which the characteristic value of each node included in the graph (710) has the same characteristic value according to the first criterion and is smoothed step by step.

[0146] At this time, the first criterion may include Laplacian smoothing for gradually modifying the characteristic values ​​of the nodes. Laplacian smoothing according to the present invention may be a smoothing method for gradually modifying the characteristic values ​​of the nodes while maintaining the structure of the graph.

[0147] More specifically, Laplacian smoothing is a smoothing method that uses the Laplacian matrix of a graph to repeatedly diffuse feature values ​​so that the feature value of each node gradually becomes homogenized with the feature values ​​of adjacent nodes.

[0148] In other words, Laplacian smoothing can refer to a graph-based low-pass filtering technique that reflects the connectivity between nodes to mitigate abrupt changes or high-frequency components of feature values, and causes the feature values ​​of each node to gradually converge to the same or similar values ​​over time or through iteration. Here, Laplacian smoothing can be represented as shown in (a) of FIG. 9.

[0149] The smoothing unit (160) applies Laplacian smoothing to each characteristic value of a node included in the input graph (710), thereby mitigating abrupt changes in the node characteristic values ​​and performing stepwise smoothing processing so that the characteristic values ​​of the nodes can converge to the same characteristic value.

[0150] At this time, the feature matrix at time t can be expressed as shown in (c) of FIG. 9. Here, the Laplacian, the order matrix, and the scaling coefficient of the input graph can each be expressed as shown in (d) of FIG. 9.

[0151] Meanwhile, the feature diffusion process according to Laplacian smoothing can be represented as a Markov chain in which the feature matrix at time t is sequentially determined based on the feature matrix at the previous time. For example, the Markov chain of the feature diffusion process can be represented as shown in (e) of Fig. 9.

[0152] Additionally, Laplacian smoothing can be performed based on matrix operations on the Laplacian matrix of the input graph (710). For example, if the normalized Laplacian matrix is ​​expressed as in (f) of FIG. 9 by eigenvalue decomposition, the feature matrix at time t can be expressed as in (g) of FIG. 9. Here, terms such as in (h) of FIG. 9 can function as a low-pass filter to cause the feature values ​​of the nodes to be attenuated to different degrees depending on the magnitude of each eigenvalue.

[0153] This may mean that the amount of change in node feature values ​​is selectively reduced in such a way that high-frequency components corresponding to large eigenvalues ​​among the spectral components of the normalized Laplacian matrix are suppressed relatively significantly, while low-frequency components corresponding to small eigenvalues ​​are suppressed relatively less.

[0154] In addition, the smoothing coefficient for each eigenvalue can be expressed as in (a) of FIG. 10, which means that the larger the eigenvalue, the greater the reduction of the corresponding component. Here, the eigenvalue can be expressed as in (b) of FIG. 10.

[0155] That is, the smoothing unit (160) can perform a transformation such that each feature value of a node included in the input graph (710) has the same feature value by performing Laplacian smoothing stepwise on the input graph (710) while maintaining the structural relationship of the graph and reducing the feature value of a node having abrupt fluctuation components. At this time, the graph transformed according to the first criterion may be a graph (711) in which each feature value of a node is the same.

[0156] Meanwhile, the edge removal unit (161) can perform structural deformation (i.e., structural diffusion process) on the edges included in the input graph (710) according to the second criterion among the pre-set criteria. At this time, the second criterion is a criterion for performing deformation on the edges included in the graph (710), and the edge removal unit (161) can determine whether to remove the edges included in the graph (710) according to the second criterion. At this time, the second criterion may be a criterion related to a pre-set probability for determining whether to remove the edges.

[0157] Here, removing an edge may mean partially disconnecting the connection of the input graph (710) by removing the edge according to the result of determining whether to remove the edge during the process of modifying the nodes included in the input graph (710).

[0158] In addition, the preset probability refers to a probability value set in advance to give each edge the possibility of being maintained or removed during the deformation process, and can mean a reference value to ensure that the edge deformation process proceeds probabilistically.

[0159] That is, the edge removal unit (161) can determine whether to remove edges included in the graph state at each point in time generated from the input graph (710) according to a preset probability.

[0160] For example, the edge removal unit (161) can generate a graph at time t by randomly removing edges included in the graph state of the previous time point according to a preset probability (e.g., 1-p) at time t. Here, the graph state of the previous time point can be represented as shown in (c) of FIG. 10. That is, existing edges are maintained with probability p, and non-edges may not exist. Through this, the structure diffusion process can be defined as the formula in (e) of FIG. 10.

[0161] Here, the fact that there may be no non-edges means that in the input graph (710), a pair of nodes that were originally not connected does not have a new edge created during the transformation process, and the unconnected state of that pair of nodes is maintained.

[0162] That is, the edge removal unit (161) can remove existing edges during the deformation process according to the second criterion, but does not add new edges at locations where they did not originally exist, so that the non-edge relationship of the graph can be maintained the same before and after the deformation process.

[0163] The edge removal unit (161) can perform edge removal included in the input graph (710) step by step, thereby maintaining or removing the edges included in the graph state of the previous time point according to a preset probability at each time point, so that the connection structure of the graph can be gradually modified over time. Here, the edge removal process can be represented as shown in (d) of FIG. 10. In addition, through the above process, a structure diffusion process such as (e) of FIG. 10 can be defined.

[0164] In addition, structural noise can be applied to the input graph (710) by removing edges according to the second criterion.

[0165] Here, the fact that noise is applied to the input graph (710) may mean that the original connection relationship of the graph is partially changed as some edges are maintained or removed during the probabilistic edge removal process according to the second criterion, and accordingly, the structure of the graph is randomly deformed.

[0166] That is, the edge removal unit (161) can modify the connection structure of the input graph (710) and impart structural noise to the graph by performing probabilistic edge removal according to the second criterion in stages. At this time, the graph modified according to the second criterion may be a graph (712) with edges removed.

[0167] In this way, the smoothing unit (160) and the edge removal unit (161) can perform deformation of the graph according to different criteria for the input graph (710). That is, the artificial intelligence model (150) can perform deformation of the input graph (710) using the smoothing unit (160) and the edge removal unit (161) to generate a deformed (noised) graph (720).

[0168] At this time, the noise-applied graph (720) generated by the artificial intelligence model (150) may mean a graph in which the value of each node included in the graph has the same value and the edges connected to each node are removed.

[0169] Meanwhile, in the present invention, a process of training an artificial intelligence model to generate a reference structure of at least one graph using at least one modified graph comprising at least one modified node and at least one modified edge may be performed (S540, see FIG. 5).

[0170] The control unit (190) can train the artificial intelligence model (150) to generate a reference structure of the graph using the modified graph.

[0171] Here, the reference structure according to the present invention may refer to the structural form of the input graph (710). For example, the reference structure may refer to the connection relationships between nodes, connection patterns, and the overall structural arrangement formed by nodes and edges that the graph originally possesses.

[0172] Additionally, generating a reference structure of a graph may mean that the artificial intelligence model reconstructs the nodes and edges of the input graph (710) using modified graphs that include modified nodes and modified edges.

[0173] That is, the control unit (190) can train the artificial intelligence model (150) to generate a reference structure of the graph by reconstructing the deformed nodes and deformed edges included in the deformed graph. At this time, the reconstruction process can be parameterized into a denoising network that predicts the state at time t-1. Here, the parameterized denoising network can be represented as (f) in FIG. 10.

[0174] To this end, as illustrated in FIGS. 6 and FIGS. 8, the artificial intelligence model (150) can input a transformed graph (810) into a graph encoding unit (180). At this time, the input transformed graph (810) may include transformed nodes and transformed edges (i.e., noise).

[0175] Additionally, the deformed graph (810) may be a graph in which the transformation has been performed once, or a graph in which the feature values ​​of the nodes are further smoothed or multiple edges are removed as the transformation process is performed repeatedly. That is, the deformed graph (810) may contain various levels of noise depending on the stage or number of times the transformation is performed.

[0176] The graph encoding unit (180) can encode the structural features of the input deformed graph (810). More specifically, the graph encoding unit (180) can generate a node representation (610) for the deformed node feature value (611) and deformed edge information (612) included in the deformed graph (810). Here, the deformed node feature value (611) and deformed edge information (612) can each be represented as in (g) of FIG. 10, and the generated node representation (610) can be represented as in (h) of FIG. 10.

[0177] Furthermore, the artificial intelligence model (150) can reconstruct the deformed graph using the node representation (610) for the deformed graph generated in the graph encoding unit (180).

[0178] More specifically, the artificial intelligence model (150) can input a node representation (610) for a deformed graph to a feature decoder (181) and a structure decoder (182) in order to reconstruct the deformed graph.

[0179] The feature decoder (181) can reconstruct the deformed nodes included in the deformed graph as in (811) using the input node representation (610). For example, the feature decoder (181) can reconstruct (or predict) feature values ​​corresponding to the node feature values ​​at the stage prior to deformation (e.g., the feature matrix at time t-1) based on the input node representation (610).

[0180] Meanwhile, the structure decoder (182) can reconstruct the deformed edges included in the deformed graph as in (812) using the input node representation (610). For example, the structure decoder (182) can reconstruct (or predict) the Laplacian component representing the structure information of the pre-deformation stage.

[0181] In this way, the artificial intelligence model (150) can generate a reconstructed graph (820) by reconstructing the deformed nodes and deformed edges included in the deformed graph using a feature decoder (181) and a structure decoder (182). At this time, the reconstructed graph (820) may include reconstructed edges and reconstructed nodes.

[0182] The artificial intelligence model (150) can be trained to generate a reference structure of the graph by restoring nodes and edges that were lost or distorted during the transformation process step by step during the process of reconstructing the transformed graph.

[0183] That is, the artificial intelligence model (150) can be trained to remove noise included in the deformed graph and generate a reference structure of the graph by repeatedly performing the process of reconstructing the deformed nodes and deformed edges included in the deformed graph.

[0184] Meanwhile, in the present invention, a process of receiving at least one graph including at least one node and at least one edge may be performed (S610, see FIG. 14).

[0185] The control unit (190) can receive at least one graph. At this time, the received graph may be a graph including nodes and edges. The graph receiving method according to the present invention can be implemented in various ways.

[0186] For example, the control unit (190) may receive pre-generated graph data from an external server via a network, and may directly generate a graph or receive an updated graph based on status information transmitted in real time from a sensor module or a data collection device.

[0187] Additionally, the control unit (190) can receive relationship information between objects entered by the user, environment configuration information, or a graph based on data to be analyzed from a user terminal or application.

[0188] As another example, the control unit (190) can receive a sensor data stream transmitted from a system internal device such as a robot, smart home device, vehicle, process equipment, etc., and convert the data into a graph form.

[0189] Meanwhile, in the present invention, at least one received graph is input into a pre-trained artificial intelligence model (S620, see FIG. 14), and in the artificial intelligence model, a process of generating a processing result for at least one graph is performed using at least one of at least one node and at least one edge included in at least one graph (S630, see FIG. 14).

[0190] The control unit (190) can process the received graph as input to the artificial intelligence model (150). At this time, the artificial intelligence model (150) may be an artificial intelligence model trained to interpret the structural relationships of nodes and edges of the received graph and analyze the overall pattern of the graph based on the learning results of graph transformation and graph restoration performed during the learning phase.

[0191] The artificial intelligence model (150) can generate a processing result for the graph by using the feature values ​​of the nodes included in the input graph, the connection relationships between the nodes, the weights assigned to the edges, or structural attribute information.

[0192] For example, the artificial intelligence model (150) can generate results such as a prediction result for a specific node state or attribute value of a graph, a result for determining the possibility or risk of existence of a specific edge within the graph, a result for determining whether it is normal or abnormal by analyzing the structural pattern of the entire graph, a result for predicting the possibility of a specific action or specific action event occurring based on the graph, a result for evaluating the validity, safety, or efficiency of a path between specific nodes within the graph, and a result for providing a specific recommendation or decision based on the structural features of the graph.

[0193] The artificial intelligence model (150) can be applied to situation judgment, event prediction, or control decision-making in each field depending on what environment or domain the input graph represents.

[0194] For example, as illustrated in FIG. 11, the graph-based data processing system according to the present invention models the interaction relationship between a plurality of home appliances operating in a smart home environment and a user in the form of a graph, and can be used to determine the state of the device or predict future events based on the graph. In this case, each home appliance, user, and environmental element within the smart home can be defined as a node of the graph, and the operational correlations, sensor-based interactions, and temporal and state-related connection information between them can be represented in the form of edges of the graph. Accordingly, the present invention can provide an artificial intelligence-based graph processing structure capable of integrally analyzing relational patterns between devices and user behavior patterns, rather than isolated operational information of individual devices.

[0195] In this case, the artificial intelligence model (150) according to the present invention may be configured to receive input in the form of a graph by converting user behavior data (e.g., refrigerator door opening, food removal), operating status data of home appliances (e.g., power consumption pattern of a dishwasher), and related events between devices (e.g., possibility of a washing operation occurring within a certain time after food removal) occurring in a smart home environment, and to learn the temporal changes of the graph, dependencies between nodes, and structural patterns. Through such a learning process, the artificial intelligence model may be trained to identify causal and statistical relationships between user behavior and device operation, detect abnormal operation in a specific device at an early stage, and perform the function of generating notifications in advance that the user is likely to need.

[0196] In addition, the artificial intelligence model (150) according to the present invention may be an artificial intelligence model trained to restore or predict the structural features of a graph and the characteristics of nodes and edges.

[0197] That is, the artificial intelligence model (150) learns a ground-truth structural pattern regarding what structural form a graph should have in a specific situation and what structural change is interpreted as an abnormal signal, and can determine whether the current state is normal or requires inspection by comparing it with a fluctuating graph collected from an actual smart home.

[0198] For example, in the embodiment of FIG. 11, the action of a user (U) taking food out of a refrigerator (1110) can be reflected as an interaction event between a “user node and a refrigerator node” in a smart home graph. At this time, the artificial intelligence model can provide an action induction message (1120), such as “Would you like to do the dishwashing in 10 minutes?” to the user terminal (20) based on an existing learning pattern that there is a high probability that the dishwasher (1130) will operate for a certain period of time after the food is taken out.

[0199] In addition, if the dishwasher sensor records higher-than-usual power consumption for a specific period, this can be interpreted as an unusual connection pattern or abnormal change between the “dishwasher node” and the “energy usage node.”

[0200] The artificial intelligence model according to the present invention can determine such structural fluctuations as abnormal patterns in the graph and generate and deliver an inspection notification to the user's smartphone (1140) stating, "The energy usage of the dishwasher is higher than usual. An inspection is required."

[0201] As another example, as illustrated in FIG. 12, the graph-based data processing system according to the present invention can also be applied to data analysis in scientific, research, and industrial fields related to the structural characteristics of chemical molecules, intermolecular bonding characteristics, reaction stability, etc.

[0202] In particular, since molecular structures can be naturally represented in the form of a graph with atoms as nodes and interatomic bonds as edges, the node- and edge-modification-based graph learning model proposed in this invention can be effectively utilized for various problems in the field of chemistry, such as molecular design, synthesis feasibility assessment, toxicity prediction, and reaction safety verification.

[0203] In this case, the artificial intelligence model (150) according to the present invention may be configured to learn structural information of specific molecules and information on reaction characteristics that may occur when these molecules bond, from graph-shaped data. The artificial intelligence model (150) can learn chemically significant structural patterns based on graphs by expressing various factors affecting the stability of molecules, such as the electron configuration, polarity, reactivity, and oxidation / reduction characteristics of each atom, as feature values ​​of nodes, and by modeling bonding relationships between atoms, bonding order, and reactivity patterns in the form of edges.

[0204] Furthermore, an AI model that has learned structural patterns can be trained to determine, based on changes in characteristics within the graph structure, whether a specific molecule and a specific target molecule (molecule A) can bind stably, or whether there is a risk of explosion, toxicity, or degradation upon binding. In other words, patterns similar to the distance between nodes in the graph, changes in bond order, and bond energy can be reflected as structural signals that trigger hazardous situations and learned as the model's reference structure.

[0205] For example, the user may input or select a question (1310) through the user terminal (30) asking, “Can this molecule be synthesized with molecule A?” At this time, the artificial intelligence model (150) analyzes the structural relationship between the two molecules and can predict whether the combination forms a safe reaction pathway or whether there is a possibility of instability occurring upon binding. As a result of the prediction, if graph analysis detects that the molecule may increase reactivity in a specific binding region, cause structural collapse, or generate toxicity when combined with molecule A, the user terminal may provide a recommendation message (1320) such as, “This molecule may be dangerous when synthesized with molecule A. We recommend synthesizing with molecule B instead of molecule A.” The recommended molecule B may be a molecule predicted to form a more stable reaction pathway based on the reference structure learned by the artificial intelligence model (150).

[0206] As another example, referring to FIG. 13, the graph-based data processing system according to the present invention can be used to identify obstacles on the robot's driving path during the process of a mobile robot transporting an object, and to search for and determine a safe driving path using node and edge information included in the graph. The robot can perceive the surrounding environment by being equipped with various sensors such as cameras, LiDAR, and ultrasonic sensors, and obstacles can be automatically identified by analyzing image information, distance information, and depth information acquired through these sensors. The identified objects are represented as nodes of the graph, and the distance between the robot and the obstacle, accessibility, risk level, etc., can be represented as edges of the graph.

[0207] The artificial intelligence model (150) according to the present invention may be a model that has learned structural patterns of a graph, safe path formation methods, and structural features that increase risk through a previously performed node deformation, edge deformation, and reference structure restoration learning process. The artificial intelligence model (150) may provide multiple candidate paths based on the connection relationships between nodes of the graph and edge information (e.g., risk level, distance, mobility, etc.). In this process, the artificial intelligence model may determine risk patterns based on the learned reference structure and perform path search to select a path among each path candidate that has a low probability of collision and high mobility efficiency.

[0208] For example, if an obstacle is detected on the path while the robot is transporting an object, the artificial intelligence model (150) can search for an alternative connection path between the robot node and the target point node within the graph, and evaluate the risk and travel cost of the nodes and edges included in each path to select a detour path instead of the existing path.

[0209] As another example, the graph-based data processing system according to the present invention models the interaction relationships between a plurality of industrial equipment, sensor devices, and process elements operating in a smart factory environment in the form of a graph, and can be used to determine the status of the equipment or predict potential abnormal events based on the graph.

[0210] In this case, each piece of equipment, sensors attached to the equipment, and process variables (temperature, pressure, vibration data, etc.) can be defined as nodes of the graph, while physical connection relationships between equipment, process correlations, and simultaneous response patterns between sensors can be represented as edges of the graph.

[0211] Therefore, unlike existing methods that diagnose based only on single sensor values ​​of individual facilities, the present invention can provide a graph-based industrial intelligence structure capable of integrally analyzing the structural relationships and process flow of the entire facility.

[0212] In this case, the artificial intelligence model according to the present invention may be configured to receive sensor data (e.g., motor vibration pattern, pressure change, temperature change) generated in a process line, equipment operation information (e.g., rotational speed, load amount, operating time), and influence relationships between equipment (e.g., the effect of overload of a previous stage equipment on a subsequent equipment) converted into a graph form and to learn the temporal change of the graph, dependencies between nodes, and process structural patterns.

[0213] Through this learning process, the artificial intelligence model can be trained to identify process flow in a steady state, load transfer patterns between equipment, and correlation patterns between sensors; to detect early any potential impact on the entire process even if minor fluctuations occur in some equipment; and to provide necessary inspection alerts to operators or the system in advance.

[0214] In addition, in this case, the artificial intelligence model may be an AI model trained to restore or predict the structural features of the graph and the characteristics of nodes and edges.

[0215] In other words, the artificial intelligence model learns a reference structure regarding what structure is appropriate for a graph in a normal equipment operating environment, and by comparing it with graphs collected from the actual process, it can determine whether the current state falls within the normal range or is a potential abnormal signal.

[0216] For example, if the vibration value of a specific piece of equipment is measured to be higher than usual or the cooling water temperature gradually rises, this may cause a change in the correlation between adjacent sensor nodes associated with the equipment, forming a structure different from the reference graph pattern.

[0217] The AI ​​model can identify these structural changes as abnormal patterns and generate and provide inspection alerts to operator terminals or process control systems, such as, “Abnormal vibration has been detected in the equipment. Preventive maintenance is recommended.” Additionally, the AI ​​model can predict a series of anomalies throughout the entire process. For example, if a pattern of abnormal pressure reduction is detected in equipment at the beginning of the process, this information is transmitted to adjacent process nodes on the graph, and there is a possibility that production quality degradation or equipment overload may occur in a specific section later.

[0218] In this case, the artificial intelligence model can derive prediction results, such as “potential for expected production quality degradation” or “expected subsequent equipment overload,” by considering the continuous change in the graph structure, and provide them to the management system.

[0219] As described above, the artificial intelligence-based graph structure learning method and system according to the present invention, and the graph-based data processing method and system using the same, can learn the standard structure of a graph by deforming the nodes and edges constituting the graph according to certain criteria to apply noise, and by using the noise-applied graph. Through this, it is possible to learn a representation that more clearly reflects the structural characteristics of the graph and the relationships between nodes, stably reconstruct a meaningful structure even in graphs containing incomplete information or structural variations, and apply it to various environments without being dependent on a specific domain.

[0220] Furthermore, the AI-based graph structure learning method and system according to the present invention is configured to simultaneously restore node characteristic information and structural change information of the graph during the diffusion process, thereby enabling the learning of patterns meaningful for actual task performance within the graph. Accordingly, rather than simple structure restoration, it is possible to generate task-appropriate structural representations, which can demonstrate consistent performance in graph-based data processing tasks with different purposes, such as link prediction, node classification, and anomaly detection. In particular, it can address incompleteness that frequently occurs in real-world environments, such as the loss of some node information or uncertain measurement of some edges, thereby increasing applicability in actual service environments. Through this, the present invention can be reliably utilized in various industrial and real-world network environments where variations in graph data quality, measurement errors in sensor-based graphs, and arbitrary dynamic deformations exist.

[0221] Furthermore, the artificial intelligence-based graph structure learning method and system according to the present invention utilizes graph Laplacian-based low-pass filtering to prevent rapid loss of high-frequency components during the noise injection process and to preserve global structural information of the graph. Through this, the problem of indiscriminate signal destruction inherent in existing diffusion models is resolved, and learning can be performed while effectively maintaining the intrinsic topological characteristics and latent structural factors of the graph data.

[0222] Furthermore, the artificial intelligence-based graph structure learning method and system according to the present invention does not require manual design of the structure, thereby providing excellent universality and business efficiency without changing the model structure in various benchmark environments. Through this, the same model can be applied to various application services in actual industrial environments that differ in data conditions, graph structures, and business objectives, thereby simultaneously achieving operational benefits such as reduced maintenance costs, ease of system integration, and improved scalability.

[0223] Meanwhile, the present invention described above can be implemented as a program that is executed by one or more processes on a computer and can be stored on a computer-readable medium (or recording medium).

[0224] Furthermore, the present invention described above can be implemented as computer-readable code or instructions on a medium on which a program is recorded. That is, the present invention can be provided in the form of a program.

[0225] Meanwhile, computer-readable media include all types of recording devices in which data that can be read by a computer system is stored. Examples of computer-readable media include HDD (Hard Disk Drive), SSD (Solid State Disk), SSD (Silicon Disk Drive), ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc.

[0226] Furthermore, the computer-readable medium may be a server or cloud storage that includes a storage and is accessible to an electronic device via communication. In this case, the computer may download the program according to the present invention from the server or cloud storage via wired or wireless communication.

[0227] A computer program may reach the system (100) through various suitable transmission mechanisms. The transmission mechanism may be, for example, a computer-readable storage medium, a computer program product, a memory device, a recording medium such as a CD-ROM or DVD, or a product that tangibly embodies the computer program. The transmission mechanism may be a signal configured to reliably transmit the computer program through air or an electrical connection. The system (100) may propagate or transmit the computer program as a computer data signal.

[0228] Furthermore, references to 'computer-readable storage media,' 'computer program products,' 'computer programs embodied in a tangible form,' etc., or to 'controller,' 'computer,' 'processor,' etc., should be understood to include not only computers with various architectures such as single / multi-processor architectures and sequential (Von Neumann) / parallel architectures, but also specialized circuits such as Field-Programmable Gate Arrays (FPGAs), Application Specific Circuits (ASICs), signal processing units, and other devices. References to computer programs, instructions, code, etc., should be understood to include software for programmable processors or firmware, such as programmable content for hardware devices, whether it is instructions for a processor or configuration settings for a fixed-function device, gate array, or programmable logic device.

[0229] Furthermore, in the present invention, the computer described above is an electronic device equipped with a processor, namely a CPU (Central Processing Unit), and no special limitations are placed on its type.

[0230] Meanwhile, the above detailed description should not be interpreted restrictively in all respects but should be considered exemplary. The scope of the invention shall be determined by a reasonable interpretation of the appended claims, and all modifications within the equivalent scope of the invention are included within the scope of the invention.

Claims

1. Regarding methods performed by a computer, A step of receiving at least one graph including at least one node and at least one edge; A step of inputting the at least one graph into at least one artificial intelligence model to learn the structural characteristics of the at least one graph; In the above-mentioned at least one artificial intelligence model, the step of performing a transformation according to a preset standard for each of the at least one node and the at least one edge included in the at least one graph to learn the structural characteristics of the at least one graph structure; and An artificial intelligence-based graph structure learning method characterized by including the step of training an artificial intelligence model to generate a reference structure of the at least one graph using a modified at least one graph comprising the modified at least one node and the modified at least one edge.

2. In Paragraph 1, The above-mentioned previously established criteria include at least one of a first criterion for performing a deformation for the at least one node and a second criterion for performing a deformation for the at least one edge, and An artificial intelligence-based graph structure learning method characterized by performing a deformation on at least one node and at least one edge using the first criterion and the second criterion in the step of performing the above deformation.

3. In Paragraph 2, In the step of performing the above modification, According to the first criterion above, Perform a modification on at least one of the above nodes, and According to the second criterion above, An artificial intelligence-based graph structure learning method characterized by performing a deformation on at least one edge.

4. In Paragraph 3, Among the aforementioned multiple pre-established standards The above first criterion is a criterion for performing a modification on the above at least one node, and The step of performing the above modification is, An artificial intelligence-based graph structure learning method characterized by including the step of performing a transformation on at least one node included in at least one graph according to the first criterion above.

5. In Paragraph 4, In the step of performing a modification on at least one node, An artificial intelligence-based graph structure learning method characterized by performing a stepwise smoothing process according to the first criterion above so that the characteristic value of each of the at least one node has the same characteristic value.

6. In Paragraph 4, Among the aforementioned multiple pre-established standards The second criterion is a criterion related to a preset probability for performing a deformation on at least one edge, and The step of performing the above modification is, An artificial intelligence-based graph structure learning method characterized by including the step of performing a deformation on at least one edge included in at least one graph according to the second criterion above.

7. In Paragraph 6, In the step of performing a deformation on at least one edge, An artificial intelligence-based graph structure learning method characterized by performing a structural transformation on at least one edge included in at least one graph according to the second criterion above.

8. In Paragraph 6, In the step of performing a deformation on at least one edge, Based on the second criterion above, it is determined whether to remove the at least one edge included in the at least one graph based on the preset probability, and An artificial intelligence-based graph structure learning method characterized by removing at least some of the at least one edge according to the above removal decision.

9. In Paragraph 8, An artificial intelligence-based graph structure learning method characterized by applying structural noise to at least one graph by removing at least a portion of at least one edge according to the second criterion above.

10. In Paragraph 9, In the above-mentioned training step, According to each of the above first standard and the above second standard, An AI-based graph structure learning method characterized by training an AI model to reconstruct the at least one graph having the reference structure using the at least one deformed graph comprising the at least one deformed node and the at least one deformed edge.

11. In Paragraph 10, In the above-mentioned training step, In order to reconstruct at least one of the above graphs, Generate at least one node representation for at least one modified graph, and Using the above at least one node representation, An AI-based graph structure learning method characterized by training the AI ​​model to reconstruct at least one of the at least one node that has undergone deformation and at least one edge that has undergone deformation.

12. In Paragraph 11, In the above-mentioned training step, Using at least one graph from the previous transformation step, An AI-based graph structure learning method characterized by training the AI ​​model to perform reconstruction on at least one of the at least one node that has undergone the above deformation and at least one edge that has undergone the above deformation.

13. In Paragraph 11, Through the reconstruction of the at least one node in which the above modification has been made, An AI-based graph structure learning method characterized by training the AI ​​model to reconstruct the characteristic values ​​of each of the at least one node that has been smoothed stepwise to have the same characteristic values.

14. In Paragraph 11, Through reconstruction of the at least one edge on which the above deformation has been performed, An artificial intelligence-based graph structure learning method characterized by removing noise applied to at least one graph.

15. In Paragraph 11, In the above-mentioned training step, Using at least one of the reconstructed at least one node and the reconstructed at least one edge, An AI-based graph structure learning method characterized by training the AI ​​model to reconstruct the at least one graph having the above reference structure.

16. In a method performed by a computer, A step of receiving at least one graph including at least one node and at least one edge; The step of inputting at least one received graph into a pre-trained artificial intelligence model; and In the above artificial intelligence model, using at least one of the at least one node and the at least one edge included in the at least one graph, A graph-based data processing method characterized by including the step of generating a processing result for at least one graph.

17. A system comprising memory configured to store executable instructions and one or more processors configured to perform operations by executing one or more instructions, The above system is, Receive at least one graph including at least one node and at least one edge, and To learn the structural characteristics of the above at least one graph, the above at least one graph is input into at least one artificial intelligence model, and In the above-mentioned at least one artificial intelligence model, to learn the structural characteristics of the above-mentioned at least one graph structure, a transformation according to a preset standard is performed for each of the above-mentioned at least one node and the above-mentioned at least one edge included in the above-mentioned at least one graph, and An AI-based graph structure learning system characterized by training an AI model to generate a reference structure of at least one graph using a modified at least one graph comprising at least one node and at least one edge that has undergone the modification.

18. A program that is executed by one or more processes in an electronic device and stored on a computer-readable recording medium, The above program is, A step of receiving at least one graph including at least one node and at least one edge; A step of inputting the at least one graph into at least one artificial intelligence model to learn the structural characteristics of the at least one graph; In the above-mentioned at least one artificial intelligence model, the step of performing a transformation according to a preset standard for each of the at least one node and the at least one edge included in the at least one graph to learn the structural characteristics of the at least one graph structure; and A program stored on a computer-readable recording medium characterized by including instructions for performing the step of training an artificial intelligence model to generate a reference structure of the at least one graph using the at least one modified graph comprising the at least one node and the at least one edge that has undergone the above modification.

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