Multi-view clustering method, device and medium based on deep non-negative matrix factorization

Abstract

The present invention discloses a multi-view clustering method, device and medium based on deep non-negative matrix decomposition, including the following specific steps: acquiring image data, obtaining a base matrix and a coefficient matrix of the image data based on DMF; constructing a multi-view DMF model according to the base matrix and the coefficient matrix, performing feature diversity constraints according to the base matrix, and determining an optimal graph regularization based on kNN; determining an optimization model according to the multi-view DMF model, feature diversity constraints and optimal graph regularization; solving the optimization model, determining a consistency coefficient matrix, clustering the consistency coefficient matrix using k-means, and obtaining a clustering result. The reconstruction error of the deep non-negative matrix decomposition is measured by using a logarithmic loss function, and on this basis, feature diversity constraints are performed using feature diversity learning items to learn a more discriminative expression, and the optimal graph learning is used to greatly reduce the number of misclassified neighbors, thereby improving the clustering performance.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to a multi-view clustering method, device and medium based on deep non-negative matrix decomposition. Background Art

[0002] In practical applications, data presents complex and high-dimensional characteristics. Therefore, finding a suitable data expression is particularly important for data clustering. Non-negative matrix factorization (NMF) is an effective data dimensionality reduction method that decomposes a data matrix X into two non-negative matrices (base matrix U and coefficient matrix V). Clustering the coefficient matrix V obtained after NMF decomposition can achieve a higher clustering performance. However, NMF is only a single-layer matrix decomposition method, which cannot capture different attribute features and hierarchical information in the original data. To this end, deep semi-non-negative matrix factorization (DSNMF) solves this problem. It is a multi-layer matrix decomposition method. DSNMF decomposes the coefficient matrix multiple times to obtain different attribute features and different hierarchical information. Recently, multi-view data has received widespread attention because multi-view data describes an object from multiple angles and contains more comprehensive information, including consistency information and diversity information. Both NMF and DSNMF are single-view methods, which cannot effectively analyze and process multi-view data. Therefore, some multi-data clustering methods based on matrix decomposition have been proposed, including methods based on NMF and deep matrix factorization (DMF). Similarly, compared with the multi-view NMF method, the multi-view DMF has the advantage of being able to capture different attribute features and hierarchical information in the original data. At present, the representative multi-view DMF methods include DMVC, AwMvDMD and MvDMFPA. Because the importance of each view in multi-view data is different, DMVC assigns different weights to each view. In addition, DMVC uses graph regularization to protect the local geometric information of the original data, which makes the data distribution structure after dimensionality reduction similar to the data distribution of the original data. Similarly, AwMvDMD adopts l 2,1 The norm is used as the loss function to improve the robustness of DMF. MvDMFPA adopts the idea of ​​partition alignment to obtain consistent information in multi-view datasets.

[0003] The existing methods have the following shortcomings: (1) Many DMF methods use the Frobenius norm (F norm) as the loss function, but the F norm is greatly affected by noise in practice; (2) Feature diversity is not fully utilized; (3) For DMF methods with graph regularization, kNN is often used to construct data graphs, which will contain many misclassified points, which will reduce the clustering performance. Summary of the invention

[0004] The technical problem to be solved by the present invention is that the F norm is greatly affected by noise in practice, feature diversity is not fully utilized, and kNN construction of data graph will reduce clustering performance. The purpose is to provide a multi-view clustering method, device and medium based on deep non-negative matrix decomposition, use the logarithmic loss function to measure the reconstruction error of deep non-negative matrix decomposition, and on this basis use feature diversity learning items to learn a more discriminative expression, and use optimal graph learning to greatly reduce the number of misclassified neighbors, thereby improving clustering performance.

[0005] The present invention is achieved through the following technical solutions:

[0006] A first aspect of the present invention provides a multi-view clustering method based on deep non-negative matrix decomposition, comprising the following specific steps:

[0007] Acquire image data, and obtain the basis matrix and coefficient matrix of the image data at different representation layers based on deep non-negative matrix decomposition (DMF);

[0008] A multi-view DMF model is constructed based on the basis matrix and coefficient matrix, feature diversity constraints are performed based on the basis matrix, and the optimal graph regularization is determined based on kNN;

[0009] Determine the optimization model based on the multi-view DMF model, feature diversity constraints and optimal graph regularization;

[0010] The optimization model is solved to determine the consistency coefficient matrix, and the consistency coefficient matrix is ​​clustered using k-means to obtain the clustering results.

[0011] The present invention obtains the basis matrix and coefficient matrix of image data through DMF, constructs a multi-view DMF model according to the basis matrix and coefficient matrix, uses the logarithmic loss function to measure the reconstruction error of deep non-negative matrix decomposition, and on this basis uses the feature diversity learning item to perform feature diversity constraints to learn a more discriminative expression, and uses optimal graph learning based on kNN to greatly reduce the number of misclassified neighbors, thereby improving clustering performance.

[0012] Furthermore, the base matrix and coefficient matrix of the image data obtained based on the DMF specifically include:

[0013] Get the p-th view data matrix X p , determine the basis matrix of the p-th view r layer as The coefficient matrix of the p-th view R layer is

[0014] Furthermore, the construction of the multi-view DMF optimization model specifically includes:

[0015] Based on the data matrix X p , basis matrix and the coefficient matrix Build a multi-view DMF model;

[0016] The multi-view DMF model is optimized by using a logarithmic loss function to obtain a multi-view DMF optimization model, wherein the multi-view DMF model includes:

[0017]

[0018] in is the F-norm of the matrix X, X p represents the data matrix, represents the basis matrix of any view, represents the basis matrix of the last layer view, represents the coefficient matrix.

[0019] Furthermore, the multi-view DMF optimization model includes:

[0020]

[0021] in, Indicates that when x i When is an outlier point, the log loss is less than the square loss.

[0022] Furthermore, the feature diversity constraint according to the base matrix specifically includes:

[0023] The basis vector is obtained based on the basis matrix, and the inner diameter between two basis vectors is minimized to obtain the feature diversity constraint, which includes:

[0024]

[0025] Among them, tr(·) is the trace operation of the matrix, l r is the decomposition dimension of the rth level, is the i-th column vector in the r-th layer basis matrix of the p-th view, is a column vector whose elements are all 1.

[0026] Furthermore, the kNN-based determination of the optimal graph regularization specifically includes:

[0027] Get a set of neighboring points of the sample and calculate the similarity matrix of each view based on kNN;

[0028] The optimal graph is calculated by selecting the smallest element in the similarity matrix of all views and combining them into a new similarity matrix;

[0029] Calculate the diagonal matrix and Laplacian matrix based on the new similarity matrix;

[0030] Based on the coefficient matrix and the Laplacian matrix, the optimal graph regularization is determined.

[0031] Furthermore, the optimal graph regularization construction step includes:

[0032]

[0033] (W * ) ij =min{(W 1 ) ij ,(W 2 ) ij ,...,(W P ) ij}

[0034]

[0035]

[0036]

[0037] Among them, when the sample It is a sample k nearest neighbors or samples It is a sample k nearest neighbors, otherwise (W p ) ij =0; W ij represents the similarity matrix, (W * ) ij represents the new similarity matrix, Denotes the diagonal matrix, L * represents the Laplacian matrix.

[0038] Furthermore, the optimization model includes:

[0039]

[0040] Among them, X p represents the data matrix, represents the basis matrix of any view, represents the basis matrix of the last layer view, represents the coefficient matrix, is a column vector with all elements set to 1, α and β are two weight parameters, L * represents the Laplacian matrix.

[0041] A second aspect of the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a multi-view clustering method based on deep non-negative matrix decomposition is implemented.

[0042] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a multi-view clustering method based on deep non-negative matrix decomposition.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] The basis matrix and coefficient matrix of the image data are obtained through DMF, and a multi-view DMF model is constructed based on the basis matrix and coefficient matrix. The logarithmic loss function is used to measure the reconstruction error of deep non-negative matrix decomposition. On this basis, the feature diversity learning item is used to constrain the feature diversity to learn a more discriminative expression. Based on kNN, optimal graph learning is used to greatly reduce the number of misclassified neighbors, thereby improving the clustering performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0046] Figure 1 is a model block diagram of the method in the embodiment of the present invention;

[0047] Figure 2 t-SNE visualization results of four multi-view DMF methods in embodiments of the present invention;

[0048] Figure 3 are the optimal similarity matrix and kNN similarity matrix of the ORL data set in the embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0050] Example 1

[0051] like Figure 1 As shown, the first aspect of this embodiment provides a multi-view clustering method based on deep non-negative matrix decomposition, including the following specific steps:

[0052] Acquire image data, and obtain the basis matrix and coefficient matrix of the image data at different representation layers based on deep non-negative matrix decomposition (DMF);

[0053] A multi-view DMF model is constructed based on the basis matrix and coefficient matrix, feature diversity constraints are performed based on the basis matrix, and the optimal graph regularization is determined based on kNN;

[0054] Determine the optimization model based on the multi-view DMF model, feature diversity constraints and optimal graph regularization;

[0055] The optimization model is solved to determine the consistency coefficient matrix, and the consistency coefficient matrix is ​​clustered using k-means to obtain the clustering results.

[0056] This paper obtains the basis matrix and coefficient matrix of image data through DMF, builds a multi-view DMF model based on the basis matrix and coefficient matrix, uses the logarithmic loss function to measure the reconstruction error of deep non-negative matrix decomposition, and uses the feature diversity learning item to constrain feature diversity to learn a more discriminative expression. Based on kNN, optimal graph learning is used to greatly reduce the number of misclassified neighbors, thereby improving clustering performance.

[0057] In some possible embodiments, for a multi-view DMF method of P views, let the p-th view data matrix be X p , the basis matrix of the p-th view r layer is The coefficient matrix of the p-th view R layer is The optimization model of the standard multi-view DMF is as follows:

[0058]

[0059] in is the F-norm of the matrix X. In this formula, the matrix X is used to refer to means All elements in are greater than 0. The non-negative constraint makes the model more interpretable. represents the basis matrix of any view, represents the basis matrix of the last layer view, represents the coefficient matrix.

[0060] When the i-th sample point x i When is an outlier, the square loss in the above formula will make the objective function very large, so the entire model will be greatly affected by noise. To address this problem, we use a logarithmic loss function to replace the F norm to increase the robustness of the multi-view DMF. The optimization model is:

[0061]

[0062] in When x iWhen is an outlier point, the log loss will be smaller than the square loss, so our method can improve the robustness of multi-view DMF.

[0063] In some possible embodiments, we utilize a feature diversity constraint to learn diverse features in the data, which will make the expression matrix more discriminative;

[0064] In the basis matrix U of the DMF, each basis vector u i They all represent different features contained in the data set. If these features are diverse, each sample will be easier to distinguish. Therefore, using feature diversity can make the obtained coefficient matrix more discriminative.

[0065] We obtain the diversity feature by minimizing the inner product between two basis vectors, so the feature diversity constraint can be expressed as:

[0066]

[0067] Among them, tr(·) is the trace operation of the matrix, l r is the decomposition dimension of the rth level, is the i-th column vector in the r-th layer basis matrix of the p-th view, is a column vector whose elements are all 1, X T It refers to the transpose operation of a matrix.

[0068] In some possible embodiments, in most multi-view DMF methods involving graph learning, kNN is often used to construct a similarity matrix, that is,

[0069]

[0070] Where kNN(x i ) represents the sample x i However, this similarity matrix contains many misclassified points, which will reduce the clustering performance. To address this problem, we use an optimal graph construction method that can reduce the number of misclassifications and effectively protect the local geometric structure of the data.

[0071] First, the kNN method is used to calculate the similarity matrix of each view, that is, when the sample It is a sample k nearest neighbors or samples It is a sample When the k nearest neighbors are p ) ij =1, otherwise (W p ) ij =0, where i=1,2,3,...n, j=1,2,3,...m.

[0072] Then, we calculate the optimal graph by selecting the smallest element in the similarity matrix of all views and combining them into a new similarity matrix, namely (W * ) ij =min{(W 1 ) ij ,(W 2 ) ij ,...,(W P ) ij};

[0073] Finally, we calculate the angle matrix and the Laplacian matrix The optimal graph regularization can be expressed as:

[0074]

[0075] Among them, when the sample It is a sample k nearest neighbors or samples It is a sample k nearest neighbors, otherwise (W p ) ij =0; W ij represents the similarity matrix, (W * ) ij represents the new similarity matrix, Denotes the diagonal matrix, L * represents the Laplacian matrix.

[0076] Based on the above analysis, the method we proposed can be expressed as the following optimization model:

[0077]

[0078] Among them, α and β are two weight parameters, which are used to weigh the importance of each part;

[0079] By solving the optimization model, we can obtain the coefficient matrix Then we get the consistency coefficient matrix Finally, k-means is used to * Perform cluster analysis.

[0080] A second aspect of this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a multi-view clustering method based on deep non-negative matrix decomposition is implemented.

[0081] A third aspect of this embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a multi-view clustering method based on deep non-negative matrix decomposition.

[0082] Example 2

[0083] In order to verify the robustness of our proposed method, we compared the clustering performance between the multi-view deep non-negative matrix factorization with F norm and the multi-view deep non-negative matrix factorization with logarithmic loss on the noisy dataset. The method for making the noise-free dataset data0 is as follows: First, 2 views are randomly generated, and the basis matrix of the 2 layers Then generate a cluster indicator matrix V∈R with 2000 samples containing 20 classes 20×2000 , where each class has 100 samples; finally, the data matrix is ​​calculated using And the samples are standardized. The method of making the noisy data set data1 is: randomly generate vectors that obey the Gaussian distribution with a mean of 0 and a standard deviation of 1 to replace 10% of the samples in each class of data0. We performed the clustering experiment 10 times and recorded the average results and standard deviation. The clustering performance is evaluated by six commonly used clustering indicators (ACC, NMI, Purity, F-score, Precision and ARI). The clustering results of the two models on these two data sets are shown in Table 1:

[0084] Table 1 - Clustering results of two models on two datasets

[0085]

[0086] From the above results, we can see that on the noise-free dataset, the performance of the two is similar. On the noise-free dataset, the deep non-negative matrix factorization with logarithmic loss is more robust.

[0087] To verify the effectiveness of the proposed method, t-SNE visualization is performed on the coefficient matrix of the ORL face dataset decomposition. In addition, we compare three existing multi-view DMF methods, including DMVC, AMvDMD, and MvDMFPA. The results are shown in Figure 2 As shown, Figure 2 (a)-(d) show the t-SNE visualization results of the four multi-view DMF methods. As can be seen from the figure, the cluster distribution of the proposed method has a smaller intra-class distance and a larger inter-class distance, and samples of different classes are easier to distinguish. Therefore, it is more discriminative and its clustering performance will be higher.

[0088] In order to verify the effectiveness of the optimal graph, the optimal similarity matrix and kNN similarity matrix of the ORL dataset are as follows Figure 3As shown in the figure, it can be seen that there are a large number of misclassified neighbors in the kNN graph, which is not conducive to data clustering. However, there are very few misclassified neighbors in the optimal graph. Therefore, the optimal graph can effectively improve the clustering performance.

[0089] We perform all methods on five commonly used multi-view DMF datasets, including ORL, COIL20, CiteSeer, 3Sources and ReutersEN datasets. In order to reflect the performance of the proposed method, we compare the clustering performance of the proposed method with the existing multi-view DMF methods (DMVC, AMvDMD and MvDMFPA). The clustering performance is evaluated by six commonly used clustering indicators (ACC, NMI, Purity, F-score, Precision and ARI). The evaluation comparison results are shown in Table 2:

[0090] Table 2 Comparison results of clustering performance evaluation between the proposed method and the existing multi-view DMF method

[0091]

[0092]

[0093] In Table 2, the best results are in bold. On the ORL and COIL20 datasets, the proposed method and DMVC achieve good performance, because both the proposed method and DMVC use graph regularization to protect the local geometric structure of the data. In addition, the optimal graph of the proposed method greatly reduces the number of misclassified neighbors, so it has higher clustering performance. On the CiteSeer dataset, the performance of the proposed method is significantly better than that of other comparison methods, mainly because the proposed method not only protects the local geometric structure of the data, but also uses feature diversity to obtain a more discriminative data expression. On the 3Sources and ReutersEN datasets, the proposed method and MvDMFPA achieve similar performance, which shows that extracting both consistency information and diversity information of the data can improve clustering performance.

[0094] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-view clustering method based on deep non-negative matrix factorization, characterized in that: The specific steps include: Acquire image data, and obtain the basis matrix and coefficient matrix of the image data at different representation layers based on deep non-negative matrix decomposition (DMF); A multi-view DMF model is constructed based on the basis matrix and coefficient matrix, feature diversity constraints are performed based on the basis matrix, and the optimal graph regularization is determined based on kNN; An optimization model is determined according to a multi-view DMF model, feature diversity constraints and optimal graph regularization, wherein the optimization model includes: Among them, X p represents the data matrix, represents the basis matrix of any view, represents the basis matrix of the last layer view, represents the coefficient matrix, is a column vector with all elements set to 1, α and β are two weight parameters, L * represents the Laplacian matrix; The optimization model is solved to determine the consistency coefficient matrix, and the consistency coefficient matrix is ​​clustered using k-means to obtain the clustering results.

2. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 1, characterized in that: The base matrix and coefficient matrix of the image data obtained based on the DMF specifically include: Get the p-th view data matrix X p , determine the basis matrix of the p-th view r layer as The coefficient matrix of the p-th view R layer is 3. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 2, characterized in that: The construction of the multi-view DMF optimization model specifically includes: Based on the data matrix X p , basis matrix and the coefficient matrix Build a multi-view DMF model; The multi-view DMF model is optimized by using a logarithmic loss function to obtain a multi-view DMF optimization model, wherein the multi-view DMF model includes: in is the F-norm of the matrix X, X p represents the data matrix, represents the basis matrix of any view, U R p Represents the basis matrix of the last layer view, V R p represents the coefficient matrix.

4. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 3, characterized in that: The multi-view DMF optimization model includes: in, Indicates that when x i When is an outlier point, the log loss is less than the square loss.

5. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 1, characterized in that: The feature diversity constraint according to the basis matrix specifically includes: The basis vector is obtained based on the basis matrix, and the inner diameter between two basis vectors is minimized to obtain the feature diversity constraint, which includes: Among them, tr(·) is the trace operation of the matrix, l r is the decomposition dimension of the rth level, is the i-th column vector in the r-th layer basis matrix of the p-th view, is a column vector whose elements are all 1.

6. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 1, characterized in that: The kNN-based determination of the optimal graph regularization specifically includes: Get a set of neighboring points of the sample and calculate the similarity matrix of each view based on kNN; The optimal graph is calculated by selecting the smallest element in the similarity matrix of all views and combining them into a new similarity matrix; Calculate the diagonal matrix and Laplacian matrix based on the new similarity matrix; Based on the coefficient matrix and the Laplacian matrix, the optimal graph regularization is determined.

7. The multi-view clustering method based on deep non-negative matrix decomposition according to claim 6, characterized in that: The optimal graph regularization construction step includes: (IN * ) ij =min{(W 1 ) ij ,(IN 2 ) ij ,...,(IN P ) ij } Among them, when the sample It is a sample k nearest neighbors or samples It is a sample k nearest neighbors, otherwise (W p ) ij =0; W ij represents the similarity matrix, (W * ) ij represents the new similarity matrix, Denotes the diagonal matrix, L * represents the Laplacian matrix.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements a multi-view clustering method based on deep non-negative matrix decomposition as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, a multi-view clustering method based on deep non-negative matrix decomposition as described in any one of claims 1 to 7 is implemented.

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