Semi-supervised non-negative matrix factorization multi-view clustering method based on double constraints

Abstract

The invention provides a semi-supervised non-negative matrix factorization multi-view clustering method based on double constraints, which is realized by adopting a double-constraint algorithm, the double-constraint algorithm comprises a point constraint propagation algorithm and a pairwise constraint propagation algorithm, and specifically, when limited label information is obtained, the point constraint propagation algorithm and the pairwise constraint propagation algorithm are combined to form a semi-supervised non-negative matrix factorization multi-view clustering algorithm. According to the double-constraint algorithm, not only is label regularization constructed by using a point constraint propagation algorithm, but also multi-view hypergraph regularization is constructed by using a hypergraph pairwise constraint propagation algorithm, so that the detection accuracy of the model on multi-view clustering is improved. According to the method, the performance of multi-view clustering can be improved by utilizing the label information and the paired supervision information.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-view clustering, and more specifically, to a semi-supervised non-negative matrix decomposition multi-view clustering method based on double constraints. Background Art

[0002] The non-negative matrix factorization technology has a stronger parsability due to its non-negative characteristics. Its core idea is to decompose a non-negative matrix into the product of two non-negative matrices. This decomposition technology can reduce the dimension and complexity of the data, so that the low-dimensional representation of the data can capture the main structural features. Therefore, this technology is widely used in image processing, text mining, community detection and other fields. Non-negative matrix factorization technology is divided into unsupervised non-negative matrix factorization and semi-supervised non-negative matrix factorization. Unsupervised non-negative matrix factorization only relies on the data itself for decomposition, without using any external labels or prior information. Unlike unsupervised, semi-supervised non-negative matrix factorization technology combines partial label information or prior knowledge to guide the decomposition process. In the real network world, network data usually has partial supervision information. This information can come from labeled samples, prior knowledge or business rules. Although labeled samples may only be part of the data set, they are very important for improving the performance and explanation ability of the model. Semi-supervised learning uses this partial supervision information to optimize the model to better handle complex data and tasks in practical applications. Therefore, semi-supervised non-negative matrix factorization technology has received more attention and research.

[0003] However, existing semi-supervised methods only use point constraints or pairwise constraints as supervision information, without considering making full use of these two constraints to further improve the effectiveness of clustering performance. Data from different views usually exist in different manifold structures. Existing methods usually do not directly consider these manifold structures, and therefore may not be able to fully utilize the intrinsic geometric features of view data. Failure to capture these geometric manifold structures may lead to reduced accuracy of clustering results. Summary of the invention

[0004] In order to overcome the problem that the above-mentioned existing multi-view clustering technology does not utilize the intrinsic geometric characteristics of view data, resulting in reduced accuracy of clustering results, the present invention proposes a semi-supervised non-negative matrix decomposition multi-view clustering method based on double constraints.

[0005] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0006] The present invention proposes a dual-constrained semi-supervised non-negative matrix decomposition multi-view clustering method, comprising:

[0007] Get multi-view data matrix and label matrix;

[0008] Constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial assignment matrix, a label matrix and a diagonal matrix according to the multi-view data matrix and the label matrix;

[0009] Establishing the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix;

[0010] Construct consensus regularization based on the initial coefficient matrix and the initial allocation matrix;

[0011] Construct multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix;

[0012] Constructing vertices and hyperedges of a multi-view hypergraph according to the multi-view data matrix, and constructing a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph;

[0013] Based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, the objective function of double-constrained semi-supervised non-negative matrix factorization is constructed, and the alternating iterative update algorithm is used to solve the objective function to obtain the clustering result.

[0014] Preferably, constructing a multi-view label matrix and a diagonal matrix according to the multi-view data matrix and the label matrix comprises:

[0015] The multi-view label matrix is ​​represented as Y = [y1, y2, ..., y n ] T , if the feature point x in the multi-view data matrix i The label of is associated with class j in the label matrix, then y i The i-th element of is set to 1, while all other elements remain 0. i All elements of are assigned the value 0;

[0016] The multi-view diagonal matrix is ​​defined as A = {A ij}, in x i When the label of is associated with class j in the label matrix, A ij =1, otherwise, A ij =0.

[0017] Preferably, the objective function of establishing non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix is ​​specifically:

[0018]

[0019] in, represents the v-th view data matrix, U (v) and V (v) Respectively represent the initial basis matrix and initial coefficient matrix of the v-th view data matrix, nv represents the number of multi-view data matrices, represents the Frobenius norm, (·) T Represents the transpose of a matrix.

[0020] Preferably, the consensus regularization is constructed according to the initial coefficient matrix and the initial allocation index matrix as follows:

[0021]

[0022] Among them, γ represents the weight parameter, V * ∈R n×k represents the initial allocation matrix.

[0023] Preferably, constructing multi-view label regularization according to the initial coefficient matrix, the label matrix and the diagonal matrix is ​​specifically as follows:

[0024]

[0025] Where Tr(·) represents the trace of the matrix.

[0026] Preferably, constructing vertices and hyperedges of a multi-view hypergraph according to a multi-view data matrix, and constructing a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph comprises:

[0027] Construct the vertices of the multi-view hypergraph based on the multi-view data matrix Super Edge Construct an association matrix based on the vertices and hyperedges of the multi-view hypergraph Elements in a matrix Represents a vertex and super edge The relationship between them is:

[0028]

[0029] Calculate the multi-view diagonal matrix based on the vertices, hyperedges and incidence matrix of the multi-view hypergraph Represents the vth view data matrix and the hyperedge in the multi-view data matrix The relevant weights, vertices The degree is recorded as Super Edge The degree is recorded as The formula definition is as follows:

[0030]

[0031] in, express and On the super edge The Euclidean distance within, the hyperparameter σ (v) Can be configured as the average distance between all vertices;

[0032] The similarity matrix of the multi-view hypergraph is calculated based on the association matrix and the multi-view diagonal matrix of the multi-view hypergraph. The similarity matrix calculation formula of the hypergraph corresponding to the v-th view data matrix is:

[0033]

[0034] in, is a diagonal matrix, each element of which is the sum of the degrees of all hyperedges;

[0035] The first Laplacian matrix is ​​calculated according to the similarity matrix of the multi-view hypergraph, specifically:

[0036]

[0037] in,

[0038] According to the pairwise constraint propagation algorithm, the initial pairwise constraint matrix Z = {Z ij}, specifically:

[0039]

[0040] Among them, (x i ,x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to the same label, (x i ,x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to different labels, M represents the same label set, and C represents different label sets;

[0041] The pairwise constraint propagation algorithm of vertical and horizontal propagation is used to calculate the final pairwise constraint learning matrix according to the first Laplace matrix and the initial pairwise constraint matrix, which is specifically:

[0042] Repeat Until convergence, where μ∈(0,1) and t represent the trade-off parameter and iteration count, respectively. represents the initialization of the vertical constraint propagation matrix;

[0043] Repeat Until convergence, where represents the initialization horizontal constraint propagation matrix, express The limit, express The limit of

[0044] is the final pairwise constraint learning matrix for the vth view of the data;

[0045] The weight matrix is ​​calculated based on the final pairwise constraint learning matrix, specifically:

[0046]

[0047] in, Represents the weight matrix The element at row i and column j;

[0048] The second Laplace matrix is ​​calculated according to the weight matrix, specifically:

[0049]

[0050] in, yes The diagonal matrix of ;

[0051] The hypergraph regularization is calculated according to the second Laplacian matrix, specifically:

[0052]

[0053] Preferably, the objective function of the dual-constrained semi-supervised non-negative matrix factorization is:

[0054]

[0055] U (v) ≥0,V (v) ≥0,V * ≥0

[0056] Wherein, α, β and γ represent the key trade-off parameters for adjusting the influence of the regularization term, and O represents the objective function.

[0057] Preferably, the adopting an alternating iterative update algorithm to solve the objective function to obtain the final allocation matrix comprises:

[0058] S8.1: Setting U (v) 、V (v) 、V * Initial value;

[0059] S8.2: Update U (v) : The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as:

[0060]

[0061] To U(v) The first-order derivative of , we get:

[0062]

[0063] According to the KKT conditions, Export The update rule is:

[0064]

[0065] S8.3: Update V (v) : The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as:

[0066]

[0067] V (v) Taking the first-order derivative, we get:

[0068]

[0069] By setting get:

[0070]

[0071] It turns out that:

[0072]

[0073] S8.4: Update V * : About V * The objective function is expressed as:

[0074]

[0075] V * Taking the first-order derivative, we get:

[0076]

[0077] set up Get V * Solution:

[0078]

[0079] S8.5: According to the updated U (v) 、V (v) and V * Calculate the objective function value of the double-constrained semi-supervised non-negative matrix factorization. If the absolute difference between the objective function value and the objective function value of the previous iteration is less than a preset threshold, output the final V * , the V *is the clustering result, otherwise, repeat steps S8.2-S8.4.

[0080] The present invention also proposes a dual-constraint based semi-supervised non-negative matrix decomposition multi-view clustering system, comprising:

[0081] A data acquisition module, used to acquire a multi-view data matrix and a label matrix;

[0082] A preprocessing module, used for constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial allocation matrix, a label matrix and a diagonal matrix according to a multi-view data matrix and a label matrix;

[0083] The objective function construction module of non-negative matrix decomposition is used to establish the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix;

[0084] A consensus regularization building module, used to build consensus regularization based on an initial coefficient matrix and an initial allocation matrix;

[0085] A label regularization building module is used to build multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix;

[0086] A hypergraph regularization construction module, used to construct vertices and hyperedges of a multi-view hypergraph according to a multi-view data matrix, and to construct a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph;

[0087] The objective function construction and solution module is used to construct the objective function of double-constrained semi-supervised non-negative matrix factorization based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, and use the alternating iterative update algorithm to solve the objective function to obtain the clustering result.

[0088] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned clustering method are implemented.

[0089] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0090] The present invention proposes a double-constraint based semi-supervised non-negative matrix decomposition multi-view clustering method, which is implemented by a double-constraint algorithm, wherein the double-constraint algorithm includes a point constraint propagation algorithm and a pair constraint propagation algorithm. Specifically, when limited label information is obtained, the double-constraint algorithm not only uses the point constraint propagation algorithm to construct label regularization, but also uses a hypergraph-based pair constraint propagation algorithm to construct multi-view hypergraph regularization, thereby improving the detection accuracy of the model for multi-view clustering. The present invention can improve the performance of multi-view clustering by using label information and paired supervision information. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a flow chart of the double-constrained semi-supervised non-negative matrix decomposition multi-view clustering method described in Example 1;

[0092] Figure 2 This is a system block diagram of the dual-constrained semi-supervised non-negative matrix decomposition multi-view clustering method described in Example 2;

[0093] Figure 3 This is a structural diagram of the dual-constraint semi-supervised non-negative matrix decomposition multi-view clustering system described in Example 3. DETAILED DESCRIPTION

[0094] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0095] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0096] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0097] First, some concepts that may be involved in this application are explained:

[0098] Point constraint propagation algorithm: The point constraint propagation algorithm obtains labels corresponding to different views each time based on the existing limited prior label information, and then propagates them to each view through optimization and iteration, so that each view can initially obtain a prior information matrix.

[0099] Pairwise constraint propagation algorithm: The pairwise constraint propagation algorithm learns based on prior information to obtain constraint matrices with linked relationships and constraint matrices with unlinked relationships. By obtaining pairwise constraint matrices, these supervised information is propagated to each sub-view in the multi-view clustering, so that each view that learns the new similarity matrix has more supervised information and obtains a deeper internal geometric structure.

[0100] Hypergraph regularization: It is a method to improve the results by using the hypergraph structure. A hypergraph is a more generalized graph structure in which a hyperedge can connect multiple nodes, which enables the hypergraph to express more complex relationships. Hypergraph regularization uses this structure to constrain the matrix decomposition process to capture the high-order correlation of the data. The hypergraph Laplacian matrix is ​​a matrix based on the hypergraph structure and is used to represent the relationship between hyperedges. By controlling the hypergraph regularization parameter a and thus the regularization strength, the internal structure between different views can be better obtained and the structural consistency can be maintained.

[0101] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0102] Example 1

[0103] This embodiment provides a semi-supervised non-negative matrix factorization multi-view clustering method based on double constraints. Figure 1 As shown, including:

[0104] Get multi-view data matrix and label matrix;

[0105] Constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial assignment matrix, a label matrix and a diagonal matrix according to the multi-view data matrix and the label matrix;

[0106] Establishing the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix;

[0107] Construct consensus regularization based on the initial coefficient matrix and the initial allocation matrix;

[0108] Construct multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix;

[0109] Constructing vertices and hyperedges of a multi-view hypergraph according to the multi-view data matrix, and constructing a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph;

[0110] Based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, the objective function of double-constrained semi-supervised non-negative matrix factorization is constructed, and the alternating iterative update algorithm is used to solve the objective function to obtain the clustering result.

[0111] In the specific implementation process, we first obtain the multi-view data matrix and label matrix, and then obtain the objective function of non-negative matrix decomposition, consensus regularization, multi-view label regularization and multi-view hypergraph regularization according to the multi-view data matrix and label matrix respectively. Then, we construct the objective function of the double-constrained semi-supervised non-negative matrix decomposition, and use the alternating iterative update algorithm to solve the objective function to obtain the clustering result.

[0112] Example 2

[0113] This embodiment proposes a dual-constrained semi-supervised non-negative matrix decomposition multi-view clustering method, including:

[0114] Get multi-view data matrix and label matrix;

[0115] According to the multi-view data matrix and label matrix, the multi-view initial basis matrix, initial coefficient matrix, initial allocation matrix, label matrix and diagonal matrix are constructed, specifically:

[0116] For point-wise constraint supervision information, the expression needs to define two key matrices: the multi-view label matrix and the diagonal matrix. According to the point constraint propagation algorithm, the multi-view label matrix is ​​expressed as Y = [y1, y2, …, y n ] T , if the feature point x in the multi-view data matrix i The label of is associated with class j in the label matrix, then y i The i-th element of is set to 1, while all other elements remain 0. i All elements of are assigned the value 0;

[0117] The multi-view diagonal matrix is ​​defined as A = {A ij}, in x i When the label of is associated with class j in the label matrix, A ij =1, otherwise, A ij =0.

[0118] The non-negative matrix decomposition technology aims to get as close as possible to the original non-negative matrix by multiplying two decomposed non-negative matrices. The objective function of non-negative matrix decomposition is established based on the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix. Specifically, it is:

[0119]

[0120] in, represents the v-th view data matrix, U (n) and V (v) Respectively represent the initial basis matrix and initial coefficient matrix of the v-th view data matrix, n v represents the number of multi-view data matrices, represents the Frobenius norm, (·) T Represents the transpose of a matrix.

[0121] The consensus regularization is constructed based on the initial coefficient matrix and the initial allocation matrix, specifically:

[0122]

[0123] Among them, γ represents the weight parameter, V * ∈R n×k represents the initial allocation matrix.

[0124] The multi-view label regularization is constructed based on the initial coefficient matrix, the label matrix and the diagonal matrix, specifically:

[0125]

[0126] Where Tr(·) represents the trace of the matrix.

[0127] According to the multi-view data matrix, the vertices and hyperedges of the multi-view hypergraph are constructed, and the multi-view hypergraph regularization is constructed according to the vertices and hyperedges of the multi-view hypergraph, specifically:

[0128] Traditional graphs can only represent binary relationships between nodes, and each edge can only connect two nodes, so it cannot directly capture more complex association information. In order to effectively utilize prior information, in this embodiment, the present invention combines a pairwise constraint propagation technology based on a hypergraph, so as to explore high-order relationships between data points. Constructing a multi-view hypergraph based on a multi-view data matrix Multi-view hypergraph contains vertices Super Edge Construct an association matrix based on the vertices and hyperedges of the multi-view hypergraph The association matrix is ​​used to describe the hypergraph structure of each view data. The elements in the matrix are Represents a vertex and super edge The relationship between them is:

[0129]

[0130] Calculate the multi-view diagonal matrix based on the vertices, hyperedges and incidence matrix of the multi-view hypergraph Represents the vth view data matrix and the hyperedge in the multi-view data matrix The relevant weights, vertices The degree is recorded as Super Edge The degree is recorded as The formula definition is as follows:

[0131]

[0132] in, express and On the super edge The Euclidean distance within, the hyperparameter σ (v) Can be configured as the average distance between all vertices;

[0133] The similarity matrix of the multi-view hypergraph is calculated based on the association matrix and the multi-view diagonal matrix of the multi-view hypergraph. The similarity matrix calculation formula of the hypergraph corresponding to the v-th view data matrix is:

[0134]

[0135] in, is a diagonal matrix, each element of which is the sum of the degrees of all hyperedges;

[0136] The first Laplacian matrix is ​​calculated according to the similarity matrix of the multi-view hypergraph, specifically:

[0137]

[0138] in,

[0139] According to the pairwise constraint propagation algorithm, the initial pairwise constraint matrix Z = {Z ij}, specifically:

[0140]

[0141] Among them, (x i ,x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to the same label, (x i ,x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to different labels, M represents the same label set, and C represents different label sets;

[0142] The pairwise constraint propagation algorithm of vertical and horizontal propagation is used to calculate the final pairwise constraint learning matrix according to the first Laplace matrix and the initial pairwise constraint matrix, which is specifically:

[0143] Repeat Until convergence, where μ∈(0,1) and t represent the trade-off parameter and iteration count, respectively. represents the initialization of the vertical constraint propagation matrix;

[0144] Repeat Until convergence, where represents the initialization horizontal constraint propagation matrix, express The limit, express The limit of

[0145] is the final pairwise constraint learning matrix for the vth view of the data;

[0146] The weight matrix is ​​calculated based on the final pairwise constraint learning matrix, specifically:

[0147]

[0148] in, Represents the weight matrix The element at row i and column j;

[0149] The second Laplace matrix is ​​calculated according to the weight matrix, specifically:

[0150]

[0151] in, yes The diagonal matrix of ;

[0152] The hypergraph regularization is calculated according to the second Laplacian matrix, specifically:

[0153]

[0154] In this embodiment, the hypergraph regularization used in the present invention has significant advantages over traditional graph regularization because it can capture high-order relationships between nodes, provide richer structural modeling, and perform better when processing complex data and feature learning. Through the high-order constraints of hyperedges, hypergraph regularization can more accurately express the intrinsic structure of the data, improve the model's robustness to noise, and optimize feature representation, making it superior to traditional graph regularization in many application scenarios.

[0155] Based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, the objective function of the double-constrained semi-supervised non-negative matrix factorization is constructed, and the alternating iterative update algorithm is used to solve the objective function to obtain the clustering result. Figure 2 As shown, first obtain the original data matrix Input, and then use the point constraint propagation algorithm to mark the constraint information on the corresponding data points to form a point constraint data matrix with constraint information That is, a multi-view hypergraph, and then the hypergraph pairwise constraint propagation algorithm is performed on the point constraint data matrix to learn deeper constraint information, and perform multi-view non-negative matrix decomposition, hypergraph regularization, label regularization and consensus regularization, and output the final distribution matrix V*, which is the clustering result.

[0156] The objective function of the dual-constrained semi-supervised non-negative matrix factorization is:

[0157]

[0158] Wherein, α, β and γ represent the key trade-off parameters for adjusting the influence of the regularization term, and O represents the objective function. (v) and V (v) Due to the non-convexity of , it is almost impossible to obtain a global optimal solution. In order to solve this problem, an iterative update algorithm is usually used to solve the optimization problem of the algorithm of the present invention, and the multiplication update rule of the algorithm is derived. The alternating iterative update algorithm is used to solve the objective function to obtain the final allocation matrix:

[0159] S8.1: Setting U (v) 、V (v) 、V * Initial value;

[0160] S8.2: Update U (v) : The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as:

[0161]

[0162] To U (v) The first-order derivative of , we get:

[0163]

[0164] According to the KKT conditions, Export The update rule is:

[0165]

[0166] S8.3: Update V (v) : The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as:

[0167]

[0168] V (v) Taking the first-order derivative, we get:

[0169]

[0170] By setting get:

[0171]

[0172] It turns out that:

[0173]

[0174] S8.4: Update V * : About V * The objective function is expressed as:

[0175]

[0176] V * Taking the first-order derivative, we get:

[0177]

[0178] set up Get V* Solution:

[0179]

[0180] S8.5: According to the updated U (v) 、V *(v) and V * Calculate the objective function value of the double-constrained semi-supervised non-negative matrix factorization. If the absolute difference between the objective function value and the objective function value of the previous iteration is less than a preset threshold, output the final V * , the V * is the clustering result, otherwise, repeat steps S8.2-S8.4.

[0181] In this embodiment, when α=100, β=1000, γ=100, and μ=0.3, the clustering method proposed in this example shows the best performance.

[0182] In this embodiment, the present invention overcomes the limitation of the traditional semi-supervised non-negative matrix decomposition method in the lack of supervised information in multi-view clustering, adopts a dual-constraint propagation algorithm combining the point-constraint propagation algorithm and the pair-constraint propagation algorithm, and uses the point-constraint propagation algorithm and the pair-constraint propagation algorithm to improve the performance of multi-view clustering, and makes full use of the prior information, effectively uses the limited prior information to reconstruct a more informative similarity matrix, and then better captures the geometric manifold structure inside the multi-view data, and gives full play to the function of the prior information, so as to obtain better multi-view clustering performance. At the same time, the dual-constraint propagation algorithm can learn a new similarity matrix for use in hypergraph regularization, which can balance the consistency and diversity between different views, thereby improving the reliability and effectiveness of the system.

[0183] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned clustering method are implemented.

[0184] Example 3

[0185] This embodiment provides a semi-supervised non-negative matrix factorization multi-view clustering system based on dual constraints. Figure 3 As shown, including:

[0186] A data acquisition module, used to acquire a multi-view data matrix and a label matrix;

[0187] A preprocessing module, used for constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial allocation matrix, a label matrix and a diagonal matrix according to a multi-view data matrix and a label matrix;

[0188] The objective function construction module of non-negative matrix decomposition is used to establish the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix;

[0189] A consensus regularization building module, used to build consensus regularization based on an initial coefficient matrix and an initial allocation matrix;

[0190] A label regularization building module is used to build multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix;

[0191] A hypergraph regularization construction module, used to construct vertices and hyperedges of a multi-view hypergraph according to a multi-view data matrix, and to construct a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph;

[0192] The objective function construction and solution module is used to construct the objective function of double-constrained semi-supervised non-negative matrix factorization based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, and use the alternating iterative update algorithm to solve the objective function to obtain the clustering result.

[0193] The same or similar reference numerals correspond to the same or similar components;

[0194] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0195] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A double-constrained semi-supervised non-negative matrix factorization multi-view clustering method, characterized in that: include: Get multi-view data matrix and label matrix; Constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial assignment matrix, a label matrix and a diagonal matrix according to the multi-view data matrix and the label matrix; Establishing the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix; Construct consensus regularization based on the initial coefficient matrix and the initial allocation matrix; Construct multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix; Constructing vertices and hyperedges of a multi-view hypergraph according to the multi-view data matrix, and constructing a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph; Based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, the objective function of double-constrained semi-supervised non-negative matrix factorization is constructed, and the alternating iterative update algorithm is used to solve the objective function to obtain the clustering result.

2. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 1, characterized in that: The constructing of a multi-view label matrix and a diagonal matrix according to the multi-view data matrix and the label matrix comprises: The multi-view label matrix is ​​represented as Y = [y1, y2, ..., y n ] T , if the feature point x in the multi-view data matrix i The label of is associated with class j in the label matrix, then y i The i-th element of is set to 1, while all other elements remain 0, whereas all elements of yi are assigned 0; The multi-view diagonal matrix is ​​defined as A = {A ij }, in x i When the label of is associated with class j in the label matrix, A ij =1, otherwise, A ij =0.

3. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 2, characterized in that: The objective function of establishing non-negative matrix decomposition based on the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix is ​​as follows: in, represents the v-th view data matrix, U (v) and V (v) Respectively represent the initial basis matrix and initial coefficient matrix of the v-th view data matrix, n v represents the number of multi-view data matrices, represents the Frobenius norm, (·) T Represents the transpose of a matrix.

4. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 3, characterized in that: The specific method of constructing consensus regularization based on the initial coefficient matrix and the initial allocation indicator matrix is ​​as follows: Among them, γ represents the weight parameter, V * ∈R n×k represents the initial allocation matrix.

5. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 4, characterized in that: The multi-view label regularization is constructed according to the initial coefficient matrix, the label matrix and the diagonal matrix as follows: Where Tr(·) represents the trace of the matrix.

6. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 5, characterized in that: The step of constructing vertices and hyperedges of a multi-view hypergraph according to a multi-view data matrix, and constructing a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph comprises: Construct the vertices of the multi-view hypergraph based on the multi-view data matrix Super Edge Construct an association matrix based on the vertices and hyperedges of the multi-view hypergraph Elements in a matrix Represents the vertex V i (v) and super edge The relationship between them is: Calculate the multi-view diagonal matrix based on the vertices, hyperedges and incidence matrix of the multi-view hypergraph Represents the vth view data matrix and the hyperedge in the multi-view data matrix The relevant weights, vertices The degree is recorded as Super Edge The degree is recorded as The formula definition is as follows: in, Indicates V i (v) and V j (v) On the super edge The Euclidean distance within, the hyperparameter σ (v) Can be configured as the average distance between all vertices; The similarity matrix of the multi-view hypergraph is calculated based on the association matrix and the multi-view diagonal matrix of the multi-view hypergraph. The similarity matrix calculation formula of the hypergraph corresponding to the v-th view data matrix is: in, is a diagonal matrix, each element of which is the sum of the degrees of all hyperedges; The first Laplacian matrix is ​​calculated according to the similarity matrix of the multi-view hypergraph, specifically: in, According to the pairwise constraint propagation algorithm, the initial pairwise constraint matrix Z = {Zij} is calculated, which is: Among them, (x i , x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to the same label, (x i , x j )∈M represents the feature point x in the multi-view data matrix i and x j Belong to different labels, M represents the same label set, and C represents different label sets; The pairwise constraint propagation algorithm of vertical and horizontal propagation is used to calculate the final pairwise constraint learning matrix according to the first Laplace matrix and the initial pairwise constraint matrix, which is specifically: Repeat Until convergence, where μ∈(0, 1) and t represent the trade-off parameter and iteration count, respectively. represents the initialization of the vertical constraint propagation matrix; Repeat the execution. Until convergence, where represents the initialization horizontal constraint propagation matrix, express The limit, express The limit of is the final pairwise constraint learning matrix for the vth view of the data; The weight matrix is ​​calculated based on the final pairwise constraint learning matrix, specifically: in, Represents the weight matrix The element at row i and column j; The second Laplace matrix is ​​calculated according to the weight matrix, specifically: in, yes The diagonal matrix of ; The hypergraph regularization is calculated according to the second Laplacian matrix, specifically:

7. The method for multi-view clustering based on semi-supervised non-negative matrix factorization with dual constraints according to claim 6, characterized in that: The objective function of the dual-constrained semi-supervised non-negative matrix factorization is: U(v)≥0,V(v)≥0,V*≥0 Wherein, α, β and γ represent the key trade-off parameters for adjusting the influence of the regularization term, and O represents the objective function.

8. The method for multi-view clustering based on semi-supervised non-negative matrix decomposition with dual constraints according to claim 7, characterized in that: The method of using an alternating iterative update algorithm to solve the objective function to obtain the final allocation matrix includes: S8.1: Setting U (v) 、V (v) 、V * Initial value; S8.2: Update U (v) : The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as: To U (v) The first-order derivative of , we get: According to the KKT conditions, Export The update rule is: S8.3: Update V(v): The objective function of the dual-constrained semi-supervised non-negative matrix factorization is rewritten as: Taking the first-order derivative of V(v), we get: By setting get: It turns out that: S8.4: Update V*: The objective function with respect to V* is expressed as: Taking the first-order derivative of V*, we get: set up The solution of V* is: S8.5: According to the updated U (v) 、V (v) and V * Calculate the objective function value of the double-constrained semi-supervised non-negative matrix factorization. If the absolute difference between the objective function value and the objective function value of the previous iteration is less than a preset threshold, output the final V * , the V * is the clustering result, otherwise, repeat steps S8.2-S8.

4.

9. A dual-constrained semi-supervised non-negative matrix factorization multi-view clustering system, characterized in that: include: A data acquisition module, used to acquire a multi-view data matrix and a label matrix; A preprocessing module, used for constructing a multi-view initial basis matrix, an initial coefficient matrix, an initial allocation matrix, a label matrix and a diagonal matrix according to a multi-view data matrix and a label matrix; The objective function construction module of non-negative matrix decomposition is used to establish the objective function of non-negative matrix decomposition according to the multi-view data matrix, the multi-view initial basis matrix, and the initial coefficient matrix; A consensus regularization building module, used to build consensus regularization based on an initial coefficient matrix and an initial allocation matrix; A label regularization building module is used to build multi-view label regularization based on the initial coefficient matrix, the label matrix and the diagonal matrix; A hypergraph regularization construction module, used to construct vertices and hyperedges of a multi-view hypergraph according to a multi-view data matrix, and to construct a multi-view hypergraph regularization according to the vertices and hyperedges of the multi-view hypergraph; The objective function construction and solution module is used to construct the objective function of double-constrained semi-supervised non-negative matrix factorization based on the objective function of non-negative matrix factorization, consensus regularization, multi-view label regularization and multi-view hypergraph regularization, and use the alternating iterative update algorithm to solve the objective function to obtain the clustering result.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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