Deep Non-Negative Matrix Factorization Method and Device for Temporal Network Evolution Clustering

Abstract

The present invention discloses a deep non - negative matrix factorization method and device for temporal network evolutionary clustering, which relates to the technical field of graph data mining, and includes: using a deep non - negative matrix factorization model to factorize the point mutual information matrix at adjacent times onto the same set of basis matrices to obtain the deep feature matrix at the first time and the deep feature matrix at the second time; using self - representation learning to train the deep feature matrix at the first time to obtain a self - representation matrix; using the self - representation matrix to impose a Laplacian regularization term constraint on the deep feature matrix at the second time; at the same time, using the point mutual information matrix at the second time to impose a Laplacian regularization term constraint on the deep feature matrix at the second time; using the l 2,1 - norm to impose a sparsity constraint on the deep feature matrix at the first time and the deep feature matrix at the second time; constructing a joint deep non - negative matrix factorization model for community detection. The present invention can effectively extract deep features for community detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of graph data mining, and particularly relates to a deep non-negative matrix factorization method and device for evolutionary clustering of temporal networks. Background Art

[0002] Community detection is a classical problem in the field of graph data mining. With the gradual increase in the amount of data and the gradual change of the topological structure in dynamic networks, community detection in dynamic networks has attracted the attention of a large number of researchers.

[0003] In the prior art, community detection of dynamic networks is usually completed based on the method of coupled graphs. However, this method easily ignores the dynamics of nodes and communities and cannot characterize the characteristics of nodes and communities changing over time. On this basis, researchers have proposed a two-stage method. Using this method is greatly affected by the network structure of the current snapshot and is sensitive to noise.

[0004] Therefore, it is urgent to improve the above-mentioned defects existing in the prior art. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a deep non-negative matrix factorization method and device for evolutionary clustering of temporal networks. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] In a first aspect, the present invention provides a deep non-negative matrix factorization method for evolutionary clustering of temporal networks, including:

[0007] Obtain a plurality of point mutual information matrices in the original network;

[0008] Use a deep non-negative matrix factorization model to factorize the point mutual information matrices at adjacent times onto the same set of basis matrices to obtain a depth feature matrix at the first time and a depth feature matrix at the second time;

[0009] Use self-representation learning to train the depth feature matrix at the first time to obtain a self-representation matrix; wherein, the self-representation matrix is the similarity degree between any two depth features at the first time;

[0010] Use the self-representation matrix to impose a Laplacian regularization term constraint on the depth feature matrix at the second time to maintain the local structure in the original network and perform the first constraint on the depth features at the second time; at the same time, use the point mutual information matrix at the second time to impose a Laplacian regularization term constraint on the depth feature matrix at the second time to perform the second constraint on the depth features at the second time;

[0011] Use the l 2,1 norm to impose a sparse constraint on the depth feature matrix at the first time and the depth feature matrix at the second time to reduce noise;

[0012] Fuse the depth feature matrix at the first processed moment and the depth feature matrix at the second processed moment, construct a joint depth non-negative matrix factorization model, and obtain the depth feature matrix at the second moment for community detection.

[0013] In a second aspect, the present invention also provides a depth non-negative matrix factorization device for temporal network evolutionary clustering, including:

[0014] A data acquisition module; used to acquire multiple point mutual information matrices in the original network;

[0015] A data decomposition module, used to decompose the point mutual information matrices at adjacent moments onto the same set of basis matrices using a joint depth non-negative matrix factorization model to obtain the depth feature matrix at the first moment and the depth feature matrix at the second moment;

[0016] A data processing module 1, used to train using self-representation learning based on the depth feature matrix at the first moment to obtain a self-representation matrix; where the self-representation matrix is the similarity degree between any two depth features at the first moment;

[0017] A data processing module 2, used to impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the self-representation matrix to maintain the local structure in the original network and perform the first constraint on the depth features at the second moment; at the same time, impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the point mutual information matrix at the second moment to perform the second constraint on the depth features at the second moment;

[0018] A data processing module 3, used to perform sparse constraints on the depth feature matrix at the first moment and the depth feature matrix at the second moment using the l 2,1 norm to reduce noise;

[0019] A community detection module, used to fuse the processed depth feature matrix at the first moment and the processed depth feature matrix at the second moment, construct a joint depth non-negative matrix factorization model, and obtain the depth feature matrix at the second moment for community detection.

[0020] Advantages of the present invention:

[0021] A method and device for deep non - negative matrix factorization for evolutionary clustering of temporal networks provided by the present invention. First, a deep non - negative matrix factorization model is used to replace the traditional non - negative matrix factorization model. Based on the local smoothing strategy, the point - mutual - information matrix at the current moment and the point - mutual - information matrix at the previous moment are decomposed simultaneously, so that the point - mutual - information matrix at the current moment and the point - mutual - information matrix at the previous moment are decomposed on the same set of basis matrices, making the extracted deep features comparable. Second, self - representation learning is used to train the deep feature matrix at the first moment to obtain a self - representation matrix, which can obtain the similarity relationship between the deep features at the previous moment. And the Laplacian regularization term is used to introduce the self - representation matrix into the trace optimization, combining self - representation learning and trace optimization, replacing the traditional F - norm for measuring the difference between two matrices, achieving better performance and interpretability. Finally, the l 2,1 - norm is used to perform sparse constraints on the deep feature matrix at the first moment and the deep feature matrix at the second moment, reducing the impact of noise on the clustering result while extracting effective features.

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0023] Figure 1 is a flowchart of a method for deep non - negative matrix factorization for evolutionary clustering of temporal networks provided by an embodiment of the present invention;

[0024] Figure 2 is another flowchart of a method for deep non - negative matrix factorization for evolutionary clustering of temporal networks provided by an embodiment of the present invention;

[0025] Figure 3 is a structural schematic diagram of a device for deep non - negative matrix factorization for evolutionary clustering of temporal networks provided by an embodiment of the present invention. Detailed Embodiments

[0026] The present invention will be further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0027] In the prior art, many problems in the real world can be modeled as networks. Nodes in the network correspond to entities in the real world, and edges in the network correspond to the interactions or connections between entities. For example, in a social network, nodes can represent people, and edges can be used to represent the social relationships between people; in a telephone network, nodes can represent users, and edges can be used to represent whether there is a connection between users. By studying the network, a lot of data beneficial to us can be mined.

[0028] At present, a great deal of effort has been invested in the research of network embedding. However, many existing algorithms are for static networks, and some classic algorithms such as Node2vec and LINE have been proposed. The so-called static network refers to a network in which nodes and edges do not change. In terms of the topological structure of the graph, there is only one network. However, the modeling ability of static networks for real-world problems is limited because things in the real world do not remain unchanged but gradually change over a certain period of time.

[0029] In view of this, the present invention uses a dynamic network to describe things in the real world. The dynamic network has a more powerful modeling ability compared to the static network, can describe more complex networks and can reveal the underlying evolution mechanism of the network, and is more capable of depicting the trends and laws of things changing over time.

[0030] Community detection is a classic problem in graph representation learning. It is generally considered that a community is a subgraph of a network. The connections between nodes within the same community are relatively dense, while the connections between nodes in different communities are relatively sparse. It is generally believed that entities in the same community have the same behavior or similar functions.

[0031] In a dynamic network, communities are gradually changing, such as the birth and death, growth and contraction, merger and division of communities, etc. At the level of nodes and edges, when nodes in the network are added or deleted or the edges in the network change, it will lead to changes in the community structure of the network. Usually, a dynamic network is modeled as a series of snapshot networks, where each snapshot represents the mutual connections between nodes at that moment. In a dynamic network, the communities in each snapshot are different, and the change in the community structure on the snapshot sequence depicts the dynamic characteristics of the community. For example, in a collaboration network, it is considered that authors belonging to the same community are closely connected or cooperate more. By studying the change in the author cooperation relationship, that is, the change in the community, if the two always belong to the same community, it can indicate that their communication is close and there is a relatively high possibility of cooperation between them in the near future.

[0032] In the prior art, community detection is usually carried out based on the coupled graph method. The method based on the coupled graph is to stack all the snapshot networks and then use the community detection algorithm of the static network to calculate the coupled graph, and regard the obtained community as the community on all snapshots. However, this algorithm ignores the dynamics of nodes and communities and cannot characterize the characteristics of nodes and communities changing over time. On this basis, researchers proposed a two-stage method, which separates the community detection of snapshots from the dynamic characteristics of communities. First, apply the static community detection algorithm to the current snapshot network to obtain its community structure, and then, according to the prior definition, combine the communities in different-sized time windows to characterize the dynamic characteristics of the community. Compared with the coupled graph method, the two-stage method avoids the coupling of the network and can characterize the dynamic characteristics of the network to a certain extent. On the one hand, the two-stage method is greatly affected by the network structure of the current snapshot. On the other hand, it shows relatively poor performance when the network structure changes greatly and is sensitive to noise.

[0033] In view of this, the present invention adopts an algorithm based on evolutionary clustering. In the algorithm of evolutionary clustering, a time smoothing framework is introduced. The time smoothing framework needs to consider both clustering accuracy and clustering drift. Among them, the time smoothing framework can be further divided into global smoothing and local smoothing.

[0034] Global smoothing considers all snapshots to measure the dynamics of communities. However, due to the fact that global smoothing needs to consider all snapshots, it leads to a high time complexity. The present invention uses local smoothing. The local smoothing framework considers two snapshots at the current moment and the previous moment to measure clustering drift. Local smoothing can avoid the high time complexity in global smoothing, and under the time smoothing framework, it is considered that the change of the network topology structure is relatively gentle, that is, no mutation will occur.

[0035] It should be noted that the present invention stores the snapshot network using a matrix. For the snapshot network at any moment t, it is represented as G [t] =(V [t] , E [t] ), where V [t] is the set of nodes at moment t, and E [t is the set of edges at moment t; for a dynamic network, a series of snapshot networks are used to represent G = G [1] , G [2] ,... G [T] , T is the number of moments. Assuming that the nodes in each snapshot network are the same, the snapshot network at moment t can also be represented as (V, E [t] ). The dynamic network G is stored using a three-dimensional matrix. For example, W ∈ R n*n*T , where W is the adjacency matrix, W = W [1] , W [2] ,... W[T] , where n is the number of nodes and T is the total number of time instants; generally, networks are relatively sparse, and so are the adjacency matrices. The information contained in sparse matrices is limited. Therefore, the pointwise mutual information matrix (PMI) of the adjacency matrix is used to represent its high-order similarity, and then the pointwise mutual information matrix (PMI) is embedded into a low-dimensional space.

[0036] In the process of community detection, the hard partition problem of communities is considered, that is, the intersection of any two communities is empty. The network is partitioned into k communities, denoted as For any different i and j, The union of all community partitions is the entire node set, that is,

[0037] The idea of evolutionary clustering mainly considers two issues, namely clustering accuracy (CS) and clustering drift (CT). Clustering accuracy refers to the clustering accuracy of the clustering result at the current time instant, while clustering drift refers to the temporal smoothness between the clustering result at the current time instant and the clustering result at the previous time instant. Evolutionary clustering balances clustering accuracy and clustering drift through linear weighting, and its expression is:

[0038] Cost = αCS+(1 - α)CT;

[0039] α is used to balance clustering accuracy and clustering drift, α ∈ (0,1). Clustering accuracy (CS) corresponds to community detection in the network. The main difference between various algorithms based on evolutionary clustering lies in how to define and quantify clustering drift (CT), that is, what kind of smoothing strategy to adopt.

[0040] In summary, a deep non-negative matrix factorization method for evolutionary clustering of temporal networks proposed by the present invention, first, uses a deep non-negative matrix factorization model to make the deep features of the pointwise mutual information matrices of two adjacent time instants comparable; second, uses self-representation learning to obtain a self-representation matrix, which represents the similarity between any two low-dimensional features, and uses a Laplacian regularization term for constraint to meet the requirement of temporal smoothness, reduce clustering drift, and strengthen clustering accuracy; third, uses the l 2,1 norm to process the deep features of the pointwise mutual information matrices of adjacent time instants extracted, and on the basis of extracting effective features, reduce the influence of noise on the clustering result.

[0041] Please refer to Figure 1 and Figure 2 as shown, Figure 1 is a flowchart of a deep non-negative matrix factorization method for evolutionary clustering of temporal networks provided by an embodiment of the present invention. Figure 2Another flowchart of the deep non-negative matrix factorization method for temporal network evolutionary clustering provided by the embodiments of the present invention. A deep non-negative matrix factorization method for temporal network evolutionary clustering provided by the present invention includes:

[0042] S101. Obtain multiple point mutual information matrices in the original network;

[0043] S102. Use the deep non-negative matrix factorization model to factorize the point mutual information matrices at adjacent times onto the same set of basis matrices to obtain the deep feature matrix at the first time and the deep feature matrix at the second time;

[0044] S103. Use self-representation learning to train the deep feature matrix at the first time to obtain a self-representation matrix; wherein, the self-representation matrix is the similarity degree between any two deep features at the first time;

[0045] S104. Use the self-representation matrix to impose a Laplacian regularization term constraint on the deep feature matrix at the second time to maintain the local structure in the original network and perform the first constraint on the deep features at the second time; meanwhile, use the point mutual information matrix at the second time to impose a Laplacian regularization term constraint on the deep feature matrix at the second time to perform the second constraint on the deep features at the second time; on the one hand, combining the self-representation matrix at the first time to impose a constraint on the deep features at the second time replaces the traditional temporal smoothing term and reduces the clustering drift in the feature extraction process; on the other hand, imposing a local distance-preserving constraint through the trace optimization term further applies the original topological structure to the deep features and strengthens the clustering accuracy;

[0046] S105. Use the l 2,1 -norm to perform sparse constraints on the deep feature matrix at the first time and the deep feature matrix at the second time to reduce the influence of noise in the original network, and at the same time perform feature selection to extract more effective features for later community detection;

[0047] S106. Fuse the processed deep feature matrix at the first time and the processed deep feature matrix at the second time to construct a joint deep non-negative matrix factorization model to obtain the deep feature matrix at the second time for community detection.

[0048] Specifically, please continue to refer to Figure 1 and Figure 2As shown in the figure, a deep non - negative matrix factorization method for temporal network evolutionary clustering provided in this embodiment first uses a deep non - negative matrix factorization model to replace the traditional non - negative matrix factorization model. Based on the local smoothing strategy, it decomposes the point mutual information matrix at the current moment and the point mutual information matrix at the previous moment simultaneously, so that the point mutual information matrix at the current moment and the point mutual information matrix at the previous moment are decomposed on the same set of basis matrices, making the extracted deep features comparable. Secondly, self - representation learning is used to train the deep feature matrix at the first moment to obtain a self - representation matrix, which can obtain the similarity relationship between the deep features at the previous moment. And the Laplacian regularization term is used to introduce the self - representation matrix into the trace optimization, combining self - representation learning and trace optimization, replacing the traditional F - norm for measuring the difference between two matrices, achieving better performance and interpretability. Finally, the l 2,1 -norm is used to perform sparse constraints on the deep feature matrix at the first moment and the deep feature matrix at the second moment, reducing the influence of noise on the clustering result while extracting effective features.

[0049] In an optional embodiment of the present invention, the model of the deep non - negative matrix factorization algorithm is:

[0050]

[0051] Among them, G [t] is the snapshot network at any time t, G [t-1] is the snapshot network at any time t - 1, i is the i - th moment, the value of i is t and t - 1, M [i] is the point mutual information matrix at the i - th moment, is the basis matrix of the H - th layer, t is the second moment, t - 1 is the first moment, F t [i] is the deep feature matrix at the i - th moment.

[0052] Specifically, in this embodiment, the deep non - negative matrix factorization model is used to factorize the point mutual information matrix at adjacent times onto the same set of basis matrices, so that the extracted low - dimensional features are mapped into the same subspace, obtaining the deep feature matrix at the first time and the deep feature matrix at the second time. Among them, both the deep feature matrix at the first time and the deep feature matrix at the second time are low - dimensional feature matrices. Generally, high - dimensional data contains noise, and in the case of a large amount of data, the effective information contained in high - dimensional data is also relatively limited. If clustering is directly performed on high - dimensional data, usually a very high accuracy cannot be achieved. Therefore, before clustering, the high - dimensional network data is reduced in dimension, that is, the low - dimensional features of the network are extracted. The traditional non - negative matrix factorization algorithm directly maps the original high - dimensional data into a low - dimensional space, and cannot fully explore the deep features and structural information of the network. Moreover, when applying the traditional non - negative matrix factorization algorithm to a dynamic network, only the snapshot structure at the current time can be considered, and the low - dimensional features at different times are under different basis matrices, and the comparability of the feature matrices under different basis matrices is poor.

[0053] In view of this, to ensure the comparability of the low - dimensional features at two adjacent times, the present invention uses the deep non - negative matrix factorization model to extract the deep features of high - dimensional data, factorizes the point mutual information matrix at two adjacent times into the product of multiple basis matrices and a feature matrix, and the obtained deep feature matrix can better represent the deep features of the network and the relationship between nodes. In addition, the community networks at two adjacent times are decomposed on the same set of basis groups to make them comparable.

[0054] It should be noted that the first time is the previous time, and the second time is the current time.

[0055] In an optional embodiment of the present invention, the expression of the self - representation matrix is:

[0056] O(F t [t-1] )=||F t [t-1] -F t [t-1] S [t-1] || 2 s.t.diag(S [t-1] )=0;

[0057] Where F t [t-1] is the deep feature matrix at the first time, S [t-1] is the self - representation matrix of the deep feature matrix at the first time, and the element in the i - th row and j - th column represents the similarity degree between the i - th low - dimensional feature and the j - th low - dimensional feature.

[0058] In an alternative embodiment of the present invention, the expression for the first constraint on the depth features at the second moment is:

[0059]

[0060] where F t [t] is the depth feature matrix at the second moment, is the Laplacian matrix of the self - representation matrix S [t-1] ; D [t-1] is the degree matrix of S [t-1] , and the element F t [t]′ is the transpose matrix of F t [t] ;

[0061] The expression for the second constraint on the depth features at the second moment is:

[0062]

[0063] where is the Laplacian matrix of the point - mutual - information matrix M [i] at the second moment;

[0064] Fusing the first constraint on the depth features at the second moment and the second constraint on the depth features at the second moment, the expression for extracting the processed depth features at the second moment is:

[0065] The point - mutual - information matrix M [i] and the Laplacian matrix of the self - representation matrix S [t-1] , D [t] is the degree matrix of M [t] , and the element

[0066] Specifically, in this embodiment, considering the changing characteristics of the dynamic network, the structural information and community information at historical moments will affect the clustering results at the current moment. Therefore, when performing community detection on the dynamic network, a temporal smoothing term is used to describe the influence of historical information on the deep features at the current moment, so as to better reflect the temporality of the dynamic community. On the one hand, the present invention uses self-representation learning to train the deep feature matrix at the first moment to obtain a self-representation matrix. For the low-dimensional representation of any node, it can be expressed as a linear combination of the low-dimensional vectors of the remaining nodes. If the low-dimensional representations of two nodes are very similar, their coefficients will be closer to 1. The obtained self-representation matrix can represent the similarity degree between any two deep features at the first moment. On the other hand, the present invention uses the Laplacian regularization term to maintain the local structure of the snapshot network. To meet the requirement of temporal smoothing, the similarity degree between the low-dimensional feature vectors at the previous moment is used to constrain the generation of the local structure at the current moment, so that when extracting the deep features at the current moment, the feature information of the historical moment closest to it is fully considered. To ensure that the obtained deep features at the current moment can reflect the topological structure of the current snapshot network, the Laplacian regularization term is used to constrain the local structure of the deep features at the current moment, making similar nodes more similar and strengthening the deep features of the nodes.

[0067] In an optional embodiment of the present invention, the expression for using the l 2,1 norm to perform sparse constraint on the deep feature matrix at the first moment and the deep feature matrix at the second moment is:

[0068]

[0069] where F t [i] is the deep feature matrix at the first moment or the deep feature matrix at the second moment.

[0070] Specifically, in this embodiment, to ensure that the learned low-dimensional deep features can contain sufficiently clear features and reduce the influence of noise on the results, the present invention uses the l 2,1 norm to perform sparse constraint on the deep feature matrix at the first moment and the deep feature matrix at the second moment, so as to make the sparsity and effectiveness of the finally obtained low-dimensional deep features, thereby further reducing the influence of noise.

[0071] In an optional embodiment of the present invention, the expression of the joint deep non-negative matrix factorization model is:

[0072]

[0073] where α is the first weight value, representing the importance degree of, β is the second weight value, representing The degree of importance.

[0074] In an alternative embodiment of the present invention, it further includes: updating some parameters in the joint deep non - negative matrix factorization model;

[0075] Updating the parameter is expressed as:

[0076]

[0077] where is the basis matrix of the H - th layer, M [t-1] is the point - mutual - information matrix at the first moment t - 1, F t [t-1]′ is the transpose matrix of F t [t-1] ; is 's transpose matrix;

[0078] Updating the parameter is expressed as:

[0079]

[0080]

[0081]

[0082] where is the basis matrix of the h - th layer, is 's transpose matrix, is 's transpose matrix;

[0083] Updating the parameter S [t-1] is expressed as:

[0084]

[0085] Updating the parameter F t [t-1] using the alternating direction method of multipliers (ADMM), is expressed as:

[0086]

[0087]

[0088]

[0089] where δ is the third weight value, indicating (F t [t-1] -Q [t-1]) importance level, Q [t-1] is to separate variables;

[0090] For parameter F t [t] perform an update, and its expression is:

[0091]

[0092]

[0093] T [t] = T [t] + δ(F t [t] - Q [t] );

[0094] wherein, T [t] is the augmented Lagrangian multiplier.

[0095] Specifically, in this embodiment, to make the joint depth decomposition model more accurate, an alternating update method is used to update the variables, that is, when updating a certain variable, other variables are first fixed, and all variables are updated alternately in this way.

[0096] Based on the same inventive concept, please refer to Figure 3 as shown in Figure 3 is a schematic structural diagram of a depth non-negative matrix factorization device for temporal network evolutionary clustering provided by an embodiment of the present invention. The present invention also provides a depth non-negative matrix factorization device for temporal network evolutionary clustering, which is applied to a depth non-negative matrix factorization method for temporal network evolutionary clustering provided by the above embodiment of the present invention. For the embodiments of the method, please refer to the above, and details will not be repeated here; the device includes:

[0097] Data acquisition module 201; used to acquire multiple point mutual information matrices in the original network;

[0098] Data decomposition module 202, used to decompose the point mutual information matrices at adjacent times onto the same set of basis matrices using a depth non-negative matrix factorization model to obtain a depth feature matrix at the first time and a depth feature matrix at the second time;

[0099] First data processing module 203, used to perform training based on the depth feature matrix at the first time using self-representation learning to obtain a self-representation matrix; wherein, the self-representation matrix is the similarity degree between any two depth features at the first time;

[0100] The data processing module two 204 is used to impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the self-representation matrix, maintain the local structure in the original network, and perform the first constraint on the depth features at the second moment; meanwhile, impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the point mutual information matrix at the second moment, and perform the second constraint on the depth features at the second moment.

[0101] The data processing module three 205 is used to perform sparse constraint on the depth feature matrix at the first moment and the depth feature matrix at the second moment using the l 2,1 norm to reduce noise.

[0102] The community detection module 206 is used to fuse the processed depth feature matrix at the first moment and the processed depth feature matrix at the second moment, construct a joint depth non-negative matrix factorization model, and obtain the depth feature matrix at the second moment for community detection.

[0103] It should be noted that after the iterative update is completed, the obtained depth feature matrix F t is used to obtain the specific community detection. The detection process is that for each low-dimensional vector, its components are regarded as the weights belonging to each class, and it is made to belong to the class with the highest membership degree.

[0104] A depth non-negative matrix factorization device for temporal network evolutionary clustering provided in this embodiment, first, uses the data decomposition module, based on the local smoothing strategy, to decompose the point mutual information matrix at the current moment and the point mutual information matrix at the previous moment simultaneously, so that the point mutual information matrix at the current moment and the point mutual information matrix at the previous moment are decomposed on the same set of basis matrices, making the extracted depth features comparable; secondly, uses the data processing module one, that is, self-representation learning to train the depth feature matrix at the first moment to obtain the self-representation matrix, which can obtain the similarity relationship between the depth features at the previous moment, and uses the data processing module two, that is, the Laplacian regularization term to introduce the self-representation matrix into the trace optimization, combines the self-representation learning and the trace optimization, replaces the traditional F norm for measuring the difference between two matrices, and achieves better performance and interpretability; finally, uses the data processing module three, that is, the l 2,1 norm to perform sparse constraint on the depth feature matrix at the first moment and the depth feature matrix at the second moment, and on the basis of extracting effective features, reduce the influence of noise on the clustering result.

[0105] It should be noted that in this text, 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 comprising a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the article or device comprising the element. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The orientation or positional relationship indicated by "upper", "lower", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore should not be construed as a limitation on the present invention.

[0106] In the description of this specification, the description with reference to terms such as "an embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0107] 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 be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A deep non - negative matrix factorization method for evolutionary clustering of temporal networks, characterized in that Including: Obtain multiple point mutual information matrices in the original network; wherein, the original network is a social network, nodes in the social network are connected by edges, the nodes represent users, the edges represent the connections between users, and the nodes in the social network form a dynamic network by adding or deleting nodes; Use the deep non-negative matrix factorization model to factorize the point mutual information matrices at adjacent times onto the same set of basis matrices to obtain the deep feature matrix at the first time and the deep feature matrix at the second time; Use self-representation learning to train the deep feature matrix at the first time to obtain a self-representation matrix; wherein, the self-representation matrix represents the similarity degree between any two deep features at the first time; Use the self-representation matrix to impose a Laplacian regularization term constraint on the deep feature matrix at the second time to maintain the local structure in the original network and perform the first constraint on the deep feature at the second time; meanwhile, use the point mutual information matrix at the second time to impose a Laplacian regularization term constraint on the deep feature matrix at the second time to perform the second constraint on the deep feature at the second time; Use The norm is used to perform sparse constraint on the depth feature matrix at the first moment and the depth feature matrix at the second moment to reduce noise; Fuse the processed deep feature matrix at the first time and the processed deep feature matrix at the second time to construct a joint deep non-negative matrix factorization model, and obtain the deep feature matrix at the second time for community detection.

2. The deep non - negative matrix factorization method for temporal network evolutionary clustering according to claim 1, characterized in that, The model of the deep non-negative matrix factorization algorithm is: ； Among them, is an arbitrary snapshot network at a moment, is an arbitrary snapshot network at a moment, is the th moment, takes values of and , is the point mutual information matrix at the th moment, is the basis matrix of the th layer, is the second moment, is the first moment, is the depth feature matrix at the th moment.

3. The deep non - negative matrix factorization method for temporal network evolutionary clustering according to claim 1, characterized in that, The expression of the self-representation matrix is: ； Among them, is the depth feature matrix at the first moment , and is the self-representation matrix of the depth feature matrix at the first moment.

4. The deep non - negative matrix factorization method for time - series network evolutionary clustering according to claim 1, characterized in that, The expression of the first constraint on the deep feature at the second time is: ； Among them, is the depth feature matrix at the second moment , is the self - representation matrix of the Laplacian matrix is the transpose matrix of; The expression of the second constraint on the deep feature at the second time is: ； Among them, is the point mutual information matrix at the second moment 's Laplacian matrix; Fuse the first constraint on the deep feature at the second time and the second constraint on the deep feature at the second time to obtain the expression for extracting the processed deep feature at the second time as: ； Among them, is the point mutual information matrix at the second moment and the self-representation matrix is the Laplacian matrix of.

5. The deep non - negative matrix factorization method for temporal network evolutionary clustering according to claim 1, wherein The usage The expression for sparsely constraining the depth feature matrix at the first moment and the depth feature matrix at the second moment using the norm is: ； Among them, is the depth feature matrix at the first moment or the depth feature matrix at the second moment.

6. The deep non - negative matrix factorization method for time - series network evolutionary clustering according to claim 1, wherein, The expression of the joint deep non-negative matrix factorization model is: ； Among them, is the first weight value, is the second weight value.

7. The deep non - negative matrix factorization method for time - series network evolution clustering according to claim 6, wherein, Also including: Update some parameters in the joint deep non-negative matrix factorization model; Update the parameter with the following expression: ； Among them, is the base matrix of the layer, is the point mutual information matrix at the first moment , is 's transpose matrix, is 's transpose matrix; Update the parameter with the following expression: ； ； ； Among them, is the layer base matrix, is 's transpose matrix, is 's transpose matrix; Update the parameter with the following expression: ； Update the parameter using the alternating direction method of multipliers, and its expression is: ； ； ； Among them, is the third weight value, is the separation variable; Update the parameter with the following expression: ； ； ； wherein, is the augmented Lagrange multiplier.

8. A deep non-negative matrix factorization device for evolutionary clustering of temporal networks, characterized in that Including: Data acquisition module; Used to obtain multiple point mutual information matrices in the original network; wherein, the original network is a social network, nodes in the social network are connected by edges, the nodes represent users, the edges represent the connections between users, and the nodes in the social network form a dynamic network by adding or deleting nodes; Data decomposition module, used to factorize the point mutual information matrices at adjacent times onto the same set of basis matrices using the joint deep non-negative matrix factorization model to obtain the deep feature matrix at the first time and the deep feature matrix at the second time; Data processing module 1, used to train based on the deep feature matrix at the first time using self-representation learning to obtain a self-representation matrix; wherein, the self-representation matrix represents the similarity degree between any two deep features at the first time; The data processing module two is used to impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the self-representation matrix, maintain the local structure in the original network, and perform the first constraint on the depth features at the second moment; meanwhile, impose a Laplacian regularization term constraint on the depth feature matrix at the second moment using the point mutual information matrix at the second moment, and perform the second constraint on the depth features at the second moment. Data processing module three, for using the norm to perform sparse constraint on the depth feature matrix at the first moment and the depth feature matrix at the second moment, so as to reduce noise; The community detection module is used to fuse the processed depth feature matrix at the first moment and the processed depth feature matrix at the second moment, construct a joint depth non-negative matrix factorization model, and obtain the depth feature matrix at the second moment for community detection.

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