A multi-agent hypergraph modeling and representation method

Abstract

The application belongs to the field of graph representation learning, and proposes a multi-agent hypergraph modeling and representation method. First, the graph representation learning process is defined as a multi-agent optimization process; second, the message passing mechanism in the existing hypergraph representation learning method is taken as an interaction mode of an agent; then, a force-based agent interaction mode is designed; finally, the two agent interaction modes are optimized together on the downstream task, and the optimized graph model is used to output the prediction result. The application formalizes the graph representation learning problem from the perspective of multi-agent, considers the high-order complex relationship of nodes in the graph, and combines message passing and force-based interaction, which improves the performance of the existing hypergraph method and is suitable for graph learning tasks in complex scenarios.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of graph representation learning, and in particular to a multi-agent hypergraph modeling and representation method. BACKGROUND

[0002] Hypergraph representation learning uses hyperedges as the structure of associated nodes, and a hyperedge can contain any number of nodes, which is suitable for non-paired relationships that general graph structure cannot express. Hypergraph work has attracted widespread attention, and in recent years, interesting work has emerged.

[0003] The current mainstream hypergraph representation learning algorithm mainly includes the following:

[0004] Feng et al. in 2019 Hypergraph neural networks proposed HGNN, which brings the Laplacian matrix on hypergraph into the traditional graph convolution, defines and approximates the convolution operation on hypergraph, and can make the model process multi-modal data. Yadati et al. in 2019 HyperGCN: A new method for training graph convolutional networks on hypergraphs proposed HyperGCN, which expands the hyperedge and filters the binary edge after expansion to achieve the purpose of filtering part of the noise. Dong et al. in 2020 HNHN: Hypergraph Networks with Hyperedge Neurons proposed HNHN, which designs graph convolution functions and activation functions for both hyperedges and nodes, and designs a normalization method for hypergraphs. Arya et al. in 2020 HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs proposed HyperSAGE, a hypergraph learning method under the inductive learning setting, which guarantees the performance advantage through the two-layer message passing strategy between hyperedge kernels. Huang et al. in 2021 UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks proposed UniGNN, which designs a unified hypergraph framework and extends the existing mainstream methods on simple graphs to hypergraphs. Jo et al. in 2021 Edge Representation Learning with Hypergraphs proposed EHGNN, which starts to focus on the representation learning of hyperedges, and then uses the method of hypergraph to solve the graph-level task in simple graph. Zhang et al. in 2021 H2MN: Graph Similarity Learning with Hierarchical Hypergraph Matching Networks proposed H2MN, which regards the hyperedge as a subgraph and proposes a hyperedge pooling operation and a subgraph matching module, which proves its effectiveness in graph classification and graph regression problems.

[0005] However, these methods do not consider the complex scenarios in the real world when designing, and lack clear, unified and effective forms in the multi-agent complex scenario, so it is difficult to extend these graph learning methods to the real scenario of multi-agent.

[0006] Although existing graph representation learning methods have achieved great success, most of the real-world graph learning scenarios are complex systems, and the existing graph methods are difficult to accurately describe these scenarios. First, in complex scenarios (e.g., bird flocks, bee swarms, and fish schools), these individuals should be regarded as intelligent individuals rather than just nodes. Intelligent agents can perceive the surrounding environment and respond appropriately to the environment according to their state, which has not been clearly defined in previous graph learning methods. Second, intelligent agents need to interact or communicate with other intelligent agents. Although the message passing-based graph learning method is one attempt, the communication mechanism between intelligent agents in graph learning still lacks a clear, unified, and effective form. In addition, the pair-wise relationship interaction between intelligent agents is not enough to accurately describe the complex topology of the real world. This is especially true when the number of interacting intelligent agents is much larger than two, such as in multi-person cooperation, multi-modal information interaction, or other forms of high-order operations. The environment under multi-agent needs a more general method to meet the complex interaction requirements between intelligent agents. SUMMARY

[0007] In view of the problems existing in the prior art, the purpose of the present application is to provide a multi-agent hypergraph modeling and representation method, which reformulates graph representation learning from the perspective of multi-agent, designs a graph learning paradigm that can be applied to complex environments, to overcome the limitations of the existing method and the performance problem caused by the inability to adapt to complex environments. By formalizing graph representation learning from the perspective of multi-agent, and introducing hyperedges to meet the needs of high-order interaction of multiple individuals in complex systems, and through message passing and force-based interaction to optimize the state of multiple intelligent agents under a given task, the optimized model is used to give the final prediction result. The present application can also help to better design graph learning methods in complex scenarios, improve the performance of existing hypergraph methods, and be suitable for graph learning tasks in complex scenarios.

[0008] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0009] A multi-agent hypergraph modeling and representation method defines the graph representation learning process as an optimization process of multi-agent, uses the message passing mechanism in the existing hypergraph representation learning method as a way of intelligent agent interaction, and designs another force-based intelligent agent interaction method; the two intelligent agent interaction methods are used to optimize the graph model together in downstream tasks such as node classification, and the optimized graph model is used to output the prediction result; the specific steps are as follows:

[0010] Step (1): formalize the graph representation learning process from the perspective of multi-agent;

[0011] Step 1.1), define intelligent agents; define physical or abstract entities that can perceive the surrounding environment and other intelligent agents as intelligent agents Agent iAn agent is able to communicate with other members in a multi-agent system and react to the current state when interacting with them; any given agent Agent i ∈Φ agent has information (x i , z i ), Φ agent is a set of agents; x i represents the intrinsic properties of Agent i , z i represents the current state of Agent i , used for decision-making processes or other tasks;

[0012] In graph representation learning, the nodes of the graph are regarded as agents with attributes X i and states z i ; the nodes of the graph represent the states of the agents, and the intrinsic properties of the nodes represent the attributes of the agents;

[0013] A group Group j ∈Φ group is a set of agents based on a specific function (e.g., cooperation, competition) and contains any number of agents; an agent can be included in multiple agent groups; Φ group is a set of agent groups; the edges in the graph are regarded as a kind of agent group; when an agent group contains only two agents, it represents a pair relationship in a simple graph;

[0014] Step 1.2), formalization of the graph representation learning process;

[0015] Agents receive information transmitted by other members through interaction and then perform operations according to their states; there are two ways of interaction in a multi-agent system: the first is global interaction, in which every agent in the multi-agent system interacts with all other agents; the second is intra-group interaction, in which agents interact within an agent group and do not communicate or influence members outside the agent group in the multi-agent system; let Interaction(Group j , type int ) represent a certain interaction mode, where Group j is an agent group representing a group of agent individuals that interact, represents a certain specific interaction operation, which is determined according to the environment of the multi-agent system in practical applications;

[0016] Given a multi-agent system, construct an agent graph where Φ agent is a set of agents, Φ group is a set of agent groups, and Φ interis the set of interaction modes of agents; the multi-agent system learns a mapping function f rep : for computing the agent state Z in downstream task T; then make prediction on downstream task through agent state Z, is the prediction of multi-agent graph model, f task is the prediction function of downstream task, such as softmax function in node classification task, Y is the real label of agent node;

[0017] optimizing the state of agent to meet the requirements of the current task in multi-agent system; according to the given downstream task T∈Φ T (e.g. decision, prediction), Φ T is the set of downstream tasks and the optimization process Opt (e.g. ant colony algorithm, particle swarm optimization), the agent iteratively updates its state information by cooperating / communicating with other members to obtain the best task performance;

[0018] Step (2): the message passing mechanism in hypergraph representation learning method is taken as an interaction mode of agent, which is the intra-group interaction;

[0019] First, refer to the message passing mechanism of general graph The message passing mechanism in general graph model:

[0020]

[0021] h i =U(h i ,m i ),

[0022] where the message function M() aggregates the neighborhood information of node v i , the update function U() outputs the new representation of the next layer, e ij represents the connection between node v i and node v j , represents the set of neighborhood nodes of node v i . The initial attribute representation of agent (node) is where x i is the attribute of the i-th agent.

[0023] According to the message passing mechanism of existing graph, it is extended to hypergraph representation learning, that is, from message passing according to ordinary edge (one edge only connects two nodes) to message passing mechanism according to hyperedge (one edge can contain multiple nodes); The message passing mechanism of hypergraph is uniformly represented as follows:

[0024] m e =M({h j} j∈e ​

[0025]

[0026] where e denotes a hyperedge, ε i is a set of hyperedges, where each hyperedge is associated with a node v i ; the message function M({h j} j∈e ) aggregates the information of node v i about its neighborhood nodes v j on the hyperedge e through the topology of the hyperedge e; the update function fuses all m i associated with node v e and the output h i of the last layer, and outputs the representation of the next layer h i ; for an agent Agent i , the representation vector is h i , and the matrix of the representation vectors of the whole graph is The output of the last layer H is labeled as the state of the agent

[0027] Step (3): design an agent interaction mode based on force, which includes an attractive force interaction mode for intra-group interaction and a repulsive force interaction mode for global interaction;

[0028] Step 3.1) extend the spring electrical model to hypergraph representation learning, which is suitable for agent groups; for a given agent Agent i , it is attracted to the agents in the same hyperedge, and the sum of the attractive forces is calculated as follows:

[0029]

[0030] where e i ∈ ε is any hyperedge containing the i-th agent, represents the state of the agent Agent i , which is output by the last layer of the graph model, and the hyperparameter is a proportion controlling the attractive force between agents, and the greater the value, the greater the attractive force, and the more the state of the corresponding agents tends to approach;

[0031] Step 3.2) define the repulsive force in the spring electrical model, and the sum of the repulsive forces of the i-th agent is represented as follows:

[0032]

[0033] where | Φ agent | is the set of agents Φagent the total number of intelligent agents, and p is also a hyperparameter that controls the size of the force, is a positive vector, and to prevent the denominator from being a zero vector, it is set to a constant vector

[0034] Step 3.3) Intelligent Agent Agent i The combined effect of attraction and repulsion is represented as

[0035] Step (4): jointly optimize the graph model of the two intelligent agent interactions of step (2) and step (3), and use the optimized graph model to predict the results;

[0036] Step 4.1) Select semi-supervised node classification as the downstream task, and use the representation of the intelligent agent to make predictions; Intelligent Agent Agent i The soft label prediction of the intelligent agent is:

[0037]

[0038] where z i is the state of the i-th intelligent agent in step (2) final output;

[0039] Step 4.2) The loss function of the downstream task is the cross-entropy loss, which is described as follows:

[0040]

[0041] where, is the label vector (one-hot vector) of node v, a total of C classes, 1 in the correct class dimension, and 0 in other dimensions.

[0042] Step 4.3) The loss function based on attraction and repulsion is represented as follows:

[0043]

[0044] Step 4.4) The final loss function includes and and is constantly trained and optimized by the Adam optimizer until the best performance is obtained; The final loss function is represented as:

[0045]

[0046] where, is a hyperparameter that controls the loss rate;

[0047] Step 4.5) Use the optimized hypergraph model to output the prediction results of the downstream task.

[0048] Compared with the prior art, the present application has the beneficial effects that: the present application re-formalizes graph representation learning by introducing the perspective of multi-agent, and uses hyper-edges to meet the needs of high-order interaction of multiple individuals in complex systems, and under a given task, the states of multiple agents are optimized collaboratively through message passing and force-based interaction, thereby overcoming the model limitations and performance problems in the prior art because of the inability to adapt to complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a schematic diagram of different interaction modes in a multi-agent system in the present application.

[0050] In the figure: is an agent group; is intra-group interaction; is global interaction.

[0051] Figure 2 is the basic framework of a multi-agent hypergraph modeling and representation method of the present application. DETAILED DESCRIPTION

[0052] The specific embodiments of the present application are further described below in combination with the drawings and technical solutions.

[0053] To make the technical problems solved by the present application, the technical solutions adopted and the technical effects achieved more clear, the present application is further described in detail below in combination with the drawings and examples. It can be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application. In addition, it should be noted that, for the convenience of description, only the parts related to the present application are shown in the drawings, but not all the contents.

[0054] The present application is divided into 5 steps when implemented: (1) reading the data in the hypergraph data set, outputting node and hyper-edge information; (2) inputting the data into a given hypergraph model and outputting node representation; (3) using force-based interaction to construct the resultant state for each node; (4) optimizing the model according to the loss function, and outputting the node classification prediction result after the model is optimized;

[0055] Step 1, read the data in the hypergraph data set, output the node and hyper-edge information.

[0056] 1.1) Read the data set to obtain the attributes X of the nodes and the structure ε of the hyper-edges in the data set.

[0057] 1.2) Process the obtained data to facilitate input into the model of the hypergraph.

[0058] Step 2, input the data into a given hypergraph model and output the node representation.

[0059] 2.1) Input node attribute X, and run message function m according to the message passing mechanism of the hypergraph e = M{h j} j∈e ) and update function L times, L is the number of model layers.

[0060] 2.2) Output the representation H of the node, and replace the representation of the node in the last layer with a symbol Z.

[0061] Third step, construct the state of the resultant force for each node by using force-based interaction.

[0062] 3.1) For all hyperedges e i containing node v i , calculate the attractive force resultant of node v i

[0063] 2) Calculate the repulsive force resultant of node v i

[0064] 3) Calculate the force-based loss

[0065] Fourth step, optimize the model according to the loss function, and output the node classification prediction result after optimization of the model.

[0066] 1) Calculate the prediction value of the graph model, and the prediction value of node v i is

[0067] 2) Calculate the cross-entropy loss of node classification

[0068] 3) Construct the joint loss and use the Adam optimizer to continuously train and optimize the model.

[0069] 4) Obtain the optimized model, and output the prediction value of node classification.

[0070] In combination with the scheme of the application, the experimental analysis is as follows:

[0071] The method uses commonly used public hypergraph data sets, and tests the current main hypergraph representation learning method, so as to evaluate the effectiveness of the application.

[0072] (1) Introduction of hypergraph data set

[0073] The optimized model is tested for performance on five public data sets. The detailed information of the data sets is shown in Table 1:

[0074] ​​Table 1 dataset statistics

[0075]

[0076]

[0077] Cora contains 2078 articles with 1433-dimensional bag-of-words attributes, where 1 indicates the presence of the word, and 0 otherwise. Cora divides the articles into 7 classes and constructs 1579 hyper-edges through citation relationships. Citeseer is a citation dataset containing 3312 papers, each with 3703-dimensional bag-of-words attributes, and 1079 hyper-edges are constructed using citation relationships, with 6 classes. Cora-CA This dataset has the same number of articles as Cora, but uses co-authorship relationships to define hyper-edges, contains 1433-dimensional bag-of-words information and 7 classes. Zoo is a dataset from the UCI Machine Learning Repository, commonly used for classification. Zoo contains 42 hyper-edges and 101 animal nodes with 17 attributes, with a total of 7 classes. TU2012 is a 3D model dataset from Taiwan University, containing 2012 3D shapes from 67 categories and 2012 hyper-edges.

[0078] (2) Experimental results of the method in mainstream methods

[0079] The experimental results of the method in mainstream methods are shown in Table 2. Among them, MLP is a multi-layer perceptron model, which is a classic multi-layer fully connected neural network and is generally considered as the basis of deep learning in related research. MLP is not used to process graph structure data, i.e. there is no message passing process. Hypergraph Neural Networks (HGNN) is a deep learning method based on hypergraph, which introduces hypergraph Laplacian into graph convolution operation. HGNN uses a simplified Chebyshev to approximate convolution hypergraph, thereby speeding up the calculation. HyperGCN converts hypergraph into weighted graph by unfolding, thereby converting the problem into a conventional semi-supervised graph representation. FastHyperGCN is an accelerated variant of HyperGCN, which uses initial attributes to construct Laplacian matrix instead of weights. HNHN designs non-linear activation functions and normalization methods for hyper-nodes and hyper-edges respectively, which applies graph convolution to hypergraph. HyperSAGE is an inductive learning method on hypergraph, which can be used for nodes that have not been seen before, increasing the applicability of the model. UniGCNII combines residual connection and identity mapping, effectively alleviating the performance decline caused by over-smoothing phenomenon when the model layer is stacked deep.

[0080] Table 2 results of node classification on mainstream methods

[0081]

[0082]

[0083] From the results in Table 2, it can be seen that in most cases, the best results are achieved by the present method, for different graph learning algorithms and different datasets, indicating the effectiveness and applicability of the present method in hypergraph representation learning.

[0084] The above-described embodiments only express the implementation of the present application, but cannot be interpreted as a limitation to the scope of the patent of the present application. It should be pointed out that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which all belong to the protection scope of the present application.

Claims

1. A method for modeling and representing multi-agent hypergraphs, characterized in that, The graph representation learning process is defined as a multi-agent optimization process. The message passing mechanism in existing hypergraph representation learning methods is used as one agent interaction method, and a force-based agent interaction method is designed. These two agent interaction methods are then used to jointly optimize the graph model on downstream tasks, and the optimized graph model is used to output the prediction results. The specific steps are as follows: Step (1): Formalize the graph representation learning process from the perspective of multi-agent agents; Step 1.1) Define the agent; define the physical or abstract entity that can perceive the surrounding environment and other agents as the agent. The agent can communicate with other members in a multi-agent system and react according to its current state when interacting with them; any given agent With information , A collection of intelligent agents; express The inherent properties, express The current state is used in the decision-making process or other tasks; In graph representation learning, nodes in the graph are considered to have attributes. and state The graph represents the state of the agent; the inherent properties of the nodes are the attributes of the agent. Intelligent agent group It is a collection of any number of intelligent agents based on specific functions; an intelligent agent is contained in multiple intelligent agent groups; It is a set of agent groups; the edges in the graph represent a type of agent group; when an agent group contains only two agents, it represents a pairwise relationship in a simple graph. Step 1.2) Formalize the learning process graphically; An agent receives information from other members through interaction and then performs actions based on its state. A multi-agent system includes two interaction methods: the first is global interaction, where each agent in the system interacts with all other agents; the second is intra-group interaction, where agents interact within their own group and do not communicate with or influence members outside their group. This represents a certain interaction method, where, It is a group of intelligent agents, representing a group of individual intelligent agents that interact with each other. It represents a specific interactive operation, which is determined by the multi-agent system environment in the actual application; Given a multi-agent system, construct an agent graph. ,in, It is a collection of intelligent agents. It is a collection of intelligent agents. A collection of agent interaction methods; a multi-agent system learns a mapping function. Used to compute downstream tasks agent states in Then through the agent's state Forecast downstream tasks. It is a prediction based on a multi-agent graph model. For the prediction function of downstream tasks, The true label of the agent node; Optimize the agent's state to meet the requirements of the current task in a multi-agent system; based on the given downstream task... , For the collection of downstream tasks and optimization process The agent iteratively updates its state information by collaborating / communicating with other members to achieve optimal task performance; Step (2): The message passing mechanism in the hypergraph representation learning method is used as an interaction method for intelligent agents, which is an intra-group interaction; Based on the existing graph message passing mechanism, it is extended to hypergraph representation learning, from the message passing of ordinary edges to the message passing mechanism of hyperedges; the message passing mechanism of hypergraphs is uniformly represented in the following form; ； in, Indicates the super edge. It is a set of hyperedges, where each hyperedge is connected to a node. Related; message functions via hyperedge Topological clustering nodes Regarding the neighboring nodes on the superedge Information; update function It integrates all nodes Related and the output of the previous layer and output the next layer. For intelligent agents The representation vector is obtained as The matrix representing the vectors of the entire graph is then... The output of the last layer The state marked as an agent ; Step (3): Design a force-based intelligent agent interaction method, including attraction interaction within the group and repulsion interaction globally; Step 3.1) Extend the spring charge model to hypergraph representation learning, making it applicable to groups of agents; for a given agent The agent in the same hyperedge attracts the agent, and the sum of the attraction forces is calculated as follows: ； in, It is any one containing the first Hyperedge of an intelligent agent Represents intelligent agents The state is output by the last layer of the graphical model, and the hyperparameters are... To control the proportion of attraction between agents, the larger the value, the greater the attraction, and the closer the states of the corresponding agents tend to be. Step 3.2) Define the repulsive force in the spring-electric model. The sum of the repulsive forces of the agents is represented as follows: ； in, It is a collection of intelligent agents The total number of intelligent agents, and Similarly, it is a hyperparameter that controls the magnitude of the force. If it is a positive vector, set it as a constant vector. ; Step 3.3) Intelligent Agent The combined effect of attraction and repulsion is expressed as ; Step (4): Combine the two agent interaction methods from Step (2) and Step (3) to optimize the graph model, and use the optimized graph model to predict the results; Step 4.1) Select semi-supervised node classification as the downstream task and use the agent's representation for prediction; agent The soft label prediction is: ； in, The final output of step (2) is the first... The state of each agent; Step 4.2) The loss function for the downstream task is cross-entropy loss, which is described as follows: ； in, For nodes The label vectors have a total of A class is 1 for the dimension of the correct category and 0 for other dimensions; Step 4.3) The loss function based on attraction and repulsion is expressed as follows: ； Step 4.4) The final loss function includes and The Adam optimizer is continuously trained and optimized until the best performance is obtained; the final loss function is expressed as: ； in, It is a hyperparameter for controlling the loss rate; Step 4.5) Use the optimized hypergraph model to output the prediction results for downstream tasks.

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