Multiview clustering method based on block-diagonal low-rank graph filtering

Abstract

This invention belongs to the field of multi-view clustering technology, and particularly relates to a multi-view clustering method based on block diagonal low-rank graph filtering. The method involves acquiring the data matrix of multi-view data and performing data preprocessing. Based on the preprocessed data, an initial similarity graph, a k-nearest neighbor graph, and a normalized Laplacian matrix are constructed. Spectral embedding processing is performed on the normalized Laplacian matrix of each view to extract low-dimensional representations and generate low-rank affinity matrices. The low-rank affinity matrices of each view are stacked into a third-order tensor. Through tensor rotation transformation and nuclear norm constraints, the shared block diagonal structure among the multiple views is learned. An adaptive weight mechanism is introduced to learn the contribution of each view, and a unified and sparse consensus graph is constructed based on the adaptive weights. A graph filter is constructed based on the consensus graph, and feature embeddings with enhanced clustering properties are generated through the graph filter while maintaining the manifold structure of the data.

Description

Technical Field

[0001] This invention belongs to the field of multi-view clustering technology, and particularly relates to a multi-view clustering method based on block diagonal low-rank graph filtering. Background Technology

[0002] Multi-view clustering integrates complementary information from heterogeneous data from multiple sources and is a key technology for processing complex data in unsupervised learning and pattern recognition, with wide applications in image analysis, data mining, and other scenarios. However, most existing multi-view clustering methods achieve view fusion only through simple weighting or single-graph learning, making it difficult to deeply explore the shared block diagonal structure between views. The combination of low-rank constraints and graph structure is relatively loose, and the methods cannot adaptively allocate view weights, resulting in the underutilization of high-quality view information and the interference of low-quality views with clustering results.

[0003] Most current methods do not combine graph filtering with multi-view clustering, making it difficult to enhance feature clustering. Furthermore, they lack effective solutions for multi-view tensor fusion and data manifold preservation, resulting in complex model solutions and low convergence efficiency. These technical shortcomings make traditional methods prone to feature information distortion and structural alignment deviations when dealing with complex multi-view data, ultimately leading to insufficient clustering accuracy, poor robustness, and an inability to adapt to complex data scenarios in real-world applications. Summary of the Invention

[0004] In view of the aforementioned problems, and in conjunction with the first aspect of the present invention, embodiments of the present invention provide a multi-view clustering method based on block diagonal low-rank graph filtering, the method comprising: The steps include: Step S1: Obtain the data matrix of the multi-view data and complete the data preprocessing. Based on the preprocessed data, construct the initial similarity graph, k-nearest neighbor graph and normalized Laplacian matrix. Step S2: Perform spectral embedding processing on the normalized Laplacian matrix of each view to extract low-dimensional representations and generate low-rank affinity matrices; Step S3: Stack the low-rank affinity matrices of each view into a third-order tensor. Through tensor rotation transformation and nuclear norm constraints, learn the shared block diagonal structure among multiple views. Step S4: Introduce an adaptive weight mechanism to learn the contribution of each view, and build a unified and sparse consensus graph based on the adaptive weight; Step S5: Construct a graph filter based on the consensus graph, and generate feature embeddings with enhanced clustering properties through the graph filter while maintaining the manifold structure of the data; Step S6: Solve the multi-view clustering model using the alternating direction multiplier method, and execute the clustering algorithm on the consensus graph obtained by the solution to output the final clustering result.

[0005] Preferably, in step S1, the Gaussian kernel function is used to calculate the similarity between samples to construct an initial similarity graph, a k-nearest neighbor graph is constructed based on the initial similarity graph, and the normalized Laplacian matrix is ​​derived from the adjacency matrix of the k-nearest neighbor graph.

[0006] Preferably, a fixed number of nearest neighbors is used when constructing the k-nearest neighbor graph, the adjacency matrix is ​​assigned a value based on the mutual nearest neighbor relationship between samples, and the degree matrix is ​​a diagonal matrix calculated based on the adjacency matrix.

[0007] Preferably, in step S2, the normalized Laplacian matrix is ​​subjected to spectral decomposition to obtain a spectral embedding matrix, and a low-rank affinity matrix is ​​generated by the outer product operation of the spectral embedding matrix.

[0008] Preferably, in step S3, a rotation transformation is performed on the stacked third-order tensor to obtain a proxy tensor, and the nuclear norm constraint of the proxy tensor is used to realize the alignment of the multi-view structure and the learning of the diagonal structure of the shared block.

[0009] Preferably, in step S4, the adaptive weights are calculated based on the difference between the consensus graph and the low-rank affinity matrix of each view, and the consensus graph satisfies the symmetry, numerical range constraints and row sum normalization conditions.

[0010] Preferably, in step S5, an adaptive graph filter is constructed based on the consensus graph, and the graph filter is applied to the original feature data to obtain enhanced feature embedding. At the same time, a manifold regularization term is introduced to maintain the data manifold structure.

[0011] Preferably, in step S6, the graph filter, consensus graph, spectral embedding matrix and surrogate tensor are updated alternately using the alternating direction multiplier method. After iteration until convergence, k-means clustering is performed on the consensus graph to obtain the result.

[0012] Preferably, it also includes a system for implementing the multi-view clustering method, the system comprising: The preprocessing module is used to acquire the multi-view data matrix, complete data preprocessing, and construct the initial similarity graph, k-nearest neighbor graph, and normalized Laplacian matrix. The spectral embedding module is used to perform spectral embedding on the normalized Laplacian matrix, extract the low-dimensional representation, and generate a low-rank affinity matrix. The tensor fusion module is used to stack the low-rank affinity matrices of each view into a third-order tensor, and learn the shared block diagonal structure through tensor rotation transformation and nuclear norm constraints. The consensus learning module is used to introduce an adaptive weight mechanism to learn the contribution of views and build a unified sparse consensus graph. The filter module is used to construct graph filters based on the consensus graph, generating feature embeddings that enhance clustering properties while preserving the manifold structure; The clustering module is used to solve the clustering model using the alternating direction multiplier method and execute the clustering algorithm to output the results.

[0013] Based on the above, by using block diagonal low-rank constraints and tensor rotation transformation to deeply mine the shared clustering structure of multi-view data, we can effectively solve the problems of heterogeneous information in multi-view data and difficulty in aligning structures between views, significantly improve the structural regularity of the low-rank affinity matrix, and dynamically allocate the contribution of each view by relying on the adaptive weight mechanism to weaken the interference of low-quality views, and construct a sparse unified consensus graph with clear cluster boundaries, so that the fusion of multi-view features is more in line with the real distribution of data.

[0014] The graph filter built on consensus graph can significantly enhance the clustering and distinguishing properties of features. It preserves the original topological structure of the data through manifold regularization, avoids distortion of feature information, and achieves efficient model solving by combining the alternating direction multiplier method. This not only improves the convergence speed and running stability of the algorithm, but also greatly optimizes the accuracy and robustness of the clustering results. It effectively overcomes the shortcomings of traditional multi-view clustering structure mining and coarse feature fusion. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the execution flow of the multi-view clustering method based on block diagonal low-rank graph filtering provided in an embodiment of the present invention.

[0016] Figure 2 This is a system schematic diagram of the multi-view clustering method based on block diagonal low-rank graph filtering provided in an embodiment of the present invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings. Figure 1 This is a flowchart illustrating a multi-view clustering method based on block diagonal low-rank graph filtering provided in an embodiment of the present invention. The following is a detailed description of this multi-view clustering method based on block diagonal low-rank graph filtering.

[0018] Reference Figure 1 This invention provides a multi-view clustering method based on block diagonal low-rank graph filtering, which includes the following steps: S1. Obtain the data matrix of the multi-view data and perform data preprocessing to construct an initial similarity map; Specifically, given a multi-view dataset containing m views, using ,in Indicates the first Data matrix of views, It is the sample size. It's a feature dimension. Data cleaning and standardization preprocessing are performed on each view.

[0019] S11. Obtain the data matrix of multi-view data; S12. Based on the data matrix of multi-view data, construct an initial similarity graph; Specifically, based on the data matrix of each view, the similarity between samples is calculated using a Gaussian kernel function to construct an initial similarity map. Its similarity matrix... Defined by element: ; Bandwidth parameter Let it be the median of the Euclidean distance between all sample pairs.

[0020] S13. Construct the k-nearest neighbor graph and the normalized Laplacian matrix; Specifically, based on Build Nearest neighbor graph Among them, the number of nearest neighbors The adjacency matrix is ​​fixed at 10. The construction rule is: if and Mutual Neighbors, Otherwise, it is 0; diagonal elements are set to 1. Then, the normalized Laplace matrix is ​​derived: ; Where the degree matrix It is a diagonal matrix. .

[0021] S2. Extract low-dimensional representations through spectral embedding to generate low-rank affinity matrices; Specifically, the normalized Laplacian matrix of each view is spectrally decomposed to obtain the spectral embedding matrix, and a low-rank affinity matrix is ​​generated through outer product operation.

[0022] S21. Perform spectral decomposition to obtain a low-dimensional representation; Specifically, L(v) is spectral decomposed, and the spectral embedding matrix is ​​obtained by solving the eigenvector problem. ,in Number of clusters: ; S22. Generate a low-rank affinity matrix; Specifically, a low-rank affinity matrix is ​​constructed through outer product. The optimization aims to minimize the difference between the initial affinity matrix and the ideal low-rank affinity matrix: ; S3. Perform multi-view low-rank tensor fusion and structure alignment to learn shared block diagonal structures; Specifically, to uncover shared structures among views, the low-rank affinity matrices of each view are stacked to form a third-order tensor. The shared block diagonal structure is then learned through tensor rotation transformation and nuclear norm constraints.

[0023] S31. Construct a multi-view tensor representation; Specifically, stacking diagonal affinity matrices Form a third-order tensor .

[0024] S32, Tensor Rotation Transformation and Structure Learning; Specifically, the surrogate tensor is obtained through tensor rotation transformation. And introduce nuclear norm constraints Learn the shared structure. The joint optimization objective is: ; S4. Adaptively learn the contribution of different views to construct a unified and sparse consensus graph.

[0025] Specifically, to balance the differences in view quality, adaptive weights are introduced to construct a consensus graph and enhance fusion robustness.

[0026] S41. Introduce an adaptive weighting mechanism; S42. Construct a unified sparse consensus graph; Specifically, by optimizing the target learning consensus graph : ; The weight update formula is: ; S5. Construct graph filters based on consensus graphs to generate feature embeddings that enhance clustering properties while maintaining the manifold structure.

[0027] Specifically, graph filters are constructed based on consensus graphs to generate feature embeddings while maintaining the manifold structure.

[0028] S51. Construct an adaptive graphical filter; Specifically, based on consensus graph Constructing graph filters: ; S52. Generate enhanced feature embeddings; Specifically, the filter is applied to the feature data: ; S53, Maintain manifold structure; Specifically, a manifold regularization term is introduced: ; S6. Solve the low-rank consensus graph filter-driven multi-view clustering model using the alternating direction multiplier method, and perform k-means clustering on the solution results; Specifically, all components are integrated to form the final objective function, which is then solved using the ADMM algorithm.

[0029] S61. Construct an overall optimization goal; Specifically, the final objective function is: ; S62. Solve using the ADMM algorithm; Specifically, Lagrange multipliers and penalty parameters are introduced to update the variables alternately: Update graph filter : Keep other variables fixed, optimize using gradient descent or closed-form solutions Update consensus graph : Using Euclidean projection onto the simplex method Update spectrum embedding Solving using the generalized power iteration algorithm Update proxy tensor Solving using tensor tubular contraction operators S63. Convergence judgment and clustering output; Specifically, the consensus graph is iteratively updated until the relative error is less than a threshold. Clustering results can be obtained by applying spectral clustering or k-means algorithm.

[0030] Reference Figure 2 A multi-view clustering system based on block diagonal low-rank graph filtering includes: The preprocessing module is used for data preprocessing and initial graph construction; The spectral embedding module is used for spectral embedding extraction and low-rank matrix generation; The tensor fusion module is used for multi-view tensor fusion and structural alignment. The consensus learning module is used for adaptive weight learning and consensus graph construction; The filter module is used for graph filter construction and feature enhancement; The clustering module is used for model solving and final clustering.

[0031] It should be noted that, in order to simplify the description of the present invention and thus help to understand one or more embodiments of the invention, multiple features may sometimes be grouped into one embodiment, drawing or description thereof in the foregoing description of the embodiments of the present invention.

[0032] The embodiments of this application have been described above with reference to the accompanying drawings. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. This application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A method of multi-view clustering based on block-diagonal low-rank graph filtering, characterized in that: Includes the following steps: Step S1: Obtain the data matrix of the multi-view data and complete the data preprocessing. Based on the preprocessed data, construct the initial similarity graph, k-nearest neighbor graph and normalized Laplacian matrix. Step S2: Perform spectral embedding processing on the normalized Laplacian matrix of each view to extract low-dimensional representations and generate low-rank affinity matrices; Step S3: Stack the low-rank affinity matrices of each view into a third-order tensor. Through tensor rotation transformation and nuclear norm constraints, learn the shared block diagonal structure among multiple views. Step S4: Introduce an adaptive weight mechanism to learn the contribution of each view, and build a unified and sparse consensus graph based on the adaptive weight; Step S5: Construct a graph filter based on the consensus graph, and generate feature embeddings with enhanced clustering properties through the graph filter while maintaining the manifold structure of the data; Step S6: Solve the multi-view clustering model using the alternating direction multiplier method, and execute the clustering algorithm on the consensus graph obtained by the solution to output the final clustering result.

2. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S1, the Gaussian kernel function is used to calculate the similarity between samples to construct an initial similarity graph. Based on the initial similarity graph, a k-nearest neighbor graph is constructed, and the normalized Laplace matrix is ​​derived from the adjacency matrix of the k-nearest neighbor graph.

3. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 2, characterized in that: When constructing the k-nearest neighbor graph, a fixed number of nearest neighbors is used. The adjacency matrix is ​​assigned values ​​based on the mutual nearest neighbor relationship between samples, and the degree matrix is ​​a diagonal matrix calculated based on the adjacency matrix.

4. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S2, the normalized Laplacian matrix is ​​spectrally decomposed to obtain the spectral embedding matrix, and a low-rank affinity matrix is ​​generated by the outer product operation of the spectral embedding matrix.

5. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S3, a rotation transformation is performed on the stacked third-order tensor to obtain a surrogate tensor. The nuclear norm constraint of the surrogate tensor is used to achieve multi-view structure alignment and shared block diagonal structure learning.

6. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S4, the adaptive weights are calculated based on the difference between the consensus graph and the low-rank affinity matrix of each view. The consensus graph satisfies the symmetry, numerical range constraints, and row sum normalization conditions.

7. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S5, an adaptive graph filter is constructed based on the consensus graph. The graph filter is applied to the original feature data to obtain enhanced feature embedding. At the same time, a manifold regularization term is introduced to maintain the data manifold structure.

8. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: In step S6, the graph filter, consensus graph, spectral embedding matrix and surrogate tensor are updated alternately using the alternating direction multiplier method. After iteration until convergence, k-means clustering is performed on the consensus graph to obtain the result.

9. The multi-view clustering method based on block diagonal low-rank graph filtering according to claim 1, characterized in that: It also includes a system for implementing the multi-view clustering method, the system comprising: The preprocessing module is used to acquire the multi-view data matrix, complete data preprocessing, and construct the initial similarity graph, k-nearest neighbor graph, and normalized Laplacian matrix. The spectral embedding module is used to perform spectral embedding on the normalized Laplacian matrix, extract the low-dimensional representation, and generate a low-rank affinity matrix. The tensor fusion module is used to stack the low-rank affinity matrices of each view into a third-order tensor, and learn the shared block diagonal structure through tensor rotation transformation and nuclear norm constraints. The consensus learning module is used to introduce an adaptive weight mechanism to learn the contribution of views and build a unified sparse consensus graph. The filter module is used to construct graph filters based on the consensus graph, generating feature embeddings that enhance clustering properties while preserving the manifold structure; The clustering module is used to solve the clustering model using the alternating direction multiplier method and execute the clustering algorithm to output the results.

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