An industry chain integrity evaluation model, system and method

Abstract

The application discloses an industry chain integrity evaluation model, system and method, relates to the technical field of industry chain evaluation, and the model comprises a node feature coding module, a candidate node set selection module, a pair coding generation module and an evaluation module; the node feature coding module is used for learning the feature representation of nodes in an industry chain implicit heterogeneous graph based on a message passing neural network; the candidate node set selection module is used for screening out nodes which have a significant influence on a target node pair from the industry chain implicit heterogeneous graph based on PPR scores; the pair coding generation module is used for calculating the pair coding of the target node pair based on a graph attention mechanism, and capturing the complex relationship between nodes; and the evaluation module is used for predicting the existence probability of the target node pair through a multilayer perceptron, and quantitatively evaluating the predicted existence probability through an integrity evaluation index. The application realizes accurate capture of the complex relationship between nodes in the industry chain implicit heterogeneous graph, and can comprehensively quantify the influence relationship between nodes.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industry chain evaluation, in particular to an industry chain integrity evaluation model, system and method based on a graph attention mechanism and a message passing network. BACKGROUND

[0002] Industry chain integrity encompasses the interdependence and coordination of each link within the industry chain, as well as the overall resilience and recovery ability. This concept not only involves the interdependence of each link within the industry chain, but also includes the ability to respond to external shocks and disturbances.

[0003] Specifically, the resistance of the industry chain refers to its ability to respond to various shocks and disturbances. An industry chain with strong resistance can minimize the impact and maintain normal operation when faced with shocks. In the modern economy, industry chains often face the adverse effects of internal and external factors such as natural disasters, market fluctuations, and supply chain disruptions. Therefore, strong resistance is crucial for reducing the losses caused by these risks and ensuring the sustainable development of the industry chain.

[0004] The recovery ability of the industry chain emphasizes the ability of the industry chain to quickly recover to normal operating conditions after being impacted, or even to transform crises into development opportunities. This ability is crucial for responding to emergencies and crises, as it can minimize production disruptions and losses and promote the rapid adaptation and upgrading of the industry chain. An industry chain with good recovery ability can better adapt to changes, create more value and competitive advantage.

[0005] Industry chain integrity is not only an important factor in ensuring the stable operation of the industry chain, but also a key element in achieving coordinated regional economic development and improving national competitiveness. By improving the resistance and recovery ability of the industry chain, the stability of the economic system can be better maintained and enhanced, while providing strong support for sustainable growth and innovation. Therefore, the evaluation and improvement of industry chain integrity has become an indispensable part of modern economic management and strategic planning. With the increasing complexity and interconnectedness of global supply chains, enterprises are not only affected by internal factors, but also by external factors such as global market fluctuations, natural disasters, and political events. As a result, evaluating the integrity of the industry chain has become an indispensable step to ensure smooth operation of the entire industry chain, enhance the resilience of the industry chain, reduce potential risks, and improve the response ability of enterprises.

[0006] In the current study, there is a relative lack of literature related to the assessment of industry chain integrity, and there is almost no quantitative research on industry chain integrity. Existing literature often analyzes the industry chain from a macro perspective, but rarely provides specific and quantifiable descriptions to assess the level of industry chain integrity. To some extent, the formation process of the industry chain is actually the formation process of the supply chain, accompanied by the formation of the value chain. Its core lies in the supply and demand relationship between different enterprises. Therefore, if we want to deeply study the integrity of the industry chain, we inevitably need to focus on an important part of the industry chain: the supply chain.

[0007] The supply chain is the core component of the industry chain, which undertakes the tasks of managing logistics, resource flow, and delivery of products or services. In practice, the management and optimization of the supply chain are of great significance to ensure the integrity and resilience of the industry chain. By establishing a transparent supply chain network, optimizing logistics and inventory management, building supplier relationships, and implementing risk management strategies, enterprises can improve the efficiency and reliability of their supply chains, thereby enhancing the overall integrity of the industry chain. However, in actual assessment, there are problems such as lack of mutual trust between enterprises, intense competitive relationship, protection of business secrets, etc., which make it difficult to obtain key information in the supply chain, thereby posing challenges to the assessment of the integrity of the entire industry chain.

[0008] Previous studies have mainly used traditional methods such as Delphi method, system analysis method, and interview method to improve the visibility of supply chain information. In addition, some technical means such as sending questionnaires by enterprises, using intermediaries to monitor the supply chain, and deploying tracking technology (including RFID, etc.) can also help to improve the visibility of hidden information. However, these methods are often influenced by the experience and bias of practitioners and researchers, which may lead to less objective and less repeatable assessments. In addition, these methods usually require cooperation between enterprises to share information, but the accuracy and completeness of the information cannot be guaranteed. Due to the lack of mutual trust, suppliers may intentionally not disclose strategic relationships, operational practices, and environmental practices. SUMMARY

[0009] The present application provides an industry chain integrity assessment model, system and method based on graph attention mechanism and message passing network, which can solve the above problems.

[0010] To solve the above problems, the technical scheme adopted by the present application is as follows:

[0011] In a first aspect, the present application provides an industry chain integrity assessment model, which comprises a node feature encoding module, a candidate node set selection module, a pair-wise encoding generation module, and an assessment module.

[0012] The node feature encoding module is configured to learn the feature representation of the nodes in the industrial chain implicit heterogeneous graph based on a message passing neural network, and obtain the feature encoding of the nodes.

[0013] The candidate node set selection module is configured to select the nodes that have a significant impact on the target node pair from the industrial chain implicit heterogeneous graph based on PPR scores according to the feature encoding of the nodes, and obtain a candidate node set.

[0014] The pair encoding generation module is configured to combine the feature encoding of the candidate nodes and the relative position encoding of the candidate nodes with respect to the target node pair, calculate the pair encoding of the target node pair based on a graph attention mechanism, and capture the complex relationship between the nodes.

[0015] The evaluation module is configured to predict the existence probability of the target node pair by a multi-layer perception, comprehensively considering the candidate node set, the feature encoding of the target node, and the pair encoding of the target node pair, and quantitatively evaluate the predicted existence probability by a completeness evaluation index.

[0016] As a further description of the above technical solution, the node feature encoding module uses a graph convolution network as an encoder to encode the features of each node in the industrial chain implicit heterogeneous graph; the graph convolution network uses a ReLU function as an activation function; the graph convolution network includes multiple graph convolution layers, each layer updates the feature representation of the nodes and can capture neighborhood information of different scales; the output of each layer becomes the input of the next layer, thereby allowing information to propagate in the entire graph structure, and after multi-layer message passing learning, the node i learns the node feature encoding containing neighbor information and global information.

[0017] As a further description of the above technical solution, before encoding the industrial chain implicit heterogeneous graph, it needs to be preprocessed, including: representing the industrial chain implicit heterogeneous graph as an adjacency matrix and a node feature matrix; adding a self-loop to each node in the adjacency matrix; and normalizing the adjacency matrix.

[0018] As a further description of the above technical solution, the PPR score calculation formula used by the candidate node set selection module is:

[0019]

[0020] Where PPR(i, k) represents the personalized PageRank value from node i to node k, a is a damping factor, N(j) represents the neighbor node set of node j, deg(k) represents the out-degree of node k, and δ ij is an indicator function, δ ij = 1 when i = j, and δ ij = 0 otherwise.

[0021] As a further description of the above technical solutions, for a target node pair (a, b) in the industry chain implicit heterogeneous graph, the method for screening out nodes that have a significant impact on the target node pair (a, b) includes:

[0022] calculating a personalized PageRank value ppr(a, u) of the node a to the node u, and a personalized PageRank value ppr(b, u) of the node b to the node u, the node u being a root node in the industry chain implicit heterogeneous graph;

[0023] for a neighbor node of a certain type in the industry chain implicit heterogeneous graph for the target node pair (a, b), setting a PPR threshold η for the neighbor node, and then retaining all nodes whose PPR scores with respect to the two nodes a and b in the target node pair (a, b) are higher than the PPR threshold η, that is, obtaining nodes that have a significant impact on the target node pair (a, b);

[0024] The specific selection formula of the filtered node set of each type of node that has a significant impact on the target node pair (a, b) is as follows:

[0025]

[0026] wherein, is the filtered node set of the neighbor node of the type π, η π is the PPR threshold corresponding to the neighbor node type π.

[0027] As a further description of the above technical solutions, the pairwise encoding formula used by the pairwise encoding generation module is as follows:

[0028]

[0029] wherein, w(a, b, u) measures the importance of the node u to the target node pair (a, b), h(a, b, u) is the feature encoding of the node u with respect to (a, b), V is the set of all nodes in the graph, and is the Hadamard product, indicating that the corresponding elements of two vectors are multiplied.

[0030] As a further description of the above technical solutions, the feature encoding h(a, b, u) of the node u with respect to (a, b) is defined as:

[0031]

[0032] wherein, h u is the feature encoding of the node u, represents the relative position encoding of the node u with respect to the target node pair (a, b), is a concatenation operator, and W is a learnable weight matrix used for linear transformation of the concatenated vector.

[0033] The importance w(a, b, u) of the target node pair (a, b) to the node u is modeled by attention as follows:

[0034]

[0035] where h a ,h b represent the feature encoding of nodes a, b, respectively; represent the set of nodes left in the graph after removing nodes a and b; φ(·) is the GATv2 attention mechanism; is the unnormalized attention weight of node u for (a, b); w(a, b, u) is the normalized attention weight obtained after using the softmax function.

[0036] As a further description of the above technical solution, the relative position encoding calculation formula of node u with respect to the target node pair (a, b) is:

[0037] rpe (a,b,u) = MLP (ppr(a, u), ppr(b, u))

[0038]

[0039] where MLP is a multi-layer perceptron used to parameterize the relative position encoding calculation method.

[0040] As a further description of the above technical solution, the prediction score function used by the evaluation module is:

[0041]

[0042] where p(a, b) is the probability of predicting that there is a link between nodes a and b; σ is the sigmoid function; is the Hadamard product; is the concatenation operator; h a represents the feature encoding of node a; s(a, b) represents the pair encoding information formed by the node pair (a, b); and belong to the candidate node set, respectively representing the number of common neighbors, the number of one-hop neighbors, and the number of more than one-hop neighbors of the node pair (a, b).

[0043] As a further description of the above technical solution, the calculation formula of the industry chain integrity score is as follows:

[0044]

[0045] where RT(C) represents the resistance capability measure of the industry chain, and RL(C) represents the recovery capability measure of the industry chain.

[0046] In a second aspect, the present application provides an industrial chain integrity evaluation system, which embeds the industrial chain integrity evaluation model of the first aspect.

[0047] In a third aspect, the present application provides an industrial chain integrity evaluation method, which evaluates the integrity of an industrial chain based on the industrial chain integrity evaluation model of the first aspect.

[0048] Compared with the prior art, the present application has the following beneficial effects:

[0049] 1) The present application introduces message passing neural networks and graph attention mechanisms, which accurately capture the complex relationships between nodes in the industrial chain implicit heterogeneous graph, effectively solving the problems of poor information visibility, strong subjectivity and poor repeatability in traditional methods. By PPR scoring to filter key nodes and generate pairwise encoding, the influence relationship between nodes can be fully quantified, improving the objectivity and accuracy of the evaluation. In addition, the multi-layer perceptron combines multi-dimensional features to quantitatively evaluate the integrity of the industrial chain, overcoming the limitations of existing research lacking specific and quantifiable descriptions, and providing a scientific basis for the optimization and risk management of the industrial chain.

[0050] 2) The industrial chain implicit heterogeneous graph abstractly represents the complex structure of the industrial chain, which can adapt to the information incompleteness and implicit connections commonly existing in real industrial chain data; the industrial chain implicit heterogeneous graph regards the enterprises, products and their interactions in the industrial chain as nodes and edges in the heterogeneous graph, enabling the model to intelligently infer those not obvious or missing connections, not only enhancing our understanding of the complex dynamics within the industrial chain, but also improving our ability to identify and fill information gaps, thus more accurately revealing the key connections and potential synergies in the industrial chain.

[0051] 3) The industrial chain resistance capacity index and the industrial chain resilience index related to integrity on the industrial chain graph dataset; these indexes provide a standard for the evaluation of the industrial chain, helping to understand the operation of the industrial chain and evaluate its resistance and resilience. To some extent, it fills the research gap in this field and provides a scientific method for evaluating the integrity of the industrial chain.

[0052] 4) The model of the present application is based on the link prediction method of the graph attention mechanism and the message passing neural network, and depicts the related indicators of the integrity of the industrial chain: the link prediction based on the attention mechanism and the message passing neural network is very suitable for industrial chain analysis, because it can comprehensively consider various structural information in the industrial chain, including local structural information, global structural information and feature similarity and other factors; in this way, the model of the present application can learn the rich feature representation between enterprises and products, and better capture the relevance between them; in the context of the industrial chain, this means that the model can identify and predict the potential connections between enterprises and between enterprises and products, which is crucial for understanding the complex dynamics of the industrial chain and optimizing the structure of the industrial chain; especially in the face of incomplete information in the industrial chain, this link prediction method can intelligently fill in the information gaps and improve the understanding of key connections in the industrial chain; therefore, the model of the present application not only improves the accuracy of link prediction, but also provides strong support for industrial chain management, and the performance of the model in the real industrial chain dataset exceeds other advanced graph neural network methods, which indicates the effectiveness and practicality of the model, and it provides a higher level of performance for the evaluation of the integrity of the industrial chain.

[0053] 5) The existing pair-wise encoding method has limitations, often only models partial potential factors such as local structure, ignoring other key factors such as node attributes, global structure and feature similarity between nodes, in addition, existing methods often use a unified pair-wise encoding strategy, using the same combination of prediction factors for all links, lacking adaptability to different link characteristics. In the industrial chain dataset, different industries and product connections may require different combinations of prediction factors. The method of the present application can adaptively model multiple link prediction factors, which is crucial for improving the prediction accuracy of the model in the industrial chain dataset.

[0054] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the following will describe the embodiments of the present application, and the accompanying drawings will be described in detail as follows. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments, it should be understood that the following drawings only show some embodiments of the present application, therefore should not be regarded as a limitation to the scope, for those skilled in the art, without paying creative labor, other related drawings can also be obtained from these drawings.

[0056] Figure 1 is the overall process of the industrial chain integrity evaluation model described in the embodiments;

[0057] Figure 2 is the heterogeneous graph and the implicit heterogeneous graph described in the embodiments;

[0058] Figure 3 Candidate node set selection module flowchart in the embodiment;

[0059] Figure 4 Pairwise encoding generation module flowchart in the embodiment;

[0060] Figure 5 Evaluation module flowchart in the embodiment. DETAILED DESCRIPTION

[0061] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application.

[0062] The embodiments of the present application provide an industry chain integrity evaluation model based on a graph attention mechanism and a message passing network, as shown in Figure 1 , which includes a node feature encoding module, a candidate node set selection module, a pairwise encoding generation module and an evaluation module. The industry chain integrity evaluation model can predict links in an implicit heterogeneous industry chain network graph, and quantitatively evaluate the prediction results through an integrity evaluation index, realize integrity evaluation on an industry chain dataset, and the specific description is as follows:

[0063] 1. Parameter definition

[0064] Node pair: In a graph G=(V,E), an ordered pair (u,v) composed of any two nodes u and v, where V is the set of all nodes in the graph, and E is the set of all edges in the graph. If (u,v)∈E, then u and v are called directly connected node pairs; if there is no direct edge between u and v, but they can reach each other through other nodes and edges in the graph, then they are called indirectly connected node pairs.

[0065] Pairwise encoding: Pairwise encoding is a technique for capturing the relationship between node pairs. It encodes node pairs to generate feature representations that can reflect the relationship between node pairs. This method is very useful in processing graph structured data, especially in tasks that need to consider the complex relationship between node pairs, such as knowledge graph completion and molecular pair similarity calculation. The core idea of pairwise encoding is to map each pair of nodes (v i ,v j ) in the graph to a feature vector, representing the relationship between the pair of nodes. For each pair of nodes (v i ,v j ) in the graph, pairwise encoding generates a feature vector e ij , which can contain nodes v i and vj The characteristics of and the characteristics of the edges between them are expressed by the formula e. ij =f(h) i ,h j ,a ij ), where h i and h j These are nodes v i and v j Feature representation, a ij is the feature of the edge between two nodes, and f is an encoding function. The encoding function can be a simple connection operation or a more complex neural network model. For example, a multilayer perceptron (MLP) can be used to encode node pairs: e ij =MLP([h i h j ||a ij ]), where (||) represents the vector concatenation operation.

[0066] Heterogeneous diagrams: such as Figure 2 As shown in (a), a heterogeneous graph is a data structure consisting of a set of nodes V and a set of links E, denoted as G = (V, E). The heterogeneous graph is also associated with a node type mapping function φ: V → A and a link type mapping function Ψ: E → R. Specifically, the node type mapping function φ maps each node in the graph to a type in a predefined set of node types A, and the link type mapping function Ψ maps each edge in the graph to a type in a predefined set of edge types R. Furthermore, |A| + |R| > 2.

[0067] Implicit Heterogeneous Graphs: For supply chain data where enterprise types and relationships are largely missing (i.e., the types of nodes and links in the heterogeneous graph are incomplete), this invention defines such heterogeneous graphs as implicit heterogeneous graphs. (See...) Figure 2 As shown in (b), for G=(V,E), there exists a missing set of node types A and a set of link types R, as well as missing mappings φ and Ψ. An extreme case is that the known set of node types A and the set of link types R are both empty sets, in which case the observed G′=(V,E) is actually an isomorphic graph.

[0068] PPR: PPR score is a random walk-based algorithm that measures the relative importance of nodes in a graph and predicts whether there is a potential link between two nodes in the graph. It is a variant of the PageRank algorithm, which was originally developed by the founders of Google to rank web pages based on their importance or quality. PPR score takes into account user preferences, allowing users to start from a specified seed node and calculate the relative importance of other nodes in the graph from these seed nodes. PPR score takes into account the transition probability from the specified seed node to other nodes, as well as a parameter called "jump probability" α. This parameter allows a certain probability of jumping out of the current path during the random walk process and visiting any node in the graph. This design allows PPR score to capture both local relationships and moderately consider the global structure of the graph. The goal of PPR score is to calculate the relative importance of all nodes with respect to the root node u. Starting from the node corresponding to the root node u, each time a node is visited, it has a probability of 1-α to stop the walk and start again from the root node u, or a probability of α to continue the walk and randomly select a node from the nodes pointed to by the current node according to a uniform distribution. After many rounds of walking, the probability of each vertex being visited will also converge to a stable value, at which point the probability can be used for ranking.

[0069] The PPR score of the root node i with transition probability α and the target node j is denoted as ppr(i,j), which represents the relative importance of node j with respect to root node i. The calculation of PPR score is based on the following formula:

[0070]

[0071] where PPR(i,j) represents the personalized PageRank value from node i to node j. α is a damping factor, usually taking a value between 0 and 1, which represents the probability of continuing to walk along the edges in the network during the random walk process. The commonly used value is 0.85. denotes the set of neighbor nodes of node j. deg(k) denotes the out-degree of node k. δ ij is an indicator function, δ ij = 1 when i = j, otherwise δ ij = 0.

[0072] Relative positional encoding (RPE): Relative positional encoding is a way of encoding positions in the Transformer model that differs from the traditional absolute positional encoding. Instead of focusing on the absolute position of elements in a sequence, RPE focuses on the relative distance between elements in a sequence. In exploring the application of relative positional encoding in industry chain datasets, the goal of the invention is to capture the positional relationships between nodes in order to differentially encode different types of information (local information and global information). RPE can provide a way for the model to understand the relative positional relationships between enterprises and products in the industry chain, which is crucial for revealing the complex structure of the industry chain. However, there are challenges in implementing RPE. One effective method is to use the double-radius node labeling (DRNL) technique, but this method has high computational cost on large graph datasets. In addition, traditional RPE methods face difficulties in handling large-scale graphs, as they typically rely on pairwise distances or eigenvectors of the Laplacian operator, which become impractical on large graphs.

[0073] The invention designs a PPR score-based RPE that can both distinguish the relationship between different nodes and the target link and efficiently calculate. Because the goal of PPR score is to calculate the relative importance of all nodes in the graph with respect to the root node u from the root node u. And PPR sets a transition probability α, so that there is a certain probability to jump out of the current path and visit any node in the graph during the random walk process. This design allows PPR scores to capture both local relationships and moderately consider the global structure of the graph. Therefore, the relative importance between nodes calculated by PPR scores can be used as the relative positional encoding between node pairs. Because PPR scores can measure the relative importance between nodes, PPR scores can be used as an intuitive and useful method to understand the structural relationship between node u and the two nodes in the target node pair (a, b). If both ppr(a, u) and ppr(b, u) are high, it means that from node a or node b, it only needs to take a short random walk path to connect to node u. This means that node u has strong influence on the nodes in the target node pair (a, b), i.e., has strong relative importance. If both PPR scores are low, it indicates that the relationship between node u and the target node pair (a, b) may be small. Therefore, PPR scores provide a convenient method to distinguish how nodes are structurally related to the target node pair.

[0074] Because the goal of PPR scores is to compute the relative importance of all nodes in the graph with respect to a root node u, in order to compute the RPE of a node u with respect to a target node pair (a, b), the present application uses the PPR scores of node u with respect to both nodes (a, b) in the target node pair (a, b), i.e., ppr(a, u) and ppr(b, u), in order to better capture the complex relationships between nodes, the present application parameterizes the relative position encoding computation using an MLP, i.e., by feeding ppr(a, u) and ppr(b, u) into an MLP to obtain the relative position encoding value of node u with respect to the target node pair (a, b), the computation formula can be expressed as

[0075] rpe (a,b,u) = MLP(ppr(a, u), ppr(b, u)) (2)

[0076] In many graph-structured data, the order of nodes does not affect the relationship between them. In order to ensure that the relative position encoding is invariant to the order of nodes in the target node pair, i.e., the relative position encodings of (a, b, u) and (b, a, u) are the same, the present application further sets RPE to be equal to the sum of the representations given by (a, b, u) and (b, a, u), avoiding the sensitivity of the model to the order of nodes, thereby improving the generalization ability of the model. The calculation formula is as follows:

[0077]

[0078] is the result obtained by summing rpe (a,b,u) and rpe (b,a,u) calculated by formula (2) respectively, and the invariance of the relative position encoding to the order of nodes in the target node pair is ensured by summing. Considering that formula (3) cannot completely distinguish the three types of relative position encodings of the CN (common neighbor) of the target node pair (a, b), the 1-hop neighbors of a and b, and the >1-hop neighbors of a and b, the present application adopts three independent MLPs, i.e., in formula (2), different MLPs are used to parameterize this computation formula for the CN of the target node pair (a, b), the 1-hop neighbors of a and b, and the >1-hop neighbors of a and b. By using different MLPs for each case, the model can learn how to distinguish these different types of nodes.

[0079] Resistance capability measurement: In an industrial chain, the resistance capability measurement is specifically the number of connections between enterprises and other enterprises, and the stronger the resistance capability, the more the number of connections of the enterprise. In an industrial chain C = (Z, R), there is an enterprise set Z = {z1, z2, …, z n}, the set of inter-enterprise link relationships R = {r1, r2, …, r m}, let A(C) = [zi,j ] n×n , The resistance capability of the industrial chain is defined as:

[0080]

[0081] The recovery capability of the industrial chain is measured: for an industrial chain C=(Z, R), there is a set of hidden relationships R'={r m+1 ,r m+2 ,…,r m+k} between enterprises in the industrial chain, the more hidden links, the stronger the recovery capability, and the recovery capability of the industrial chain is defined as:

[0082]

[0083] 2. Node feature encoding module

[0084] The node feature encoding module is used to learn the feature representation of the nodes in the industrial chain implicit heterogeneous graph based on the message passing neural network, and obtain the feature encoding of the nodes, as follows:

[0085] In the industrial chain implicit heterogeneous network, there are different types of relationships between nodes, and these relationships may carry different meanings. In order to better understand these relationships, the embodiment first uses MPNN (i.e. message passing neural network, which is not a specific model, but a general framework containing the common characteristics of a series of graph neural network models) to extract features of nodes in the industrial chain implicit heterogeneous graph, and generate a code for each node. Through the message passing neural network, the surrounding enterprise nodes exchange information for learning, so that the feature encoding of the node can learn the feature information of the surrounding nodes.

[0086] In the node feature encoding module, the embodiment uses a graph convolutional network (GCN) as an encoder to encode the features of each node in the industrial chain.

[0087] First, the industrial chain implicit heterogeneous graph needs to be represented as an adjacency matrix A and a node feature matrix X.

[0088] The adjacency matrix A is an N×N matrix, where N is the number of nodes, and A ij represents whether there is an edge between node i and node j. The node feature matrix X is an N×D matrix, where D is the feature dimension of each node.

[0089] In order to enable each node to consider its own features in the convolution operation, a self-loop needs to be added to each node in the adjacency matrix. This can be achieved by adding an identity matrix I to the adjacency matrix A, that is,

[0090] After that, the adjacency matrix is normalized. The calculation formula is: Wherein is the degree matrix of

[0091] After completing the preprocessing of the graph data set (i.e. the implicit heterogeneous graph of the industrial chain), the GCN model is constructed, and the core operation of GCN is graph convolution, and its basic form can be represented as:

[0092]

[0093] Wherein, H l represents the node feature matrix of the lth layer, H (l+1) represents the output feature matrix of the l+1 layer, W l is the weight matrix of the lth layer, and sigma is a nonlinear activation function, and ReLU function is adopted as the activation function here. The GCN model can contain multiple graph convolution layers, each layer will update the feature representation of the node, and can capture the neighborhood information of different scales. The output of each layer becomes the input of the next layer, thereby allowing information to propagate in the entire graph structure, and after learning through multi-layer message passing, the node i will learn the node feature encoding h i .

[0094] 3, candidate node set selection module

[0095] In processing large-scale graph data, the link prediction task faces significant challenges, especially in complex data sets such as industrial chains. Directly performing link prediction on all possible node pairs not only has high computational cost, but also dramatically increases the demand for memory. In order to solve this problem, the invention adopts a selective and sparse attention mechanism, so that the model only focuses on a small part of the nodes in the graph, thereby improving the efficiency of completing the missing edges in the industrial chain.

[0096] ​In the candidate node set selection module, it is necessary to determine the node set of value for the target node pair (a, b) of interest. Through the selection of this small part of the node set, they provide important context information for the target node pair (a, b) in a small number of cases to best learn the paired information. The goal of PPR score is to calculate the relative importance of all nodes in the graph relative to the root node u from the root node u. Therefore, PPR score can be a good tool to measure the influence of one node on another node. The present application measures the relative importance of node u to the two nodes in the target node pair (a, b) by using PPR score, and the calculation formula of PPR score is shown in formula (1).

[0097] That is, for the target node pair (a, b), the PPR scores of node u for nodes a and b in the 1-hop neighbors of CN, a and b of the target node pair (a, b) and the >1-hop neighbors of a and b are calculated, that is, ppr(a, u) and ppr(b, u) are calculated, as shown in formula (2). Figure 3 The present application sets a threshold for different types of neighbor nodes, and then retains all nodes with PPR scores higher than a certain threshold η relative to the two nodes in the target node pair, so as to select the node set of value for the target node pair (a, b). In specific implementation, the present application selects different types of high-value nodes for the target node pair (a, b) by applying different thresholds to CN, 1-Hop and >1-Hop nodes. The specific selection formula of the filtered node set of each type of node is as follows:

[0098]

[0099] Wherein, is the filtered node set of neighbor nodes of type π, η π is the PPR threshold corresponding to the neighbor node type π, where π∈{CN, 1-Hop, >1-Hop}.

[0100] 4, Pairwise encoding generation module

[0101] In the industrial chain data set, the link prediction task faces significant challenges because these data sets contain numerous entities and complex relationship networks. In order to cope with this complexity, the link prediction model needs to be able to adapt to the diversified link types formed by multiple factors.

[0102] The present application introduces an attention mechanism and proposes a pairwise encoding generation module that can widely cover potential link prediction factors and adaptively generate pairwise encoding information for each target node pair, as shown in formula (3). Figure 4As shown, the pair encoding generation module comprehensively considers three link prediction factors, i.e., local structure information, global structure information and feature similarity, and can realize sufficient feature extraction for the target node pair (a, b).

[0103] The present application proposes the following formula of pair encoding:

[0104] s(a,b)=∑ u∈V w(a,b,u)⊙h(a,b,u) (8)

[0105] wherein w(a,b,u) measures the importance of node u to the target node pair (a, b), h(a,b,u) is the feature encoding of node u relative to (a, b), V is the set of all nodes in the graph, and is the Hadamard product, which means that the corresponding elements of two vectors are multiplied.

[0106] We hope that for the target node pair (a, b), node u can learn the weight for the target node pair (a, b) according to the comprehensive consideration of link prediction factors such as local structure information, global structure information and feature similarity, and the present application uses softmax attention which can dynamically learn the relevance of different nodes to the target node pair. In this way, for multiple target links, the contributions of different nodes can be emphasized, so that different LP factors can be flexibly modeled. The attention here is between different sequences (i.e., target node pairs and nodes), so we can regard it as a form of cross-attention.

[0107] In order to enhance the adaptability of pair encoding to various links, various types of information need to be combined and fused together. This enables the attention mechanism to identify and prioritize the relevant information of each target link, facilitating effective modeling of various LP factors.

[0108] The present application considers two types of information, i.e., node feature information and relative position information.

[0109] The node feature information includes the feature representation of the two nodes in the target node pair and the node being processed. The node feature plays a role in link formation and contains structural information features.

[0110] The relative position information reflects the relative position of node u and the target node pair (a, b) in the graph in the local and global structure context.

[0111] By considering the node feature information and the relative position information, the space of potential LP factors can be covered, i.e., three link prediction factors related to links are comprehensively considered, i.e., local structure information, global structure information and feature similarity.

[0112] In the present embodiment, the feature representation of node u is h u, the relative position encoding (RPE) is represented as

[0113] The node importance w(a, b, u) is modeled by attention as follows:

[0114]

[0115] where, denotes the set of nodes left in the graph after removing nodes a and b; φ(·) is the GATv2 attention mechanism; is the unnormalized attention weight of node u for (a, b); w(a, b, u) is the normalized attention weight after using the softmax function. The attention weight w(a, b, u) can be considered as the influence of node u on (a, b) relative to all nodes in G. This enables the model to emphasize different LP factors for each target node pair.

[0116] The node encoding h(a, b, u) contains the combination of the features of node u and RPE, defined as:

[0117]

[0118] where h u denotes the feature representation of node u, rpe (a,b,u) denotes the position encoding of node u relative to (a, b), || is the concatenation operator, and W is a learnable weight matrix used for linear transformation of the concatenated vector.

[0119] By calculating the attention weight w(a, b, u) and the node feature h(a, b, u) respectively, the pair-wise encoding information s(a, b) of the node pair (a, b) can be calculated. This pair-wise encoding s(a, b) not only integrates the local structural features in the industrial chain dataset, but also comprehensively considers the global structural information, making it more comprehensive to capture the complex link relationships between enterprises, products, and products and enterprises. The advantage of this encoding method is that it can adapt to the diversity and dynamics of the industrial chain data, thereby effectively completing the missing edges in the industrial chain. In this way, the model not only can identify the key nodes and potential links in the industrial chain, but also can predict new or missing links, providing data support for the optimization and expansion of the industrial chain.

[0120] 5. Evaluation module

[0121] In the evaluation module shown in Figure 5 , the present application integrates the candidate node set, the feature encoding of the target node, and the pair-wise encoding of the target node pair to predict the missing edges of the dataset in the industrial chain and complete the completion of these missing edges.

[0122] To fully capture the local and global structural information, the present application adopts a comprehensive method that combines node feature encoding, pair encoding, and the structural information of node pairs, including the number of common neighbors, the number of 1-hop neighbors, and the number of more than 1-hop neighbors. This method not only reveals the direct connection between nodes, but also reveals the more complex interactions and dependencies in the industrial chain. The score function is:

[0123]

[0124] where p(a, b) is the probability of predicting the existence of a link between nodes a and b; σ is the sigmoid function, which is used to convert the output of MLP into a probability value; is the Hadamard product, also known as element multiplication, which represents the multiplication of corresponding elements of two vectors; is the concatenation operator, which is used to concatenate two vectors or matrices to form a new vector or matrix; h a represents the feature encoding of node a, s(a, b) represents the pair encoding information formed by node pair (a, b), and represent the number of common neighbors, the number of 1-hop neighbors, and the number of more than 1-hop neighbors of node pair (a, b), respectively.

[0125] After obtaining the model prediction result p(a, b), a threshold is set. If the prediction probability value p(a, b) is greater than the threshold, it is considered that there is an edge connected to the target node pair (a, b), i.e., the value is set to 1 in the adjacency matrix. After traversing all target links (i.e., target node pairs), the task of completing the missing edges of the industrial chain is completed.

[0126] Then, according to the adjacency matrix, the resistance RT(C) and recovery RL(C) of the industrial chain are calculated;

[0127] Then, according to the formula for calculating the integrity score of the industrial chain, the integrity score of the industrial chain is calculated. The higher the score, the stronger the integrity. The formula for calculating the integrity score of the industrial chain is as follows:

[0128]

[0129] where RT(C) represents the resistance of the industrial chain, and RL(C) represents the recovery of the industrial chain.

[0130] 6. Experiment and analysis

[0131] The application compares the link predictor with attention and position encoding (LPAPE) proposed in the application with other state-of-the-art methods on real-world industry chain datasets, and gives the experimental settings and experimental result analysis. The prediction performance of the LPAPE model is evaluated on the Cora, Citeseer and Pubmed datasets, and the generalization performance of the model is further evaluated.

[0132] 6.1, Dataset

[0133] Table 1 Integrated circuit industry chain data size table

[0134]

[0135] The integrated circuit industry chain dataset used in this experiment covers the real financial data of 1732 listed companies in China from 2018 to 2023 and 430 upstream and downstream product data compiled, totaling more than 40,000 data. Among them, the financial data contains 18 financial related indicators such as liquidity ratio, net asset yield, asset-liability ratio, inventory turnover rate, etc., which reflect the financial and operating conditions of these listed companies. Through these data, the supply relationship and value link of the industry chain can be deeply analyzed, so as to find important features hidden in it. Data collection and sorting work adopts multiple ways. Among them, financial data mainly comes from RESSET financial research database, and is obtained by manual query and website download sorting, and part of the financial indicator data is supplemented and improved by Wind database and Tianyancha, to ensure the comprehensiveness and accuracy of the data.

[0136] In addition, for each listed company, the dataset also contains a timestamp data, a company risk score data and two company investment relationship data. The company risk score data mainly comes from the Wind database, and the current timestamp of the company's operating risk is evaluated in detail. These risk scores can reflect the company's market position, financial stability and future development potential. The two company investment relationship data mainly involve the number of investors and the number of external investments. These data provide important reference for deep mining of hidden competition or partnership information. The number of investors can reflect the financing ability and investor confidence of the enterprise, while the number of external investments can show the strategic expansion and industrial layout of the enterprise.

[0137] In addition, the upstream and downstream product data is the integrated circuit industry chain graph structure composed of upstream and downstream connection relationship, which directly reflects the complete appearance and internal mechanism of the industry chain, and is the main framework of the integrated circuit industry chain dataset.

[0138] Table 2 Scientific literature graph dataset introduction

[0139]

[0140] As shown in Table 2, the Cora dataset contains 2708 scientific publications, divided into 7 classes, such as case-based, genetic algorithms, neural networks, etc. Each publication is described by a 1433-dimensional 0 / 1 value word vector, indicating the absence / presence of corresponding words in the dictionary. The citation network consists of 5429 edges, representing the citation relationship between papers. The Citeseer dataset consists of 3312 scientific publications, divided into six categories, including Agents, AI, DB, IR, ML and HCI. Each node has a 3703-dimensional binary feature vector representing the content of the paper. The citation network contains 4732 edges, recording the citation or cited information between papers. The Pubmed dataset contains 19717 scientific publications on diabetes, divided into three categories, such as Diabetes Mellitus, Experimental, Diabetes Mellitus Type 1 and Diabetes Mellitus Type 2. Each publication is described by a TF / IDF weighted word vector in a dictionary consisting of 500 unique words. The citation network consists of 44338 links, showing the citation relationship between papers.

[0141] The three datasets of Cora, Citeseer and Pubmed are well-known scientific literature graph datasets, containing research papers in the fields of computer science, computer science and biomedical science, respectively. The nodes in these datasets represent papers, and the edges represent the citation relationship between papers. The node features are usually based on the text content of the papers, and are used for graph machine learning tasks such as node classification and link prediction.

[0142] 6.2, Experimental setup

[0143] Table 3 Experimental environment configuration

[0144]

[0145] In the experimental phase, we evaluated the performance of the model on real industry chain datasets, using evaluation metrics commonly used in link prediction tasks, including Accuracy, Auprc, Auroc, and F1 score. Each method was adjusted to the optimal parameter setting on our dataset, and each training was over 200 rounds. At the same time, each method was trained 5 times independently, and the average value of the evaluation index was taken as the final evaluation result of the model. The learning rate of our LinkPredictor with Attention and Position Encoding (LPAPE) model was set to 0.005, and the η π , π∈{CN,1-Hop,>1-Hop} were set to 0.01, 0.01, 0.0001, respectively, and the weight decay coefficient was 0.0001. The dataset was divided into training set, validation set and test set according to 85:5:10 to obtain the best experimental results. All training and validation processes of the above experiments were completed through a server cluster and a personal computer, and the experimental environment configuration is shown in 2-3.

[0146] After that, in order to further evaluate the generalization performance and adaptability of the LPAPE model we proposed on various datasets, we conducted link prediction evaluation experiments on three scientific literature graph datasets, using the MRR (Mean Reciprocal Rank) index widely used in link prediction to evaluate the performance of the LPAPE model we proposed. The purpose of this step is to verify that the LPAPE model still has excellent prediction performance when facing various graph data, and has excellent generalization performance and robustness.

[0147] 6.3, Comparative method

[0148] In order to make a comprehensive comparison, we compared with other 6 advanced link prediction neural network models:

[0149] 1. GraphSAGE (Graph Sample and Aggregated) is a graph neural network method for node classification and link prediction. It learns the representation of nodes by sampling and aggregating the features of neighboring nodes.

[0150] 2. GIN (Graph Isomorphism Network) is a graph neural network with graph isomorphism properties, which can maintain the invariance of node arrangement.

[0151] 3. GAT (Graph Attention Network) is a graph neural network that allows nodes to dynamically focus on their neighbor nodes.

[0152] 4. GCN (Graph Convolutional Network), a classic graph neural network that learns node representations by aggregating information from neighboring nodes.

[0153] 5. GAE (Graph Auto-Encoders), an unsupervised learning model for graph-structured data that learns low-dimensional embeddings of nodes using an encoder-decoder architecture.

[0154] 6. NCNC (Neural Common Neighbor with Completion), a graph neural network model specifically designed for link prediction tasks. This model improves link prediction performance by studying the incompleteness of the graph.

[0155] 6.4. Experimental Results

[0156] Table 4: Objective Index Evaluation Results

[0157]

[0158] The objective index evaluation results shown in Table 4 show that the LPAPE model outperforms other methods in the link prediction task. Specifically, LPAPE achieved the highest scores in Accuracy, Auprc, Auroc, and F1 score, which are 0.930, 0.914, 0.889, and 0.922, respectively. This outstanding performance highlights the high accuracy and robustness of LPAPE in handling link prediction problems.

[0159] Compared with the sub-optimal NCNC model, LPAPE improved by 28%, 16.4%, 14.9%, and 24.2% in Accuracy, Auprc, Auroc, and F1 score, respectively. This significant improvement indicates that LPAPE can effectively capture complex relationships and dependency information in the implicit heterogeneous graph of the industrial chain when dealing with link prediction problems. These significant improvement percentages indicate that LPAPE can effectively capture complex relationships and dependency information in the heterogeneous graph of the industrial chain, resulting in significant performance improvements in the link prediction task.

[0160] The relatively poor performing models, GCN and GAE, failed to meet expectations on certain metrics. This could be related to GCN's over-reliance on first-order neighbor information, ignoring higher-order neighbor information, which limits its ability to handle complex graph structures. While GAE achieved some success in Auprc and Auroc, it performed poorly in Accuracy and F1 score, which could be due to its limitations in handling specific types of data, such as being more suitable for graph data with explicit edge labels, and being affected in performance when dealing with missing or ambiguous edge labels. Additionally, GAE may not have fully explored the potential relationships between nodes when encoding graph structure information, affecting its performance in link prediction tasks.

[0161] Table 5 Integrity Assessment Results

[0162]

[0163] Table 5 presents the evaluation metrics of the seven methods on integrated circuit industry chain data. Among these data, our model (LPAPE) achieved the highest score in the industry chain integrity assessment. According to the definition of the parameters, the resistance of the industry chain is measured by the number of connections between enterprises and other enterprises, and the more connections, the stronger the resistance of the enterprise. Similarly, the resilience of the industry chain is evaluated by the number of potential connections (i.e., hidden edges), and the more hidden edges, the faster the enterprise can recover when facing risks.

[0164] Our experimental results clearly reveal that our model (LPAPE) has made significant progress in the three industry chain integrity assessment indicators: Resistance, Resilience, and Integrity score, with improvements of 0.05, 0.27, and 0.16 compared to the suboptimal NCNC model. This fully demonstrates the outstanding performance of LPAPE in mining the dependence relationships between enterprises in the industry chain. Further analysis of the underlying reasons, compared to NCNC, our model first uses GCN for feature extraction, then introduces attention mechanisms and position encoding, greatly expanding the model's capture range of feature information, almost covering the entire feature space of industry chain data. Unlike NCNC, which only focuses on structural features, LPAPE considers both local and global features during feature extraction, and performs detailed preprocessing on industry chain data nodes through GCN. On this basis, combined with the attention mechanism, different weights are given to different features, which explains the performance improvement of our LPAPE model.

[0165] Table 6 Link Prediction Results for Scientific Literature Graph Dataset

[0166]

[0167] After that, we also conducted link prediction experiments on the scientific literature graph dataset, as shown in Table 6. In the link prediction experiments on the scientific literature graph dataset, the LPAPE model showed excellent performance on the Cora, Citeseer and Pubmed datasets, with MRR values of 39.50, 65.50 and 40.20 respectively, significantly leading other models. Taking the Citeseer dataset as an example, the MRR value of LPAPE is 15.55 higher than that of GCN, which is 49.95, and on the Pubmed dataset, the MRR value of LPAPE is almost twice that of GCN. These significant differences reveal the significant advantage of LPAPE in identifying the link relationship between nodes, which may be derived from the position encoding and attention mechanism integrated in the LPAPE model. These mechanisms can comprehensively cover potential link prediction factors in the feature encoding stage, thereby providing the model with deeper graph representation learning and link prediction capabilities. Therefore, the LPAPE model not only performs well in the link prediction task, but also provides a new perspective for the analysis and understanding of graph data with its advanced technical strategies.

[0168] The preferred embodiments of the present application have been described above with reference to the drawings, but the present application can be variously changed and modified by those skilled in the art without departing from the spirit and principle of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the present application.

Claims

1. An industry chain integrity evaluation model, characterized in that, The method comprises a node feature encoding module, a candidate node set selection module, a pair encoding generation module and an evaluation module. The node feature encoding module is configured to learn feature representation of nodes in the industrial chain implicit heterogeneous graph based on a message passing neural network, and obtain feature encoding of the nodes. The candidate node set selection module is configured to select nodes that have a significant impact on the target node pair from the industrial chain implicit heterogeneous graph based on PPR scores according to the feature encoding of the nodes, and obtain a candidate node set. The pair encoding generation module is configured to combine feature encoding of the candidate nodes and relative position encoding of the candidate nodes relative to the target node pair, calculate pair encoding of the target node pair based on a graph attention mechanism, and capture complex relationships between the nodes. The evaluation module is configured to predict an existence probability of the target node pair by integrating the candidate node set, feature encoding of the target node pair, and pair encoding of the target node pair through a multilayer perceptron, and quantitatively evaluate the predicted existence probability through a completeness evaluation index. The PPR score calculation formula used by the candidate node set selection module is as follows: where PPR(i, k) denotes the personalized PageRank value from node i to node k, a is a damping factor, denotes the set of neighbor nodes of node j, deg(k) denotes the out-degree of node k, and ij is an indicator function, which is equal to 1 when i = j, and 0 otherwise. ij ij is an indicator function, which is equal to 1 when i = j, and 0 otherwise.​ The prediction score function used by the evaluation module is as follows: where p(a, b) is the probability of predicting the existence of a link between nodes a and b; σ is the sigmoid function; is the Hadamard product; || is the concatenation operator; h a ,h b denote the feature encoding of nodes a, b, respectively; s(a, b) denotes the pair-wise encoding information formed by the node pair (a, b); and belong to the candidate node set, respectively denote the number of common neighbors, the number of one-hop neighbors, and the number of more than one-hop neighbors of the node pair (a, b); MLP is a multi-layer perceptron; The industrial chain completeness score calculation formula is as follows: Wherein, RT(C) represents a resistance capability measure of the industrial chain, and RL(C) represents a recovery capability measure of the industrial chain.

2. The industry chain integrity assessment model according to claim 1, characterized in that, The node feature encoding module uses a graph convolution network as an encoder to encode features of each node in the industrial chain implicit heterogeneous graph; the graph convolution network uses a ReLU function as an activation function; the graph convolution network comprises multiple graph convolution layers, each layer updates feature representation of the nodes and captures neighborhood information of different scales; the output of each layer becomes the input of the next layer, thereby allowing information to propagate in the entire graph structure, and after multiple-layer message passing learning, the node i learns the node feature encoding containing neighbor information and global information; Before encoding the industrial chain implicit heterogeneous graph, preprocessing is required, including: representing the industrial chain implicit heterogeneous graph as an adjacency matrix and a node feature matrix; adding a self-loop to each node in the adjacency matrix; and normalizing the adjacency matrix.

3. The industry chain integrity assessment model according to claim 1, wherein, Supposing that the industrial chain implicit heterogeneous graph has a target node pair (a, b), the method for selecting nodes that have a significant impact on the target node pair comprises: Calculating a personalized PageRank value ppr(a, u) of node a to node u and a personalized PageRank value ppr(b, u) of node b to node u, where node u is a root node in the industrial chain implicit heterogeneous graph; For a neighbor node of the target node pair (a, b) in the industrial chain implicit heterogeneous graph, a PPR threshold η is set for the neighbor node, and all nodes having a PPR score higher than the PPR threshold η relative to the two nodes a and b of the target node pair (a, b) are retained, thereby obtaining nodes that have a significant impact on the target node pair (a, b); The specific selection implementation formula of the filtered node set of each type of node that has a significant impact on the target node pair (a, b) is as follows: wherein, is the set of filtered nodes of neighbor nodes of type π, η π is the PPR threshold corresponding to the neighbor node type π.

4. The industry chain integrity assessment model according to claim 3, characterized in that, The pair encoding formula used by the pair encoding generation module is as follows: where w(a, b, u) measures the importance of node u to the target node pair (a, b), h(a, b, u) is the feature encoding of node u with respect to (a, b), V is the set of all nodes in the graph, is the Hadamard product, which means the multiplication of the corresponding elements of two vectors; The feature encoding of node u with respect to (a, b) is defined as: where h u characteristic encoding of a table node u, denotes the relative position encoding of node u with respect to the target node pair (a, b), || is the concatenation operator, and W is a learnable weight matrix used to perform a linear transformation on the concatenated vector. The importance of node u to the target node pair (a, b) is modeled by attention as follows: wherein, denotes the set of nodes left after removing nodes a and b from the graph; φ(·) is the GATv2 attention mechanism; is the unnormalized attention weight of node u for (a, b); w(a, b, u) is the normalized attention weight after using the softmax function.

5. The industry chain integrity assessment model according to claim 4, wherein, The relative position encoding of node u with respect to the target node pair (a, b) is calculated as: rpe (a,b,u) = MLP(ppr(a, u), ppr(b, u)) where MLP is a multi-layer perceptron used to parameterize the relative position encoding calculation.

6. An industry chain integrity evaluation system characterized by, The system embeds the industrial chain integrity evaluation model of any one of claims 1-5.

7. An industry chain integrity evaluation method characterized by, The method is based on the industrial chain integrity evaluation model of any one of claims 1-5 to evaluate the integrity of the industrial chain.

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