A Multi-View Clustering Image Segmentation Method and System Based on Embedding Approximation Learning

Abstract

The present invention discloses a multi-view clustering image segmentation method and system based on embedded approximate learning. The method includes the following steps: obtaining an image multi-view data set to be subjected to image segmentation; inputting the image multi-view data set into a pre-constructed clustering model, iteratively updating the parameters of the clustering model according to an optimization objective, and when the change value of the optimization objective is less than a set threshold, obtaining an optimized clustering model; inputting the image multi-view data set into the optimized clustering model, outputting a clustering result, thereby completing multi-view subspace clustering; and performing image segmentation according to the clustering result to obtain an image segmentation result. By combining self-representation learning, robust principal component analysis technology, and Grassmann manifold space approximate learning, the present invention avoids an increase in computational cost caused by eigenvalue decomposition of a similarity matrix during the optimization process, and improves the efficiency and quality of clustering.

Description

Technical Field

[0001] The present invention relates to the technical fields of machine learning, data mining technology, graph optimization, etc., and particularly relates to a multi-view clustering image segmentation method and system based on embedding approximation learning. Background Art

[0002] As a basic technology in unsupervised learning, clustering has promoted innovation and transformation in various disciplines. Its application scope is extensive, covering multiple fields such as computer vision, recommendation systems, community detection, etc. The core goal of clustering is to reveal the internal patterns of data and divide the data into different categories according to similarity. With the rapid development of Internet technology, how to effectively represent multi-source or heterogeneous information has become the focus of research. For example, a piece of information can be presented through text, images, or documents written in multiple languages, and can even be used to identify an individual through fingerprints, personality traits, or voiceprints. Compared with single-view clustering methods, multi-view clustering makes full use of the complementarity between views and significantly improves the performance of clustering.

[0003] In recent years, with the continuous development of multi-view clustering algorithms, researchers have mainly utilized the complementarity and distinctiveness between different views to improve the clustering performance. Self-representation techniques can effectively learn the specific information features in each view and fully exploit the complementarity and distinguishability between different views. However, this learning method often relies on the self-expression matrix obtained from the original data, which may introduce outliers and noise, thus affecting the robustness of the clustering model (J. Zhao and G. Lu, “Clean affinity matrix learning with rank equality constraint for multi-view subspace clustering,” Pattern Recognit., vol. 134, p. 109118, 2023.). To mitigate the influence of outliers and noise, researchers usually use graph filters to smooth the feature information, which can not only maintain the inherent diversity of the input features but also eliminate certain noise (Z. Lin, Z. Kang, L. Zhang and L. Tian, "Multi-View Attributed Graph Clustering," in IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 2, pp. 1872-1880, 2023.). However, most of the research directly uses graph filters to process the dataset, merely as a preprocessing technique and not effectively introduced into the model optimization process. Therefore, noise cannot be effectively filtered out during model iteration, affecting the robustness of the model. To improve the robustness of the model, researchers have adopted the Robust Principal Component Analysis (RPCA) algorithm to decompose the input matrix into a clean and rich similarity matrix and a noise matrix, thus effectively capturing the noise in the input data (J.-B. Zhao and G.-F. Lu, “Clean and robust affinity matrix learning for multi-view clustering,” Appl. Intell., vol. 52, no. 14, pp. 15899–15915, 2022.). However, the RPCA method ignores the connections between views, resulting in a certain weakening of the clustering performance. To strengthen the connections between different views, researchers have proposed a clustering method that integrates different embeddings of multiple views on the Grassmann manifold from the perspective of spectral clustering. By using adaptive embeddings to reconstruct the similarity graph of each view, the topological information and local structure in each view are maintained, further improving the accuracy and robustness of clustering (F. Qi, J. Guo, J. Li, Y. Liao, W. Liao, H. Cai, J. Chen, “Multi-kernel clustering with tensor fusion on grassmann manifold for high-dimensional genomic data”, Methods, vol. 231, pp. 215–225, 2024.).

[0004] There are currently many problems in the field of multi-view clustering. First, the construction of the similarity matrix is affected by different measurement criteria. For example, graph construction based on Euclidean distance requires adjusting the number of neighbor nodes included in the nodes, thus affecting the clustering performance of the model. Second, the original dataset contains a large amount of redundancy and noise, and a large amount of noise is introduced during graph construction. Finally, from the perspective of views, directly fusing different views ignores the local structure between each view. Summary of the Invention

[0005] The present invention proposes a multi-view clustering image segmentation method and system based on embedding approximation learning, aiming to adaptively approximate and learn a pure and rich similarity matrix in the Grassmann manifold space, effectively eliminating the noise influence of the original data set and improving the robustness and clustering accuracy of the model. Specifically, first, a self-expression matrix is obtained from the original multi-view data set through a self-representation method; then, the self-expression matrix is decomposed by using robust principal component analysis to obtain the pure similarity matrix of each view; finally, in order to strengthen the connection between each view, an adaptive approximation learning is performed on each similarity matrix in the manifold space to obtain rich embedding features of the model for clustering of the model, and image segmentation is performed according to the clustering result.

[0006] The object of the present invention is achieved by at least one of the following technical solutions.

[0007] A multi-view clustering image segmentation method based on embedding approximation learning includes the following steps:

[0008] S1. Obtain an image multi-view data set of the image to be segmented;

[0009] S2. Input the image multi-view data set into a pre-constructed clustering model, iteratively update the parameters of the clustering model according to the optimization objective, and end the iteration when the optimization objective meets the requirements to obtain an optimized clustering model;

[0010] S3. Input the image multi-view data set into the optimized clustering model, output the clustering result, thereby completing multi-view subspace clustering;

[0011] S4. Perform image segmentation according to the clustering result to obtain an image segmentation result.

[0012] Further, in the clustering model, a self-expression matrix is obtained from the input image multi-view data set by using a self-representation technique. In order to remove the noise in the self-expression matrix, robust principal component analysis is used to decompose the self-expression matrix to obtain a pure similarity matrix; in order to strengthen the connection between each view, an approximation learning is performed on the Grassmann manifold space to adaptively reconstruct the pure similarity matrix to obtain an optimal embedding, and the optimal embedding is used for clustering to output a clustering result.

[0013] Further, the image multi-view data set is , where is the number of views in the image multi-view data set, represents the th view in the image multi-view data set, is the number of samples for clustering in each view of the image multi-view data set, represents the Dimensions of each view;

[0014] Based on the image multi-view dataset, use self-representation technology to obtain the self-expression matrix of each view , Denote the self-expression matrix of the th view in the image multi-view dataset, .

[0015] Furthermore, in order to remove the noise in the self-expression matrix, robust principal component analysis is used to decompose the self-expression matrix to obtain a pure similarity matrix, as follows:

[0016] Since the self-expression matrix of the view is from the image multi-view dataset and contains a lot of noise, which affects the clustering result of the clustering model, the robust principal component analysis (RPCA) algorithm is used to decompose the self-expression matrix of each view into a pure similarity matrix and a noise matrix , , as follows:

[0017] ;

[0018] where, is the number of views in the image multi-view dataset, is the third regularization parameter, ; and respectively represent the similarity matrix and the noise matrix of the th view in the image multi-view dataset obtained by the robust principal component analysis algorithm, , ; represents the nuclear norm of the matrix, is norm; The RPCA algorithm uses the nuclear norm for the decomposed similarity matrix, thus ensuring a low-rank property of the similarity matrix to remove redundant information. At the same time, a norm operation is also performed on the obtained noise matrix, so that the noise matrix satisfies sparsity to improve the robustness of the model. The present invention borrows the main idea of RPCA to separate noise. For more convenient optimization, is used to replace and , represents the F-norm of the matrix, as follows:

[0019] ;

[0020] ;

[0021] Among them, and are the first regularization parameter and the second regularization parameter respectively, , ; represents a column vector of all 1s, represents the transpose of the similarity matrix ; Obviously, the above formula combines the ideas of self-representation learning and RPCA. First, the self-expression matrices of each view are obtained, and then the similarity matrix and noise matrix of each self-expression matrix are obtained by borrowing the RPCA algorithm. Using to constrain the similarity matrix and the noise matrix ensures the compactness of the structure;

[0022] Taking the sum of the Frobenius norms of the differences between the views in the image multi-view dataset and the product of this view and the self-expression matrix of this view as the component error based on the robust principal component analysis algorithm; Taking the sum of the Frobenius norms of the

[0023] similarity matrices of views as the regularization error of the similarity matrix; Taking the sum of the Frobenius norms of the

[0024] noise matrices of views as the regularization error of the noise matrix.

[0025] Furthermore, the approximate learning on the Grassmann manifold space to adaptively reconstruct the pure similarity matrix and obtain the optimal embedding is as follows:

[0026] To strengthen the connection between each view in the image multi-view dataset while maintaining the topological information between each view, from the perspective of spectral clustering, the Laplacian matrix of the similarity matrix of different views is eigen-decomposed to obtain the orthogonal embedding of different views. The specific process is as follows:

[0027]

[0028] Among them, is the Laplacian matrix of the similarity matrix of the th view in the image multi-view dataset, ​, it contains more refined feature information compared to the similarity matrix; represents the trace operation of the matrix, represents the identity matrix, is the orthogonal embedding generated from the perspective of spectral clustering for the th view in the image multi-view dataset; in order to obtain an embedding rich in informative features on the Grassmann manifold space for the adaptive reconstruction of the similarity matrix, an approximate learning method is adopted to obtain an optimal embedding from different orthogonal embeddings , , , represents the clustering categories of the image multi-view dataset;

[0029] Taking the orthogonal embedding of the views and the optimal embedding the sum of the squares of the projection distances between them as the projection error; by finding the minimum value of the square of the projection distance between different orthogonal embeddings and the optimal embedding , the optimality of the optimal embedding is guaranteed from the perspective of the views, as follows:

[0030] .

[0031] Furthermore, in order to enable the optimal embedding to be continuously learned, the optimal embedding is adaptively reconstructed with all the similarity matrices through the weight parameter , so that the learned optimal embedding is coupled and influenced by the similarity matrices of each view in the multi-view dataset, and the specific process is as follows:

[0032] ;

[0033] where represents the weight parameter for the reconstruction of the optimal embedding and the th similarity matrix. This weight parameter is in the form of a vector, is the th element in the weight vector , represents the 2-norm of the weight vector ; the similarity matrix after adaptive reconstruction is ;​

[0034] The adaptive reconstruction error is ones The similarity matrix after adaptive reconstruction is and the similarity matrix The sum of the products of the Frobenius norms of the differences between them is as follows:

[0035] .

[0036] Furthermore, applying the K-Means technique to the learned optimal embedding gives the clustering result.

[0037] Furthermore, in step S2, using views in the image multi-view dataset, iteratively update the parameters of the clustering model according to the optimization objective, where the optimization objective is to traverse the similarity matrices of views in the image multi-view dataset, the noise matrix , the optimal embedding , and the optimal embedding and the similarity matrix The reconstructed weight parameter to perform iterative optimization to minimize the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error, as follows:

[0038] ;

[0039] ;

[0040] where is a balance parameter used to accelerate the convergence speed of the model; this optimization objective reflects the innovation points of the present invention from the perspectives of self-representation technology, the RPCA algorithm, and adaptive reconstruction in the Grassmann manifold space.

[0041] Furthermore, when the change value of the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error in two consecutive iterative optimizations is less than the set threshold, it indicates that the clustering model has reached the optimal state, and the iterative optimization is terminated to obtain the optimized clustering model.

[0042] Compared with the prior art, the advantages of the present invention are:

[0043] The present invention proposes a multi-view clustering image segmentation method and system based on embedded approximate learning, aiming to adaptively approximate and learn a pure and rich similarity matrix in the Grassmann manifold space, eliminate the noise in the self-expression matrix caused by the original data set, improve the robustness and clustering accuracy of the clustering model, and segment the image according to the clustering result. The present invention models the acquisition of the self-expression matrix as a self-representation learning process, eliminates its noise through robust principal component analysis to obtain a pure similarity matrix, and uses embedded approximate learning to reconstruct the similarity matrix in the Grassmann manifold space, thereby obtaining rich embedding features. By combining self-representation learning, robust principal component analysis technology, and Grassmann manifold space approximate learning, the present invention avoids the increase in computational cost caused by eigenvalue decomposition of the similarity matrix during the optimization process, and improves the efficiency and quality of clustering. Description of the Drawings

[0044] Figure 1 It is a flowchart of the steps of a multi-view clustering image segmentation method based on embedded approximate learning in an embodiment of the present invention.

[0045] Figure 2a 、 Figure 2b 、 Figure 2c and Figure 2d They are respectively schematic diagrams of the results of the ablation experiments of three clustering models in an embodiment of the present invention in terms of accuracy, normalized mutual information, purity, and Rand index.

[0046] Figure 3 It is a schematic diagram of the results of the scalability experiment in an embodiment of the present invention.

[0047] Figure 4a and Figure 4b They are respectively schematic diagrams of the results of the convergence experiments on the data set ORL and the data set MSRC in an embodiment of the present invention.

[0048] Figure 5a 、 Figure 5b 、 Figure 5c and Figure 5d They are respectively schematic diagrams of the segmentation results of the number "4" on the data set HW in an embodiment of the present invention. Detailed Embodiment

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the following takes the accompanying drawings as examples to elaborate on the specific implementation of the present invention in detail.

[0050] In one embodiment, a multi-view clustering image segmentation method based on embedded approximate learning includes the following steps:

[0051] S1. Obtain an image multi-view data set that needs to be segmented.

[0052] S2. Input the multi-view image dataset into a pre-constructed clustering model. In the clustering model, use the self-representation technique to obtain a self-expression matrix from the input multi-view image dataset.

[0053] The multi-view image dataset is , where is the number of views in the multi-view image dataset, represents the -th view in the multi-view image dataset, is the number of samples for clustering in each view of the multi-view image dataset, represents the -th dimension of the

[0054] Based on the multi-view image dataset, use the self-representation technique to obtain the self-expression matrix of each view , represents the self-expression matrix of the -th view in the multi-view image dataset, .

[0055] To remove the noise in the self-expression matrix, perform robust principal component analysis on the self-expression matrix to obtain a pure similarity matrix, as follows:

[0056] Since the self-expression matrix of the view is derived from the multi-view image dataset and contains a large amount of noise, which affects the clustering result of the clustering model, use the Robust Principal Component Analysis (RPCA) algorithm to decompose the self-expression matrix of each view into a pure similarity matrix and a noise matrix , , as follows:

[0057] ;

[0058] Where is the number of views in the multi-view image dataset, is the third regularization parameter, , in one embodiment, ; and respectively represent the similarity matrix and the noise matrix of the -th view in the multi-view image dataset obtained by the robust principal component analysis algorithm, , ; represents the nuclear norm of the matrix, is Norm; the RPCA algorithm uses the nuclear norm for the decomposed similarity matrix, thereby ensuring a low-rank property of the similarity matrix to remove redundant information. At the same time, a norm operation is also performed on the obtained noise matrix, making the noise matrix satisfy sparsity to improve the robustness of the model. The present invention borrows the main idea of RPCA to separate noise. For more convenient optimization, is used to replace and , represents the F-norm of the matrix, specifically as follows:

[0059] ;

[0060]

[0061] where and are the first regularization parameter and the second regularization parameter, respectively, , , in one embodiment, , ; represents a column vector of all 1s, represents the similarity matrix transpose; obviously, the above formula combines the ideas of self-representation learning and RPCA. First, the self-expression matrices of each view are obtained, and then the similarity matrix and noise matrix of each self-expression matrix are obtained by borrowing the RPCA algorithm. is used to constrain the similarity matrix and the noise matrix, ensuring the compactness of the structure;

[0062] Regarding the views in the image multi-view dataset and the of this view and the product of the self-expression matrix of this view, the sum of the F-norms of the differences is used as the component error based on the robust principal component analysis algorithm;

[0063] Regarding views, the sum of the F-norms of the similarity matrix is used as the regularization error of the similarity matrix;

[0064] Regarding views, the sum of the F-norms of the noise matrix is used as the regularization error of the noise matrix.

[0065] To strengthen the connection between each view, approximate learning is carried out in the Grassmann manifold space to adaptively reconstruct a pure similarity matrix and obtain an optimal embedding, which is specifically as follows:

[0066] To strengthen the connection between each view in the image multi-view dataset while maintaining the topological information between each view, from the perspective of spectral clustering, for the similarity matrix of the Laplacian matrix perform eigenvalue decomposition to obtain the orthogonal embedding of different views , and the specific process is as follows:

[0067] ;

[0068] Among them, is the Laplacian matrix of the similarity matrix of the th view in the image multi-view dataset, , which contains more refined feature information compared to the similarity matrix; represents the trace operation of the matrix, represents the identity matrix, is the orthogonal embedding generated for the th view in the image multi-view dataset from the perspective of spectral clustering; The present invention can obtain the orthogonal embedding of different views by performing eigenvalue decomposition on the Laplacian matrix of different views. To obtain an embedding with rich information features on the Grassmann manifold space for the adaptive reconstruction of the similarity matrix , an approximate learning method is used to obtain an optimal embedding from different orthogonal embeddings , , , represents the clustering category of the image multi-view dataset;

[0069] Taking the sum of the squares of the projection distances between the orthogonal embedding of views and the optimal embedding as the projection error; By finding the minimum value of the square of the projection distance between different orthogonal embeddings and the optimal embedding , the optimality of the optimal embedding is guaranteed from the perspective of the view, which is specifically as follows:

[0070] .

[0071] To make the optimal embedding It can continuously learn through weight parameters to perform adaptive reconstruction on the optimal embedding and all similarity matrices such that the learned optimal embedding is coupled and influenced by the similarity matrices of each view in the multi-view dataset. The specific process is as follows:

[0072] ;

[0073] Among them, represents the weight parameter for reconstructing the optimal embedding and the th similarity matrix. This weight parameter is in the form of a vector, is the th element in the weight vector . represents the 2-norm of the weight vector ; The similarity matrix after adaptive reconstruction is ;

[0074] The adaptive reconstruction error is times the sum of the products of and the F-norm of the difference between the similarity matrix after adaptive reconstruction and the similarity matrix . The specific is as follows:

[0075] .

[0076] Use the optimal embedding for clustering and output the clustering result

[0077] In one embodiment, apply the K-Means technique to the optimal embedding to obtain the clustering result

[0078] Use the views in the image multi-view dataset to iteratively update the parameters of the clustering model according to the optimization objective. The optimization objective is to iteratively optimize by traversing the similarity matrices of the views in the image multi-view dataset, the noise matrix , the optimal embedding , and the optimal embedding and the weight parameter for reconstructing the similarity matrix to minimize the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error. The specific is as follows:

[0079] ​ ;

[0080] ；

[0081] Among them, is a balance parameter used to accelerate the convergence rate of the model. In one embodiment, take ; The optimization objective reflects the innovation points of the present invention from the perspectives of self-representation technology, RPCA algorithm, and adaptive reconstruction of Grassmann manifold space.

[0082] When the change value of the sum of the component error, regular error of the similarity matrix, regular error of the noise matrix, projection error, and adaptive reconstruction error based on the robust principal component analysis algorithm in two consecutive iterative optimizations is less than the set threshold, it indicates that the clustering model has reached the optimal state, and the iterative optimization ends, obtaining the optimized clustering model. In one embodiment, the set threshold is 0.0001.

[0083] S3. Input the image multi-view data set into the optimized clustering model, and output the clustering result, thereby completing multi-view subspace clustering;

[0084] S4. Perform image segmentation according to the clustering result (see H. Zhang, X. Lu, P. Ma, J. Liu, J. Lian and Y. Ma, "Cluster fusion based cross teaching for semi-supervised medical image segmentation", Neurocomputing, vol. 618, pp. 129 - 147, 2025.), and obtain the image segmentation result.

[0085] In one embodiment, the advantages are reflected by the performance of the accuracy (ACC), normalized mutual information (NMI), purity (P), and adjusted rand index (ARI) of the clustering model on 8 common image multi-view datasets (HW, ORL, COIL20, 100Leaves, YaleB, MSRC, Scene, and ALOI-100). Specifically, the present invention first illustrates the advantages of the robust principal component analysis technology and Grassmann manifold space approximation learning based on self-representation technology in the clustering model through ablation experiments, followed by scalability experiments to illustrate the efficiency of the clustering of the present invention, thereby reflecting its application value. Finally, the convergence experiment of the clustering model is used to illustrate its theoretical value.

[0086] In the ablation experiment, in order to reflect the role of the robust principal component analysis technology in removing noise, a first clustering model J1 is constructed as follows:

[0087]

[0088] ;

[0089] In the first clustering model J1, and are the first regularization parameter and the second regularization parameter respectively, , , in one embodiment, take , ; represents a column vector of all 1s, represents the self-expression matrix transpose, represents an optimal embedding obtained from different orthogonal embeddings , is the weight vector in the element, represents the optimal embedding and the th self-expression matrix reconstructed weight parameter, which is in the form of a vector, represents the 2-norm of the weight vector ; all self-expression matrices are adaptively reconstructed through the weight parameter so that the learned optimal embedding is related to each view in the multi-view dataset Coupled with each other and influencing each other. Here, the robust principal component analysis module is removed, and the self-expression matrix is directly used. And the optimal embedding generated on the Grassmann manifold space Perform adaptive reconstruction learning.

[0090] To reflect the close connection of the Grassmann manifold space to different views, a second clustering model J2 is constructed as follows:

[0091]

[0092] ;

[0093] ;

[0094] In the second clustering model J2, and Are the first regularization parameter and the second regularization parameter respectively, , ; Is a balance parameter, , Is the fourth regularization parameter, , in one embodiment, take , , and ; Represents a column vector of all 1s, Represents the self-expression matrix Of the transpose, Represents a fusion similarity matrix adaptively fused by all similarity matrices , Is the weight vector In the Element, Represents And the Similarity matrix Reconstruction weight parameter, which is in the form of a vector, Represents the weight vector Of the 2-norm; through the weight parameter To adaptively reconstruct all similarity matrices, so that the fusion similarity matrix Is coupled with and influences each other with the similarity matrices of each view in the multi-view dataset Here, the module for approximate learning in the Grassmann manifold space is removed, and the similarity matrix obtained by the robust principal component analysis technology is directly Fused, so the fused similarity matrix , applying K-Means to the fused similarity matrix can obtain the clustering result.

[0095] The results of the ablation experiment are as Figure 2a , Figure 2b , Figure 2c and Figure 2d shown.

[0096] It can be seen from the results of the ablation experiment that: based on the same evaluation metrics, the clustering model of the present invention has a slightly lower accuracy than the first clustering model J1 only on the ALOI-100 dataset, and is superior to the first clustering model J1 and the second clustering model J2 in the remaining cases. Overall, the clustering model of the present invention has obvious advantages in clustering by introducing robust principal component analysis technology and Grassmann manifold space approximation learning.

[0097] In one embodiment, a scalability experiment is performed. To demonstrate the high efficiency of the present invention in clustering, the ALOI-100 dataset is selected to calculate the running time under different input ratios: the ALOI-100 dataset is evenly divided into 10 parts, and different numbers of parts are randomly input each time, and then the time for different input ratios is fitted to verify its high efficiency.

[0098] The results of the scalability experiment are as Figure 3 shown. From the Figure 3 fitting curve in it, it can be seen that for the running time of different input ratios of the ALOI-100 dataset, the fitting curve of the clustering model of the present invention can well satisfy the distribution of the quadratic function, indicating that the clustering model of the present invention has extremely high application value.

[0099] In one embodiment, the convergence of the clustering model can ensure that the model optimization can obtain an optimal result, thereby proving the theoretical significance of the model. The present invention selects the ORL dataset and the MSRC dataset to perform a convergence experiment for convergence proof. The convergence curves of these two datasets are respectively as Figure 4a and Figure 4b shown.

[0100] From the convergence of the clustering model of the present invention on the ORL dataset and the MSRC dataset: as the number of iterations increases, the objective value rapidly and monotonically decreases until it finally converges to a fixed value. This shows that the clustering model of the present invention has good convergence and has scientific theoretical significance.

[0101] In one embodiment, according to the clustering model results, the number "4" as shown in Figure 5a in the HW dataset is segmented. By adjusting different clustering centers, the great prospect of the present invention in image processing is demonstrated. The segmentation results of the number "4" are as Figure 5b andFigure 5c As shown. In order to reflect the segmentation effect of the present invention on image data, the segmentation results generated by the region growing algorithm are used for comparison, such as Figure 5d As shown. It can be seen from the comparison that the segmented images generated by the present invention can segment subtle changes in the same region, and the effect is better.

[0102] The preferred embodiments of the present application disclosed above are only used to help understand the present invention and its core idea. For those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific application scenarios and implementation operations. This specification should not be construed as a limitation to the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A multi-view clustering image segmentation method based on embedded approximation learning, characterized in that It includes the following steps: S1. Obtain the multi-view dataset of the image to be segmented; S2. Input the multi-view dataset of the image into the pre-constructed clustering model, and iteratively update the parameters of the clustering model according to the optimization objective. When the optimization objective meets the requirements, end the iteration to obtain the optimized clustering model. In the clustering model, the self-expression matrix is obtained from the input multi-view dataset of the image by using the self-representation technique; the robust principal component analysis is used to decompose the self-expression matrix to obtain the similarity matrix; Perform approximate learning on the Grassmann manifold space to adaptively reconstruct the similarity matrix to obtain the optimal embedding, and use the optimal embedding for clustering to output the clustering result; The image multi-view dataset is , where is the number of views in the image multi-view dataset, represents the th view in the image multi-view dataset, , is the number of samples for clustering in each view of the image multi-view dataset, represents the dimension of the th view; Based on the multi-view dataset of images, the self-representation matrix of each view is obtained using self-representation technology , denotes the self-representation matrix of the th view in the multi-view dataset of images, ; the multi-view dataset of images is , where is the number of views in the multi-view dataset of images, denotes the th view in the multi-view dataset of images, is the number of samples for clustering in each view of the multi-view dataset of images, denotes the dimension of the th view; Based on the image multi-view dataset, use self-representation technology to obtain the self-expression matrix of each view , denote the self-expression matrix of the th view in the image multi-view dataset, ; decompose the self-expression matrix of each view into a pure similarity matrix and a noise matrix , as follows: ； Among them, is the number of views in the image multi-view dataset, is the third regularization parameter, ; and respectively represent the similarity matrix and the noise matrix of the th view in the image multi-view dataset obtained by the robust principal component analysis algorithm, , ; represents the nuclear norm of the matrix, is norm; It ensures a low-rank property of the similarity matrix to remove redundant information. At the same time, a norm operation is also used on the obtained noise matrix, so that the noise matrix satisfies sparsity to improve the robustness of the model; Use to replace and , represents the F-norm of the matrix, which is specifically as follows: ； ； Among them, and are the first regularization parameter and the second regularization parameter respectively, , ; represents a column vector of all 1s, represents the transpose of the similarity matrix . Obviously, the above formula combines the ideas of self-representation learning and RPCA. First, the self-expression matrices of each view are obtained, and then the similarity matrix and noise matrix of each self-expression matrix are obtained by borrowing the RPCA algorithm. Using to constrain the similarity matrix and the noise matrix ensures the compactness of the structure; Among the views in an image multi-view dataset and the self-expression matrix of this view is the sum of the F-norms of the differences between the products , taken as the component error based on the robust principal component analysis algorithm; Take The sum of the F-norms of the similarity matrices of as the regularization error of the similarity matrix; ​ Taking the sum of the F-norms of the noise matrices of each view as the regularization error of the noise matrix; Further, the approximate learning on the Grassmann manifold space to adaptively reconstruct the pure similarity matrix to obtain the optimal embedding is specifically as follows: Similarity matrix for different views The Laplacian matrix of Perform eigenvalue decomposition to obtain the orthogonal embedding of different views , and the specific process is as follows: Among them, is the Laplacian matrix of the similarity matrix of the th view in the image multi-view dataset, which contains more refined feature information compared to the similarity matrix; denotes the trace operation of the matrix, denotes the identity matrix, is the orthogonal embedding generated for the th view in the image multi-view dataset from the perspective of spectral clustering; An embedding rich in information features is obtained on the Grassmann manifold space for the adaptive reconstruction of the similarity matrix and an optimal embedding is obtained by an approximate learning method from different orthogonal embeddings ; , , , denotes the clustering categories of the image multi-view dataset; Take the sum of the squares of the projection distances between the orthogonal embedding of a view and the optimal embedding as the projection error; By finding the minimum value of the square of the projection distance between different orthogonal embeddings and the optimal embedding from the perspective of the view, the optimality of the optimal embedding is guaranteed, as follows: is guaranteed, as follows: is guaranteed, as follows: ； To enable the optimal embedding to continuously learn through weight parameters the optimal embedding is adaptively reconstructed with all similarity matrices such that the learned optimal embedding is coupled with and influences the similarity matrices of each view in the multi-view dataset interactively, and the specific process is as follows: ； Among them, represents the weight parameter for the optimal embedding and the reconstruction of the -th similarity matrix. This weight parameter is in the form of a vector, which is the -th element in the weight vector ; represents the 2-norm of the weight vector ; The similarity matrix after adaptive reconstruction is ; The adaptive reconstruction error is ones The product of the sum of the F-norms of the differences between the similarity matrix after adaptive reconstruction and the similarity matrix is as follows: ； Further, using views in the image multi-view dataset, iteratively update the parameters of the clustering model according to the optimization objective, where the optimization objective is to traverse the similarity matrix of views in the image multi-view dataset, the noise matrix , the optimal embedding , and the optimal embedding and the similarity matrix and the weight parameter reconstructed by the optimal embedding to perform iterative optimization, so as to minimize the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error, specifically as follows: ； ； Among them, is a balance parameter used to accelerate the convergence rate of the model; S3. Input the multi-view dataset of the image into the optimized clustering model, output the clustering result, and thus complete the multi-view subspace clustering; S4. Perform image segmentation according to the clustering result to obtain the image segmentation result.

2. The multi-view clustering image segmentation method based on embedding approximate learning according to claim 1, characterized in that: Optimal embedding through weight parameters Perform adaptive reconstruction with all similarity matrices; Take as the product of the sum of the F-norms of the differences between the similar matrix after adaptive reconstruction and the similar matrix as the adaptive reconstruction error; Denote the optimal embedding and the th similar matrix as the weight parameter for reconstruction. The weight parameter is in the form of a vector, which is the th element in the weight vector .

3. A multi-view clustering image segmentation method based on embedded approximate learning according to claim 1, characterized in that, Apply the K-Means technique to the optimal embedding to obtain the clustering result.

4. A multi-view clustering image segmentation method based on embedded approximate learning according to any one of claims 1 to 3, characterized in that In step S2, the optimization objective is to iteratively optimize by traversing the similarity matrix, noise matrix, optimal embedding of views, optimal embedding and the weight parameters for similarity matrix reconstruction, so as to minimize the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error.

5. A multi-view clustering image segmentation method based on embedded approximate learning according to claim 4, characterized in that, When the change value of the sum of the component error based on the robust principal component analysis algorithm, the regularization error of the similarity matrix, the regularization error of the noise matrix, the projection error, and the adaptive reconstruction error in the current and previous two iterative optimizations is less than the set threshold, it indicates that the clustering model reaches the optimal state, end the iterative optimization, and obtain the optimized clustering model.

6. A multi-view clustering image segmentation system based on embedded approximate learning for implementing the method according to claim 1, characterized in that, It includes the following modules: Data acquisition module: Obtain the multi-view dataset of the image to be segmented; Clustering model optimization module: Input the multi-view dataset of the image into the pre-constructed clustering model, and iteratively update the parameters of the clustering model according to the optimization objective. When the change value of the optimization objective is less than the set threshold, obtain the optimized clustering model; Clustering module: Input the multi-view dataset of the image into the optimized clustering model, output the clustering result, and thus complete the multi-view subspace clustering; Image segmentation module: Perform image segmentation according to the clustering result to obtain the image segmentation result.

Images