A Feature Self-Representation Learning Method for Multi-Layer Social Network Structure Mining

Abstract

The present invention discloses a feature self-representation learning method for multi-layer social network structure mining, including: constructing a social-oriented multi-layer network structure and an adjacency matrix; constructing a PMI matrix of the network based on the adjacency matrix of each layer of the social network and constructing an objective function for decomposing the adjacency matrix of the social network into a basis matrix and a feature matrix; performing eigen-decomposition on the PMI matrix to obtain shared features and layer-specific features; using a self-representation strategy to learn the mutual relationship between social network nodes, projecting the shared features into the node affine subspace and updating the objective function; repeating the above steps to obtain the final self-representation matrix; performing spectral clustering on the self-representation matrix to obtain the community detection result of the multi-layer social network. By decomposing the features of nodes into shared and layer-specific parts, the present invention proposes a new strategy for characterizing conservative communities in multi-layer social networks, and solves the problem of inter-layer heterogeneity in multi-layer social networks.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-layer networks, and particularly relates to a feature self-representation learning method for multi-layer social network structure mining. Background Art

[0002] Networks (graphs) are important tools for describing and analyzing complex systems in social, biological, information, and engineering sciences, and these networks play an important role in people's daily lives. Among them, the nodes in the network represent the entities in the complex system, and the interaction relationships between the entities are represented by the edges connecting the nodes in pairs. For example, in a social network, the nodes correspond to users, and the edges correspond to the social relationships between users; in a cancer network, the nodes correspond to biological modules (proteins, genes, etc.), and the edges represent the interactions between biological modules. In contemporary society, graphs widely exist in various fields of the world. With the advent of the big data era (especially the rise of online self-media networks), graph data mining has become a necessary means for analyzing various relationships between analysis objects and data and understanding the complex structure of the underlying graph. Exploring the information in complex networks is particularly important for understanding the characteristics of nodes in social networks or for predicting future network behaviors.

[0003] Graph clustering (community detection) refers to finding densely distributed sub-networks in a graph structure, such that the nodes within the same cluster are closely connected, and the connections between different clusters are sparse. Communities are ubiquitous in nature and are the basic units that make up complex systems. Therefore, detecting communities in complex networks helps to mine the potential characteristics in the network and reveal the hidden but meaningful structures in the network.

[0004] However, most current methods only focus on identifying communities in single-layer networks, where the edges between nodes are homogeneous. In fact, the complex systems in real-world networks are composed of the superposition of coupled networks at different layers, and each layer of the network represents an interaction relationship. Considering the cross-network information propagation characteristics between layers of multi-layer networks, analyzing multi-layer networks can obtain more interesting patterns in the real world. For example, people communicate with each other in a social network using multiple communication methods, such as telephone, email, and WeChat; by setting the interaction of each communication type as a layer, a multi-layer social network is formed. Compared with single-layer networks, multi-layer networks effectively overcome the disadvantage of the single representation of the underlying complex system. Therefore, multi-layer networks provide scholars with an opportunity to make full use of the structure and function of multi-layer network systems. For example, in a multi-layer breast cancer network, genes with higher priorities are more likely to be pathogenic genes, and these genes can be used as biomarkers to assist doctors in cancer diagnosis and treatment. In a multi-layer traffic network, the conserved connected subgraphs correspond to areas with frequent communication, which is convenient for traffic management departments to adjust strategies in a timely manner.

[0005] Therefore, detecting conservative communities in a multi-layer network, that is, clustering results where communities are well-connected at all levels, is of extremely important significance for revealing the mechanisms of complex systems. Compared with a single-layer network that only needs to consider the strength and connectivity of the internal structure of the community, a multi-layer network must consider the relationship of the inter-layer coupling structure. In addition, the specific modules and noises in each layer of the multi-layer network also add difficulties to the identification of the network. Summary of the Invention

[0006] To solve the above problems existing in the prior art, the present invention provides a feature self-representation learning method for multi-layer social network structure mining. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0007] The present invention provides a feature self-representation learning method for multi-layer social network structure mining, including:

[0008] S1: Construct a social-oriented multi-layer network structure and the adjacency matrix of the multi-layer network structure;

[0009] S2: Based on the adjacency matrix of each layer of the social network, construct the PMI matrix of the network and construct an objective function for decomposing the adjacency matrix of the social network into a basis matrix and a feature matrix;

[0010] S3: Perform eigen-decomposition on the PMI matrix to obtain the shared features and layer-specific features of the multi-layer social network;

[0011] S4: Use the self-representation strategy to learn the mutual relationship between social network nodes, project the shared features into the node affine subspace, and update the objective function;

[0012] S5: Repeat steps S3 and S4 until the objective function converges or reaches the preset maximum number of iterations to obtain the final self-representation matrix Z;

[0013] S6: Perform spectral clustering on the self-representation matrix Z to obtain the community detection result of the multi-layer social network.

[0014] In an embodiment of the present invention, the S1 includes:

[0015] S1.1: Construct a multi-layer social network where G [l] =(V [l] , E [l] ) represents the l-th layer network, τ is the number of layers of the network, V [l] ={v1,…,v n} represents the set of nodes in the l-th layer network, and E [l] ={(v i , v j)} represents the set of edges between two nodes in the l-th layer of the network;

[0016] S1.2: Obtain the adjacency matrix of the multi-layer social network W [1] , …, W [l] , …, W [τ] respectively represent the adjacency matrices of each layer of the network, and their element w ijl represents the edge (v l , v i , v j ) in the l-th layer of the network G [l] with a weight, that is, it represents whether there is an edge connecting the i-th node and the j-th node in the l-th layer of the network G

[0017] In an embodiment of the present invention, the S2 includes:

[0018] S2.1: Obtain the basis matrix and the feature matrix by non-negative matrix factorization of the adjacency matrix of the l-th layer of the social network. The objective function is:

[0019]

[0020] where W [l] represents the adjacency matrix of the l-th layer of the social network, B [l] represents the basis matrix of the l-th layer of the social network, F [l] represents the feature matrix of the l-th layer of the social network, |||| 2 represents the square of the Frobenius norm of the matrix;

[0021] Extended to the multi-layer social network, the objective function is defined as:

[0022]

[0023] where τ is the number of layers of the social network;

[0024] S2.2: Use the PMI matrix M to replace the adjacency matrix W to obtain a redefined objective function:

[0025]

[0026] where the element m ij in the matrix M is defined as:

[0027]

[0028] where w ij represents whether there is an edge connecting the i-th node and the j-th node, represents the number of negative samples, di represents the degree of the i-th node, t represents an unknown variable, and d t represents the degree of t.

[0029] In one embodiment of the present invention, S3 includes:

[0030] S3.1: Decompose the features of the node into the shared feature C of the node and the layer-specific feature D specific to the layer [l] , then the objective function is expressed as:

[0031]

[0032] Apply a 2-norm constraint penalty to the specific feature to express the objective function as:

[0033]

[0034] where α represents the regularization term parameter.

[0035] In one embodiment of the present invention, S4 includes:

[0036] S4.1: Represent the shared feature C as the self-representation matrix Z of the node and the error term E, and express the objective function as:

[0037]

[0038] S4.2: Apply a 2,1-norm constraint to the error term E:

[0039]

[0040] S4.3: Based on the diversity principle, perform specific module discriminative regularization on the error term E and the layer-specific feature matrix D [l] :

[0041]

[0042] where γ represents the regularization parameter, tr() represents the trace of the matrix, and D [l]′ represents D [l] matrix's transpose matrix;

[0043] S4.4: Update the operator and the auxiliary variable using the alternating direction method of multipliers.

[0044] In one embodiment of the present invention, S4.4 includes:

[0045] S4.41: Introduce auxiliary variables H and Lagrange multipliers Y1, Y2, and define the objective function as:

[0046]

[0047] Among them, the matrix H represents the auxiliary variable matrix, <Y1, H - HZ - E> represents the standard Euclidean inner product of the matrix Y1 and the matrix H - HZ - E, and <Y2, H - C> represents the standard Euclidean inner product of the matrix Y2 and the matrix H - C;

[0048] S4.42: Optimize the basis matrix B using the updated objective function [l] , the shared feature matrix C, the layer - specific feature D [l] , the auxiliary variable matrix H, and the self - representation matrix Z.

[0049] In an embodiment of the present invention, the optimization process of the basis matrix B of the l - th layer network [l] is as follows:

[0050]

[0051] The optimization process of the shared feature matrix C of the nodes is as follows:

[0052]

[0053] Among them, μ > 0 represents the penalty coefficient, and I represents the identity matrix;

[0054] The layer - specific feature D [l] The optimization process is as follows:

[0055]

[0056] The optimization process of the auxiliary variable matrix H is as follows:

[0057]

[0058] And the optimization process of the self - representation matrix Z is as follows:

[0059]

[0060] The update process of the multipliers Y1, Y2 and the parameter μ is as follows:

[0061] Y1 = Y1 + μ(H - HZ - E)

[0062] Y2 = Y2 + μ(H - C)

[0063] μ = min{ρμ, μ max}

[0064] Among them, ρ, μ max represent two constants.

[0065] On the other hand, the present invention provides a storage medium storing a computer program for executing the steps of the feature self-representation learning method for multi-layer social network structure mining according to any one of the above embodiments.

[0066] On yet another aspect, the present invention provides an electronic device, characterized by comprising a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, the steps of the feature self-representation learning method for multi-layer social network structure mining according to any one of the above embodiments are implemented.

[0067] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0068] 1. The present invention provides a feature self-representation learning method for multi-layer social network structure mining. Taking multi-layer networks as the research object, using machine learning and complex network theory, and combining feature decomposition, self-representation learning method and discriminative regularization constraints, a multi-layer social network clustering model based on feature self-representation learning is constructed. Multiple experiments show that the present invention provides an effective strategy for data analysis of multi-layer social networks.

[0069] 2. By decomposing the features of nodes into shared and layer-specific parts, the present invention proposes a new strategy for characterizing conservative communities in multi-layer social networks, solves the problem of inter-layer heterogeneity in multi-layer social networks, and provides a basis for the analysis of user portraits in downstream recommendation system applications. The present invention quantifies the local specificity of the topological structure at the feature level and also solves the relationship between the parts of the specific module, thereby providing a more comprehensive strategy for characterizing communities in multi-layer social networks.

[0070] 3. The present invention combines the topological structure self-representation to represent the similarity relationship between nodes in the multi-layer social network, so as to better act on downstream analysis, such as the recommendation of community users and the prediction of user behavior in the recommendation system.

[0071] The present invention will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 is a flowchart of a feature self-representation learning method for multi-layer social network structure mining provided by an embodiment of the present invention;

[0073] Figure 2 is a schematic diagram of a conservative community detection algorithm for feature self-representation learning based on multi-layer social networks provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] To further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following provides a detailed description of a feature self-representation learning method for multi-layer social network structure mining proposed according to the present invention in combination with the accompanying drawings and specific embodiments.

[0075] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the intended purpose can be obtained. However, the attached drawings are only for reference and illustration, and are not used to limit the technical solutions of the present invention.

[0076] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including", or any other variant are intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the article or device including the element.

[0077] Embodiment 1

[0078] The embodiments of the present invention mainly solve three technical problems: one is how to effectively extract the structural features of vertices in the case of insufficient information in the graph sparse matrix for further joint learning of self-representation; the second is how to mine the common attributes of heterogeneous information between network layers and explore the mutual relationship between the global module and the local module of the specific topological structure; the third is how to project the shared matrix related to the network into the common subspace and effectively extract the shared latent representation of the self-representation object for the final community detection.

[0079] Please refer to Figure 1 , Figure 1 which is a flowchart of a feature self-representation learning method for multi-layer social network structure mining provided by an embodiment of the present invention. The feature self-representation learning method includes:

[0080] S1: Construct a social-oriented multi-layer network structure and the adjacency matrix of the multi-layer network structure.

[0081] The step S1 of this embodiment includes:

[0082] S1.1: Construct a multi-layer social network.

[0083] Specifically, the social network data of this embodiment is statistically obtained by intercepting the interaction record data of the Amazon social network in the purchase behaviors of users of different products (books, music CDs, DVDs, and VHS videotapes). Taking each product as the basic unit, this embodiment constructs three-layer networks for the co-purchase records of users on books, music CDs, and DVDs respectively. Among them, users represent nodes. If user i and user j purchase the same product, an edge will be constructed between user i and user j. The l-th layer network is denoted as G [l] =(V [l] , E [l] ), where V [l] ={v1,…, v n} is the set of nodes, n represents the number of nodes, and E [l] ={(v i , v j )} is the set of edges, representing the interaction of users within the l-th layer social network.

[0084] S1.2: Obtain the adjacency matrix of the multi-layer social network.

[0085] In this embodiment, it is assumed that the node sets of all layers in the social network are fixed, that is, V [l] =V. The three-dimensional matrix W [1] ,…, W [l] ,…, W [τ] respectively represent the adjacency matrices of each layer of the network. Its element w ijl represents the weight on the edge (v l , v i , v j ) in the l-th layer network G [l] , that is, it represents whether there is an edge connection between the i-th node and the j-th node in the l-th layer network G ijl . If there is, the value of w ijl is 1, and if not, the value of w [l] is 0.

[0086] S2: Construct the high-order PMI (Precoding Matrix Indicator) matrix M [l] of the network based on the adjacency matrix of each layer of the social network.

[0087] It should be noted that given a multi-layer social network the node set V in the network is divided into k groups {C1,…, C k}, and it is required that the intersections of different groups are empty sets, that is In addition, based on the requirements for the internal connectivity of the community, the community detection of the multi-layer social network requires the clustering result C iIt is highly connected in all layers, that is, C shows a tight clustering structure in each layer.

[0088] Please refer to Figure 2 , Figure 2 which is a schematic diagram of a conservative community detection algorithm for feature self-representation learning based on a multi-layer social network provided by an embodiment of the present invention. The main body of the feature self-representation learning method in this embodiment includes feature decomposition and self-representation learning. The basic framework is to use feature decomposition to obtain the shared features and layer-specific features of the multi-layer social network; on this basis, the affinity graph representation matrix Z of the multi-layer social network is jointly learned through a regularization method and a self-representation learning strategy, and finally spectral clustering is applied to the affinity graph representation of the network to obtain the final clustering result.

[0089] For a single-layer network, the most intuitive feature extraction strategy is to use matrix decomposition to obtain the low-rank representation of the nodes in the network, that is:

[0090] W [l] ≈B [l] F [l] (1)

[0091] where W [l] represents the adjacency matrix of the l-th layer network, and B [l] and F [l] represent the basis matrix and the feature matrix of the l-th layer network, respectively.

[0092] On this basis, the objective function for obtaining the basis matrix and the feature matrix by non-negative matrix factorization of the adjacency matrix of the l-th layer network is defined as:

[0093]

[0094] Extending Equation (2) to a multi-layer social network, the objective function can be defined as:

[0095]

[0096] where τ is the number of layers of the network, and |||| 2 represents the square of the Frobenius norm of the matrix.

[0097] It should be noted that Equation (3) has two problems, so that it is not sufficient to fully describe the topology of the multi-layer network. First, Equation (3) only focuses on the first-order structure of the network, which is far from sufficient for expressing the high-order connectivity of the graph network; second, it assumes that the relationships of all layers in the network are independent, without distinguishing the shared structure of all layers in the network and the layer-specific structure of each layer, so it cannot be effectively used for community detection of conservative structures in multi-layer networks.

[0098] Therefore, first, to address the problem of low-order topological limitations, embodiments of the present invention use a PMI (Precoding Matrix Indicator) matrix M to replace the adjacency matrix W to overcome the deficiency of low-order topological connectivity. The element m in the M matrix ij is defined as:

[0099]

[0100] where w ij indicates whether there is an edge connecting the i-th node and the j-th node. ι represents the number of negative samples. For each node v i , the sum of the weights on all connected edges is the degree of v i , denoted by d i (the node degree refers to the number of edges associated with the node, simply called the degree). t represents an unknown variable, and d t represents the degree of node t.

[0101] That is, formula (3) is redefined as:

[0102]

[0103] S3: Perform eigen-decomposition on the PMI matrix M [l] to obtain the shared features C and layer-specific features D of the social network [l] .

[0104] Specifically, in the purchase behavior of users, users have certain preferences and fixed behavioral characteristics, which are related to people's personalities and user portraits. This is what the shared features in the network describe. However, in the purchase behavior of different products, users also have some specificities, that is, other behavioral preferences in the purchase of different products. This is what the layer-specific features in each layer depict.

[0105] Specifically, in a multi-layer network, the shared structure serves as the backbone of the network topology, and the layer-specific structure of each layer, as the specific part of each layer, together with the shared structure, forms the intra-layer topology. Therefore, in this embodiment, the features of the nodes are decomposed into the shared features C of the nodes and the layer-specific features D specific to the layer [l] , and the objective function can be expressed as:

[0106]

[0107] In the problem of conservative community detection in a multi-layer social network, the main research content of this embodiment is the clustering of the common structure of multi-layer social network modules. Therefore, the selection of the shared feature C is particularly important. The embodiment of the present invention imposes restrictions on the specific information within a layer, and a 2-norm constraint is imposed on the specific terms. The larger the regular term parameter α, the stronger the penalty on the specific modules in the network, and the greater the prominence of the shared feature C in representing the backbone of the network model. Therefore, the objective function can be further expressed as:

[0108]

[0109] Among them, α represents the regular term parameter.

[0110] Imposing a 2-norm constraint penalty on the specific features highlights the influence of the shared features on the clustering result. That is: for users, the shared features reflect the fixed purchase behavior preferences of users at different layers, which is a specific manifestation of a user portrait. However, the specific preferences for different products are the individual behaviors of users. Therefore, it is necessary to penalize the specific behaviors to highlight the influence of the user's fixed behavior preferences, so as to better depict the user portrait.

[0111] S4: Based on the feature definition in step S3, use the self-representation strategy to learn the mutual relationship between nodes in the social network and project the shared features obtained in step S3 into the node affine subspace.

[0112] The description of the user's fixed behavior characteristics is represented by the shared features. However, the low-rank latent features often cannot well depict the association between users in different communities. Therefore, project the low-rank representation into the node affine subspace and use other users to represent the current user.

[0113] Specifically, step S4 of this embodiment includes:

[0114] S4.1: Represent the shared feature C as the self-representation matrix Z of the nodes and the error term E. Among them, the element Z in the self-representation matrix Z ij represents the similarity degree between node i and node j. If the similarity degree is higher, the weight value is larger.

[0115] S4.2: Impose a 2,1-norm constraint on the error term E.

[0116] Directly using the shared feature C for downstream clustering analysis fails to fully consider and utilize the relationship between different objects in the projection space. In this embodiment, it is expected that nodes belonging to the same community have similar expression patterns, that is, each node can be expressed by several other nodes in the same community. By combining graph learning and the feature decomposition in S1, the topology of the network is better combined, which will be beneficial to depicting the communities in the network. Equation (7) can be expressed as:

[0117]

[0118] Among them, Z is the self-representation matrix of the shared feature C, and E represents the error term (the global structure of the specificity module).

[0119] Self-representation learning proves that each node can be described by using its neighbors, which provides an alternative for constructing an affinity graph. In terms of the specificity of the network structure, the layer-specific topology only exists in some layers. Therefore, it is natural to use sparsity to characterize the specificity of the structure. In the specificity term, the algorithm of this embodiment imposes a 2,1-norm constraint. The larger λ is, the sparser the obtained E is, and thus a more accurate feature ranking can be obtained to a certain extent.

[0120]

[0121] Among them, λ represents the regularization parameter, which reflects the penalty on the error term, |||| 2,1 represents the 2,1-norm.

[0122] S4.3: Based on the diversity principle, perform discriminative regularization on the error term E and the layer-specific feature matrix D [l] for the specificity module.

[0123] Specifically, to solve the discriminative problem of features, make the things learned by the error term E (the global structure of the specificity module) and the layer-specific features (the local structure of the specificity module) as distinguishable as possible. Based on the diversity principle, the embodiments of the present invention expect the learned specificity module to have better discriminability, so an orthogonal constraint is imposed on the error term and the layer-specific features here.

[0124]

[0125] Among them, γ represents the regularization parameter, tr() represents the trace of the matrix, and D [l] ′ represents the transpose matrix of the D [l] matrix.

[0126] It should be noted that the basis for using the discriminative relationship of the module structure is: it is known that the modules of a specific layer are well-connected in the corresponding layer and weakly connected in other layers. Separating the overall global structure of the specificity module from the local structures of other layer-specific modules requires that the layer-specific features be different from the specificity features of the overall module. Thus, the network learns the largest feasible result for conservative community detection.

[0127] S4.4: Use the ADMM (Alternating Direction Method of Multipliers) to update the operator and the auxiliary variables.

[0128] Specifically, in this embodiment, the algorithm uses the ADMM method to update and calculate all variable matrices, introduces auxiliary variables H and Lagrange multipliers Y1, Y2, and the objective function can be defined as:

[0129]

[0130] Among them, the matrix H represents the auxiliary variable, <Y1, H - HZ - E> represents the standard Euclidean inner product of the matrix Y1 and the matrix H - HZ - E, and <Y2, H - C> represents the standard Euclidean inner product of the matrix Y2 and the matrix H - C.

[0131] Furthermore, the basis matrix B of the l-th layer network [l] has the following optimization process:

[0132]

[0133] The optimization process of the shared feature matrix C of the nodes is as follows:

[0134]

[0135] Among them, μ > 0 represents the penalty coefficient, and I represents the identity matrix.

[0136] The layer-specific feature D [l] has the following optimization process:

[0137]

[0138] The optimization process of the matrix H is as follows:

[0139]

[0140] The optimization process of the matrix Z is as follows:

[0141]

[0142] The update processes of the multipliers Y1, Y2 and the parameter μ are as follows:

[0143] Y1 = Y1 + μ(H - HZ - E)

[0144] Y2 = Y2 + μ(H - C)

[0145] μ = min{ρμ, μ max}

[0146] Among them, ρ = 1.1, μ max = 10 6 represent two constants for the update formula.

[0147] S5: Repeat steps S3 and S4 until the objective function converges or reaches the preset maximum number of iterations to obtain the final self-representation matrix Z.

[0148] S6: Perform spectral clustering on the self-representation matrix Z to obtain the community detection results of the multi-layer social network.

[0149] Specifically, performing spectral clustering on the self-representation matrix Z to obtain the community detection results of the multi-layer social network. Each community represents a "circle of friends", meaning a group with similar preferences or behaviors. Subsequently, the clustering results in step S6 are used for downstream analysis of the recommendation system and to label the characteristic attributes of the user group. For example, if the users in this community belong to the type of users with a preference for literary and fresh styles, the recommendation system can recommend suitable products to the users in the community according to their preferences, thereby helping users make decisions and improving the satisfaction of users' purchases.

[0150] This embodiment provides a feature self-representation learning method for multi-layer social network structure mining. Taking the multi-layer social network as the research object, using machine learning and complex network theory, combining feature decomposition, self-representation learning method and discriminative regularization constraint conditions, a multi-layer social network clustering model based on feature learning is constructed. Multiple experiments show that the present invention provides an effective strategy for data analysis of multi-layer social networks.

[0151] Another embodiment of the present invention provides a storage medium in which a computer program is stored, and the computer program is used to execute the steps of the feature self-representation learning method for multi-layer social network structure mining described in the above embodiment. Another aspect of the present invention provides an electronic device, including a memory and a processor. A computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the feature self-representation learning method for multi-layer social network structure mining described in the above embodiment are implemented. Specifically, the above integrated module implemented in the form of a software functional module can be stored in a computer-readable storage medium. The above software functional module is stored in a storage medium and includes several instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs that can store program codes.

[0152] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A feature self-representation learning method for multi-layer social network structure mining, characterized in that Including: S1: Construct a social-oriented multi-layer network structure and the adjacency matrix of the multi-layer network structure. The multi-layer network structure is obtained based on social network data, and the social network data is obtained by intercepting and statistically analyzing the interaction record data of users' purchase behaviors of different products on the Amazon social network. The products include books, music CDs, and DVDs. Taking the books, the music CDs, and the DVDs as basic units, a three-layer network is constructed for the co-purchase records of users on the books, the music CDs, and the DVDs respectively. Among them, the users represent nodes. If user i and user j purchase the same product, then user i and user j will build an edge between them. S2: Based on each layer of the social network adjacency matrix, construct the PMI matrix of the network and construct an objective function for decomposing the adjacency matrix of the social network into a basis matrix and a feature matrix; S3: Perform eigen-decomposition on the PMI matrix to obtain the shared features and layer-specific features of the multi-layer social network; S4: Use the self-representation strategy to learn the mutual relationship between social network nodes, project the shared features into the node affine subspace, and update the objective function; S5: Repeat steps S3 and S4 until the objective function converges or reaches the preset maximum number of iterations to obtain the final self-representation matrix; S6: Perform spectral clustering on the self-representation matrix to obtain the community detection results of the multi-layer social network.

2. The feature self-representation learning method for multi-layer social network structure mining according to claim 1, wherein The S1 includes: S1.1: Construct a multi-layer social network , where represents the -th layer network, is the number of layers of the network, represents the set of nodes in the -th layer network, represents the set of edges between two nodes in the -th layer network; S1.2: Obtain the adjacency matrix of the multi-layer social network , respectively represent the adjacency matrices of each layer of the network, and its elements represent the layer of the network in the edge on the weight, that is, it represents the layer of the network in the i th node and the j th node are connected by an edge or not.

3. The feature self-representation learning method for multi-layer social network structure mining according to claim 2, characterized in that The S2 includes: S2.1: Obtain the basis matrix and the eigenmatrix by non - negative matrix factorization of the adjacency matrix of the l -layer social network. The objective function is as follows: Among them, represents the basis matrix of the l th layer of the social network, represents the feature matrix of the l th layer of the social network, represents the square of the Frobenius norm of the matrix; When extended to a multi-layer social network, the objective function is defined as: Among them, is the number of layers of the social network; S2.2: Use the PMI matrix to replace the adjacency matrix , and obtain a redefined objective function: Among them, the matrix M in which the elements Among them, indicates whether there is an edge connection between the i -th node and the j -th node. represents the number of negative samples. indicates the degree of the i -th node. t represents an unknown variable. represents t 's degree.

4. The feature self-representation learning method for multi-layer social network structure mining according to claim 3, characterized in that The S3 includes: S3.1: Decompose the features of the node into the shared features of the node and the layer-specific features specific to the layer , then the objective function is expressed as: ； Apply a 2-norm constraint penalty to the specific features to represent the objective function as: Among them, represents the regular item parameter.

5. The feature self-representation learning method for multi-layer social network structure mining according to claim 3, wherein The S4 includes: S4.1: Represent the shared feature as the self-representation matrix of the node and the error term , and represent the objective function as: S4.2: Apply the to the norm constraint: S4.3: Based on the diversity principle, for the error term and the layer-specific feature matrix perform specific module discriminative regularization: Among them, represents the regularization parameter, represents the trace of the expression matrix, represents the transpose matrix of the matrix; S4.4: Update the operator and the auxiliary variable using the alternating direction method of multipliers.

6. The feature self-representation learning method for multi-layer social network structure mining according to claim 5, wherein The S4.4 includes: S4.41: Introduce auxiliary variable H and Lagrange multipliers Define the objective function as follows: where the matrix H represents an auxiliary variable matrix, represents the matrix and the matrix of the standard Euclidean inner product, represents the matrix and the matrix of the standard Euclidean inner product; S4.42: Optimize the basis matrix using the updated objective function , the shared feature matrix layer-specific features , the auxiliary variable matrix H, and the self-representation matrix .

7. The feature self-representation learning method for multi-layer social network structure mining according to claim 6, wherein The basis matrix of the l-th layer network The optimization process is as follows: ； Shared feature matrix of nodes The optimization process is as follows: Among them, > 0 represents the penalty coefficient, represents the identity matrix; Layer-specific features The optimization process is as follows: Auxiliary variable matrix H The optimization process is as follows: Self-representing matrix The optimization process is as follows: Multiplier , and the parameter are updated as follows: Among them, , represent two constants.

8. A storage medium, characterized in that, A computer program is stored in the storage medium, and the computer program is used to execute the steps of the feature self-representation learning method for multi-layer social network structure mining according to any one of claims 1 to 7.

9. An electronic device, characterized in that, Including a memory and a processor, a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the feature self-representation learning method for multi-layer social network structure mining according to any one of claims 1 to 7 are implemented.

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