Multi-view clustering method and device

Abstract

The invention relates to the technical field of multi-view clustering, in particular to a multi-view clustering method and device, and can solve the problem that the overall effect of an existing method in a large-scale clustering task is limited due to the fact that the existing method has problems in the aspects of calculation efficiency, robustness and multi-view information integration to a certain extent. The method comprises the following steps: dynamically learning an anchor matrix and a projection matrix for each view, and constructing a bipartite graph to generate a similarity matrix; calculating a graph Laplacian matrix based on the similarity matrix of each view, and extracting spectrum embedding; the spectrums of multiple views are embedded and stacked into a third-order tensor, and cross-view shared information is extracted by using a low-rank tensor constraint; multi-view atlas embedding is aligned through a spectrum rotation technology, and a discrete clustering indication matrix is directly output.

Description

Technical Field

[0001] The present application relates to the technical field of multi-perspective clustering, and in particular to a multi-perspective clustering method and device. Background Art

[0002] In real-world applications, data is often collected from multiple perspectives, such as images, text descriptions, or sensory signals. This type of data is called multi-view data, which can provide complementary information about the same object and a more comprehensive representation than single-view data. Multi-view data is ubiquitous in various fields, including medical imaging, natural language processing, instance segmentation, etc. In order to fully explore the underlying structure of multi-view data, multi-view clustering can optimize the fusion of information from multiple views and assign highly similar instances to the same cluster. By leveraging the complementary information of each view, this method can obtain more accurate and robust clustering results compared to single-view clustering methods, especially when a single view is incomplete or noisy. Integrating multiple views can not only address these limitations, but also provide a more comprehensive understanding of the underlying structure of the data.

[0003] Existing multi-view clustering methods are all developed to address the challenge of integrating information from different views. These methods can be roughly divided into several categories, including graph-based multi-view clustering, subspace-based multi-view clustering, and kernel-based multi-view clustering.

[0004] Specifically, graph-based methods aim to build similarity graphs for each view and then fuse them to find a consensus graph for clustering. Subspace-based methods focus on learning a shared low-dimensional representation that can capture the common structure across views. Kernel-based methods map data to a high-dimensional feature space through a specific kernel function and then combine these kernels linearly or nonlinearly to perform clustering in the feature space. These three multi-view clustering methods provide a solid theoretical foundation and practical support for clustering analysis of multi-view data. However, although these methods have achieved some success, there is still room for improvement.

[0005] Existing methods face several challenges that limit their performance and scalability, especially when dealing with large-scale datasets. To address this challenge, many methods rely on building a similarity matrix for each view by computing pairwise distances between data samples. Due to its complexity, the computational complexity increases rapidly with the size of the dataset, making it infeasible for practical applications. To reduce the computational complexity, anchors have attracted widespread attention. Most methods use predefined anchors, which are usually selected through random sampling or k-means clustering.

[0006] However, these strategies rely heavily on the quality of the sampled anchor points. If the anchor points do not represent the data distribution well, redundancy and noise will be introduced into the graph, thereby reducing the overall clustering quality. In addition, many existing methods adopt a multi-stage clustering framework. Typically, they first learn spectral embeddings from the similarity graph and then apply clustering algorithms (such as k-means) to obtain the final result. This separation of embedding learning and clustering will cause information loss because the two stages are not jointly optimized, which affects the clustering performance. Finally, some methods focus on capturing pairwise relationships within each view, but often ignore high-order correlations between views, which are crucial for fully utilizing the complementary information in multi-view data. In summary, existing methods have problems in computational efficiency, robustness and multi-view information integration, which limits their overall effectiveness in large-scale clustering tasks. Summary of the Invention

[0007] In order to solve the problems of existing methods in computational efficiency, robustness and multi-view information integration, which limit their overall effectiveness in large-scale clustering tasks, the present application provides a multi-view clustering method and device.

[0008] The embodiment of the present application is implemented as follows:

[0009] In a first aspect, the present application provides a multi-perspective clustering method, comprising:

[0010] Dynamically learn the anchor matrix and projection matrix for each view, and construct a bipartite graph to generate a similarity matrix;

[0011] Calculate the graph Laplacian matrix based on the similarity matrix of each view and extract the spectral embedding;

[0012] The spectral embeddings of multiple views are stacked into a third-order tensor, and the shared information across views is extracted using low-rank tensor constraints.

[0013] Multi-view spectral embeddings are aligned via spectral rotation techniques, and discrete cluster indicator matrices are directly output.

[0014] In one possible implementation, in the step of dynamically learning the anchor matrix and projection matrix for each view and constructing a bipartite graph to generate a similarity matrix, the optimization objective function of the dynamically learning the anchor matrix and projection matrix is:

[0015]

[0016] in, Represents the original data of the v-th view, containing dimensions d v n data points, is the projection matrix that maps the data to the anchor space, represents the anchor matrix, is a bipartite graph connecting the anchor points and the original data points.

[0017] In one possible implementation, the dynamic learning is implemented by an alternating optimization strategy, which includes:

[0018] Fixed projection matrix W (v) and anchor matrix A (v) , optimize the bipartite graph G through singular value decomposition (SVD) (v) ;

[0019] Fixed bipartite graph G (v) and anchor matrix A (v) , optimize the projection matrix W by minimizing the Frobenius norm (v) ;

[0020] Fixed bipartite graph G (v) and the projection matrix W (v) , optimize the anchor matrix A through quadratic programming (QP) (v) .

[0021] In a possible implementation, in the step of calculating the graph Laplacian matrix based on the similarity matrix of each view and extracting the spectral embedding, the graph Laplacian matrix is ​​defined as:

[0022] L (v) =I n -D -1 / 2 S (v) D -1 / 2 ,

[0023] Among them, I n is an n×n identity matrix, D is S (v) The degree matrix is ​​a diagonal matrix where each diagonal element d i It's S (v) The sum of the i-th row of .

[0024] In one possible implementation, in the step of stacking the spectral embeddings of multiple views into a third-order tensor and extracting shared information across views using a low-rank tensor constraint, the low-rank tensor constraint is implemented by minimizing the tensor nuclear norm:

[0025]

[0026] Among them, the parameters α and β are the trade-off coefficients of different terms in the balance objective function, F represents the result of multi-view spectral embedding fusion, and the spectral rotation matrix of the vth view is expressed as The function f(·) represents the operation for multi-view spectral embedding fusion.

[0027] In one possible implementation, in the step of aligning the multi-view spectral embeddings by using a spectral rotation technique and directly outputting a discrete cluster indicator matrix, the spectral rotation technique is implemented by optimizing the discrete cluster indicator matrix Y, including:

[0028]

[0029] Where Y is the cluster assignment matrix containing only 0 or 1 elements;

[0030] The final objective function is expressed as:

[0031]

[0032] st.(H (v) ) T H (v) =I k ,(R (v) ) T R (v) =I k , Y ij ∈{0,1},Y i，； 1 k =1.

[0033] In one possible implementation, the low-rank tensor constraint and spectral rotation both need to be implemented through the alternating direction multiplier method (ADMM) framework, which includes:

[0034] Decompose the augmented Lagrangian function into four subproblems, namely, tensor variables Spectral rotation matrix Cluster indicator matrix Y and Lagrange multiplier J;

[0035] Fixed update of tensor variables Spectral rotation matrix and Lagrange multiplier J, solve the cluster indicator matrix Y;

[0036] Fixed update of tensor variables Cluster indicator matrix Y and Lagrange multiplier J, solve the spectral rotation matrix

[0037] Fixed, spectral rotation matrix Cluster indicator matrix Y and Lagrange multiplier J, solve for tensor variables

[0038] Fixed update of tensor variables Spectral rotation matrix and the cluster indicator matrix Y, solve the Lagrange multiplier J.

[0039] In one possible implementation, the four sub-problems are solved as follows:

[0040] The cluster indicator matrix Y selects the best non-zero element in each row through an incremental mechanism and optimizes row by row;

[0041] The spectral rotation matrix Updated by singular value decomposition (SVD);

[0042] The tensor variable Updated via the generalized power iteration (GPI) algorithm;

[0043] The Lagrange multiplier J is updated according to the current variable residual.

[0044] In one possible implementation, the evaluation indicators of the clustering results include:

[0045] Accuracy (ACC): the proportion of correctly clustered samples;

[0046] Normalized Mutual Information (NMI): the consistency between the predicted clusters and the true labels;

[0047] Purity: the proportion of dominant categories in the cluster;

[0048] F-score: A comprehensive indicator that balances precision and recall.

[0049] In a second aspect, the present application provides a multi-view clustering device, comprising:

[0050] A building module that dynamically learns the anchor matrix and projection matrix for each view and constructs a bipartite graph to generate a similarity matrix;

[0051] The extraction module is used to calculate the graph Laplacian matrix based on the similarity matrix of each view and extract the spectral embedding;

[0052] The stacking module is used to stack the spectral embeddings of multiple views into a third-order tensor and extract shared information across views using low-rank tensor constraints;

[0053] The output module is used to align multi-view spectral embeddings through spectral rotation techniques and directly output discrete cluster indicator matrices.

[0054] The technical solution provided by this application can achieve at least the following beneficial effects:

[0055] The present application provides a multi-view clustering method and device, which introduces a self-learning anchor strategy to construct a similarity matrix for each view. It does not rely on predefined anchors, but dynamically learns a small number of representative anchors from the data. These anchors are then used to construct a bipartite graph, effectively capturing the underlying structure of the data. By integrating anchor selection and graph construction into a unified framework, unnecessary information loss is eliminated, the quality of the anchors and bipartite graphs is ensured, and redundancy in data representation is reduced, thereby improving clustering performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0057] Figure 1 This is a flowchart of a multi-view clustering method shown in an exemplary embodiment of the present application;

[0058] Figure 2 1 is a schematic diagram of the overall framework of HAG-TSEF shown in an exemplary embodiment of the present application;

[0059] Figure 3 This is a schematic diagram of the overall process of implementing HAG-TSEF according to an exemplary embodiment of the present application;

[0060] Figure 4 1 is a schematic diagram of an algorithm flow of a generalized power iteration (GPI) according to an exemplary embodiment of the present application;

[0061] Figure 5 1 is a schematic diagram of an algorithm flow for updating Lagrange multipliers according to an exemplary embodiment of the present application;

[0062] Figure 6 It is a structural diagram of a multi-view clustering device shown in an exemplary embodiment of the present application.

[0063] Reference numerals:

[0064] 1. Construction module; 2. Extraction module; 3. Stacking module; 4. Output module. DETAILED DESCRIPTION

[0065] In order to make the purpose, implementation methods and advantages of the present application clearer, the exemplary implementation methods of the present application will be clearly and completely described below in conjunction with the drawings in the exemplary embodiments of the present application. Obviously, the described exemplary embodiments are only part of the embodiments of the present application, not all of the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0066] It should be noted that the brief descriptions of terms in this application are only for the purpose of facilitating the understanding of the embodiments described below, and are not intended to limit the embodiments of this application. Unless otherwise specified, these terms should be understood according to their ordinary and usual meanings.

[0067] In the specification and claims of this application and the accompanying drawings, the terms "first," "second," "third," etc. are used to distinguish similar or similar objects or entities, and are not necessarily intended to limit a particular order or sequence, unless otherwise noted. It should be understood that the terms used in this manner are interchangeable under appropriate circumstances.

[0068] The terms "comprise," "include," and "have," and any variations thereof, are intended to cover but not exclude inclusion; for example, a product or device comprising a list of components is not necessarily limited to all the components expressly listed but may include other components not expressly listed or inherent to such product or device.

[0069] Before explaining the multi-perspective clustering method provided in the embodiment of the present application, the application scenario and implementation environment of the embodiment of the present application are first introduced.

[0070] In real-world applications, data is often collected from multiple perspectives, such as images, text descriptions, or sensory signals. This type of data is called multi-view data, which provides complementary information about the same object and a more comprehensive representation than single-view data. Multi-view data is ubiquitous in various fields, including medical imaging, natural language processing, and instance segmentation. To fully explore the underlying structure of multi-view data, multi-view clustering can optimize the fusion of information from multiple views and assign highly similar instances to the same cluster. By leveraging the complementary information of each view, this method can achieve more accurate and robust clustering results compared to single-view clustering methods, especially when a single view is incomplete or noisy. Integrating multiple views not only addresses these limitations but also provides a more comprehensive understanding of the underlying structure of the data.

[0071] Existing multi-view clustering methods are all developed to address the challenge of integrating information from different views.

[0072] These methods can be roughly divided into several categories, including graph-based multi-view clustering, subspace-based multi-view clustering, and kernel-based multi-view clustering.

[0073] Specifically, graph-based methods aim to build similarity graphs for each view and then fuse them to find a consensus graph for clustering. Subspace-based methods focus on learning a shared low-dimensional representation that can capture the common structure across views. Kernel-based methods map data to a high-dimensional feature space through a specific kernel function and then combine these kernels linearly or nonlinearly to perform clustering in the feature space. These three multi-view clustering methods provide a solid theoretical foundation and practical support for clustering analysis of multi-view data. However, although these methods have achieved some success, there is still room for improvement.

[0074] Existing methods face several challenges that limit their performance and scalability, especially when dealing with large-scale datasets. To address this challenge, many methods rely on building a similarity matrix for each view by calculating the pairwise distance between data samples. Due to its complexity, the computational complexity increases rapidly with the increase in the size of the dataset, which makes it infeasible in practical applications. In order to reduce the computational complexity, anchors have attracted widespread attention. Most methods use predefined anchors, which are usually selected by random sampling or k-means clustering.

[0075] However, these strategies heavily rely on the quality of the sampled anchors. If the anchors do not represent the data distribution well, redundancy and noise will be introduced into the graph, thus reducing the overall clustering quality. In addition, many existing methods adopt a multi-stage clustering framework.

[0076] Typically, they first learn spectral embeddings from similarity graphs and then apply clustering algorithms (such as k-means) to obtain the final result. This separation of embedding learning and clustering will cause information loss because the two stages are not jointly optimized, thus affecting the clustering performance.

[0077] Finally, some methods focus on capturing pairwise relationships within each view, but often ignore the high-order correlations between views, which are crucial for fully leveraging the complementary information in multi-view data. In summary, existing methods have problems in computational efficiency, robustness, and multi-view information integration, which limits their overall effectiveness in large-scale clustering tasks.

[0078] As can be seen, multi-view clustering has attracted considerable attention due to its ability to integrate complementary information from heterogeneous feature spaces, thereby improving clustering performance. However, existing multi-view clustering methods suffer from inefficiencies in graph construction and lead to information redundancy. Furthermore, many methods use a separate multi-stage clustering process, which can also lead to performance degradation.

[0079] Based on this, the present application provides a multi-view clustering method based on the fusion of anchor graph learning and tensorized spectral embedding (Hybrid Anchor Graph Learning and Tensorized Spectral Embedding Fusion for Multi-View Clustering, HAG-TSEF), which introduces a self-learning-based anchor mechanism to effectively construct a similarity matrix for each view, thereby capturing the intrinsic data structure and eliminating redundant information. In order to explore the high-order correlations between different views, HAG-TSEF stacks the spectral embeddings of multiple views into a third-order tensor. In addition, by utilizing the spectral rotation strategy, HAG-TSEF effectively fuses the spectral embeddings of different views and directly obtains the clustering results, avoiding the information loss caused by the multi-stage clustering process. Experimental results on various multi-view datasets show that HAG-TSEF outperforms the state-of-the-art methods in both performance and scalability.

[0080] Next, the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems will be described in detail through embodiments and in conjunction with the accompanying drawings. The various embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. Obviously, the described embodiments are only part of the embodiments of the present application, not all of them.

[0081] Figure 1 It is a flowchart of a multi-view clustering method shown in an exemplary embodiment of the present application.

[0082] In an exemplary embodiment, Figure 1 As shown, a multi-perspective clustering method is provided. In this embodiment, the method may include the following steps:

[0083] Step 100: Dynamically learn the anchor matrix and projection matrix for each view and construct a bipartite graph to generate a similarity matrix.

[0084] Step 200: Calculate the graph Laplacian matrix based on the similarity matrix of each view and extract the spectral embedding.

[0085] Step 300: Stack the spectral embeddings of multiple views into a third-order tensor, and use low-rank tensor constraints to extract shared information across views.

[0086] Step 400: Align the multi-view spectral embeddings through spectral rotation technology and directly output the discrete cluster indicator matrix.

[0087] Figure 2 is a schematic diagram of the overall framework of HAG-TSEF shown in an exemplary embodiment of the present application, Figure 3 It is a schematic diagram of the overall flow of the specific implementation process of HAG-TSEF shown in an exemplary embodiment of the present application.

[0088] In a possible implementation, the method is specifically implemented as follows: Figure 2 As shown, multi-view data is used as the input of the entire process, a bipartite graph is constructed for each view, the spectral embedding of each view is calculated based on the completed graph construction, and the discrete cluster indicator matrix is ​​obtained using the spectral rotation step. In addition, the spectral embedding of each view is stacked into a third-order tensor, and the high-order correlations between views are captured through low-rank tensor learning, so that the spectral embedding can better reflect the underlying structural information of the multi-view data.

[0089] The details are as follows:

[0090] like Figure 3 As shown, a novel framework consists of two key parts: an anchor graph learning strategy and a tensor spectral embedding fusion strategy.

[0091] The first part uses a self-learning anchor mechanism to efficiently construct high-quality similarity graphs, thereby reducing the complexity of graph construction.

[0092] The second part uses tensor methods to optimize the spectral embeddings of multiple views to explore high-order correlations between different views, and uses spectral rotation techniques to integrate the spectral embeddings of multiple views to directly obtain clustering results.

[0093] 1. Anchor graph learning strategy

[0094] The objective function of the anchor graph learning strategy is as follows:

[0095]

[0096] st(W (v) ) T W (v) =I k , (A (v) ) T A (v) =I k , G (v) ≥0, (G (v) ) T 1=1,; (1)

[0097] in, Represents the original data of the v-th view, containing dimensions d v n data points, is the projection matrix that maps the data to the anchor space, represents the anchor matrix, is a bipartite graph connecting the anchor points and the original data points.

[0098] This formulation tightly integrates anchor learning and graph construction, enabling the model to automatically adapt the similarity graph to the data structure. By minimizing the reconstruction error in the projected anchor space, the proposed method ensures that the bipartite graph accurately reflects the intrinsic relationships of the data while removing redundancy and noise.

[0099] Obtain a bipartite graph Afterwards, the complete similarity matrix of the v-th view is constructed by the following formula:

[0100] S (v) =(G (v) ) T G (v) (2)

[0101] 2. Tensor Spectral Embedding Fusion Strategy

[0102] Given the final similarity matrix of the v-th view Graph Laplacian matrix L (v) Defined as:

[0103] L (v) =I n -D -1 / 2 S (v) D -1 / 2 , (3)

[0104] Among them, I n is an n×n identity matrix, D is S (v) The degree matrix is ​​a diagonal matrix where each diagonal element d i It's S (v) The spectral embedding H of the v-th view can then be obtained as follows (v) :

[0105]

[0106] After obtaining the spectral embedding H for each view (v) After merging, the next step is to fuse these embeddings into a unified representation that captures the high-order correlations between different views. This fusion process is achieved by introducing low-rank tensor constraints and utilizing spectral rotations to align the embeddings between views.

[0107] To explore high-order correlations between different views, we integrate the spectral embedding matrix into a third-order tensor.

[0108] Specifically, the tensor Defined as The front slice is a low-rank matrix of n×n, and each front slice corresponds to a specific view. In order to explore the correlation between different views, this paper uses Instead of H, where the first front slice of T is n×n v Then, this paper minimizes its tensor nuclear norm ‖T‖ * A low-rank constraint is imposed on T. This encourages T to maintain a low-rank structure, which helps preserve common patterns across multiple views. The low-rank constraint on T is integrated into the overall objective function of spectral embedding fusion:

[0109]

[0110] st(H (v) ) T H (v) =I k ,(R (v) ) T R (v) =I k , (5)

[0111] Among them, the parameters α and β are the trade-off coefficients of different terms in the balance objective function, F represents the result of multi-view spectral embedding fusion, and the spectral rotation matrix of the vth view is expressed as The function f(·) represents the operation for multi-view spectral embedding fusion.

[0112] To avoid the limitations of a two-stage clustering procedure, where the fused spectral embeddings are used as input to a separate clustering algorithm (e.g., k-means), this paper aims to achieve clustering results within an end-to-end framework. Two-stage approaches typically result in degraded performance due to information loss during the clustering phase. To address this issue, this paper introduces a discrete cluster indicator matrix Y, where each row represents the cluster assignment of a data point with a single non-zero value (0 or 1).

[0113] Incorporating Y directly into the overall objective function (5) of the spectral embedding fusion mentioned above enables us to learn clustering results together with the spectral embedding fusion. Specifically, we no longer rely on the fused embedding F, but instead integrate the discrete clustering indicator Y with the rotated spectral embedding H (v) R (v) This results in the following additional term in the objective function:

[0114]

[0115] Therefore, the final objective function is expressed as:

[0116]

[0117] st(H (v) ) T H (v) =I k ,(R (v) ) T R (v) =I k ,Y ij ∈{0,1},Y i,； 1 k =1. (7)

[0118] The methods proposed in some embodiments of this application introduce an anchor graph learning strategy and a tensor-based spectral embedding fusion strategy for MVC. The anchor graph learning strategy efficiently constructs a similarity matrix by using self-learned anchor points, capturing the underlying structure of the data, and reducing redundancy. The spectral embedding fusion strategy integrates spectral embeddings across multiple views into a unified tensor representation, enforcing low-rank constraints and leveraging spectral rotations to align the embeddings.

[0119] 3. Optimization of anchor chart learning strategy

[0120] 1) Fixed A (v) and G (v) , solve for W (v) .

[0121] In this case, formula (1) is about W (v) The optimization problem can be simplified to:

[0122]

[0123] st(W (v) ) T W (v) =I k . (8)

[0124] By expanding the Frobenius norm and removing the (v) Irrelevant, this question is equivalent to:

[0125] max W(v) Tr((W (v) ) T B (v) ),

[0126] st(W (v) ) T W (v) =I k , (9)

[0127] Among them, B (v) =X (v) (G (v) )T (A (v) ) T .W (v) The optimal solution can be obtained by B (v) =UΣV T The singular value decomposition (SVD) of is obtained:

[0128] W (v) =UV T (10)

[0129] 2) Fixed W (v) and G (v) , solve A (v) .

[0130] When W (v) and G (v) When fixed, relative to A (v) The optimization problem can be expressed as:

[0131]

[0132] st(A (v) ) T A (v) =I k . (11)

[0133] By expanding the Frobenius norm and removing the (v) Irrelevant items, this question becomes:

[0134] max A(v) Tr((A (v) ) T C (v) ),

[0135] st(A (v) ) T A (v) =I k , (12)

[0136] Among them, C (v) =(W (v) ) T X (v) (G (v) ) T . And this paper solves W (v) Similar to the method of A (v) The optimal solution can be obtained by C (v) =UΣV T get:

[0137] A (v) =UV T . (13)

[0138] 3) Fixed W (v) and A (v) , solve for G (v) .

[0139] When W (v) and A (v) When fixed, relative to G (v) The optimization problem can be expressed as:

[0140]

[0141] stG (v) ≥0,(G (v) ) T v1=1. (14)

[0142] This problem can be rewritten as the following quadratic programming (QP) problem:

[0143]

[0144] stG (v) ≥0,(G (v) ) T 1=1, (15)

[0145] Among them, Q (v) =2(A (v) ) T (W (v) ) T W (v) A (v) ,f T =-2X (v)T W (v) A (v) This optimization problem can be solved using a standard quadratic programming solver.

[0146] Figure 4 is a schematic diagram of the algorithm flow of generalized power iteration (GPI) shown in an exemplary embodiment of the present application, Figure 5 1 is a flowchart of an algorithm for updating Lagrange multipliers according to an exemplary embodiment of the present application.

[0147] 4. Optimization of tensor quantization spectrum embedding fusion strategy:

[0148] Alternating iterative optimization procedure based on the Alternating Direction Method of Multipliers (ADMM) framework:

[0149]

[0150] st(H (v) ) H(v) =I k ,(R (v) )T R (v) =I k ,Y ij ∈{0,1},Y i,: 1 k =1,J=T. (16)

[0151] The augmented Lagrangian in formula (16) is:

[0152]

[0153] in, is the Lagrangian multiplier, μ>0 is the adaptive penalty parameter. In addition, using the enhanced Lagrangian function, formula (17) can be transformed into the following equivalent function:

[0154]

[0155] The optimization problem in formula (18) can be divided into four sub-problems, corresponding to solving four different variables: Y, and J.

[0156] Therefore, each of these four variables is updated alternately while the others are held constant until convergence is achieved.

[0157] 1) Fixed and J$, solve for Y.

[0158] When R (v) 、H (v) When and J are fixed, the problem in (18) can be rewritten as:

[0159]

[0160] The problem in formula (19) is equivalent to the following optimization problem:

[0161] max Y tr((Y T Y) -1 / 2 Y T Q),

[0162] stY ij ∈{0,1},Y i,: 1 k =1, (20)

[0163] in, Formula (20) can be rewritten as:

[0164]

[0165] sty im∈{0,1},Y i,: 1 k =1, (21)

[0166] Among them, y m is the mth column of Y, q {im} denotes the i-th column of Q. Here Y can be solved row by row, and each row of Y has a closed-form solution.

[0167] Specifically, each row of Y can be obtained by the incremental mechanism. Assume that the optimal solution of the equation is Y in the previous iteration. Let y i is the i-th row of Y, and then this paper adopts the increment of the objective function value in the equation, ranging from arrive The incremental mechanism can be expressed as:

[0168]

[0169] Let y i is the optimal solution for the i-th row of Y, where the w-th element is 1 and the other elements are 0. w can be calculated using the following formula:

[0170] w=argmax 1≤m≤c ρ im . (twenty three)

[0171] The iterative optimization process terminates during the iteration when the convergence condition is met, that is:

[0172] ‖JT‖ max <ε, (24)

[0173] Where ε is a small constant, for example, ε = 10 -6 .

[0174] 2) Fixed Y, and J, solve

[0175] When H (v) After , Y and J are fixed, the problem in equation (18) can be rewritten as:

[0176]

[0177] st(R (v) ) T R (v) =I k . (25)

[0178] The optimization question in formula (25) is equivalent to:

[0179] max R(v) Tr((R (v) )T (H (v) ) T Y(Y T Y) -1 / 2 )

[0180] st(R (v) ) T R (v) =I k . (26)

[0181] Similar to solving W in equation (9) (v) , R in formula (26) (v) The optimal solution can be expressed as:

[0182]

[0183] Where K=(H (v) ) T Y(Y T Y) -1 / 2 , the economic SVD of matrix K is

[0184] 3) Fixed Y, and J, solve

[0185] When Y, R (v) When and J are fixed, Equation (18) can be rewritten as:

[0186]

[0187] st(H (v) ) T H (v) =I k . (28)

[0188] set up Formula (28) becomes:

[0189]

[0190] in, And N (v) =βY(Y T Y) -1 / 2 (R (v) ) T .

[0191] In addition, this article also includes:

[0192]

[0193] set up The problem in formula (30) can be rewritten as:

[0194]

[0195] st(H (v) ) T H (v) =I k . (31)

[0196] The optimal solution can be obtained by Figure 4 The generalized power iteration (GPI) algorithm shown is obtained.

[0197] 4) Fixed Y, and Solve for J.

[0198] When R (v) , Y and H (v) When is fixed, the problem in Equation (18) can be rewritten as:

[0199]

[0200] This problem can be solved by Figure 5 The algorithm shown is used to solve the problem. The update scheme of Lagrange multiplier R and penalty parameter μ is as follows:

[0201] R (v) ←R (v) +μ(JT), (33)

[0202] μ←min(ρμ,μ max ), (34)

[0203] Among them, ρ and μ max is a constant.

[0204] It should be understood that, although the various steps in the flowcharts involved in the above-described embodiments are displayed in sequence according to the instructions, these steps are not necessarily executed in the order indicated. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the above-described embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0205] Corresponding to the aforementioned embodiment of the multi-view clustering method and adopting the same technical concept, the present application also provides an embodiment of a multi-view clustering device.

[0206] Figure 6It is a structural diagram of a multi-view clustering device shown in an exemplary embodiment of the present application.

[0207] In an exemplary embodiment, Figure 6 As shown, the multi-view clustering device includes:

[0208] Building module 1, which is used to dynamically learn the anchor matrix and projection matrix for each view and construct a bipartite graph to generate a similarity matrix;

[0209] Extraction module 2, for calculating the graph Laplacian matrix based on the similarity matrix of each view and extracting the spectral embedding;

[0210] Stacking module 3, used to stack the spectral embeddings of multiple views into a third-order tensor and extract shared information across views using low-rank tensor constraints;

[0211] Output module 4 is used to align the multi-view spectral embeddings through spectral rotation technology and directly output the discrete cluster indicator matrix.

[0212] For the specific definition of the multi-perspective clustering device, please refer to the definition of the multi-perspective clustering method above, which will not be repeated here. The various modules in the above-mentioned multi-perspective clustering device can be implemented in whole or in part by software, hardware, or a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0213] It can be seen that some embodiments of the present application provide a novel multi-view clustering framework that combines an anchor graph learning strategy and a tensor spectral embedding fusion method. HAG-TSEF effectively addresses the key challenges in existing methods, including inefficient graph construction, redundancy and noise in the similarity matrix, and performance degradation caused by the multi-stage clustering process. By introducing a self-learning anchor selection mechanism, the proposed method constructs a high-quality similarity graph that is computationally efficient and robust. In addition, tensor spectral embedding fusion utilizes high-order correlations across views to achieve direct and accurate clustering results. Experimental results on multiple datasets verify the effectiveness of HAG-TSEF, consistently achieving excellent clustering accuracy and robustness compared to state-of-the-art methods. Convergence analysis further confirms the stability of the proposed optimization process, highlighting its efficiency and reliability in MVC scenarios.

[0214] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0215] The embodiments described above merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A multi-view clustering method, characterized in that: include: Dynamically learn the anchor matrix and projection matrix for each view, and construct a bipartite graph to generate a similarity matrix; Calculate the graph Laplacian matrix based on the similarity matrix of each view and extract the spectral embedding; The spectral embeddings of multiple views are stacked into a third-order tensor, and the shared information across views is extracted using low-rank tensor constraints. Multi-view spectral embeddings are aligned via spectral rotation techniques, and discrete cluster indicator matrices are directly output.

2. The multi-view clustering method according to claim 1, wherein: In the step of dynamically learning the anchor matrix and projection matrix for each view and constructing a bipartite graph to generate a similarity matrix, the optimization objective function of the dynamic learning of the anchor matrix and projection matrix is: s.t(W (v) ) T W (v) =I k ,(A (v) ) T A (v) =I k ,G (v) ≥0,(G (v) ) T 1=1,; in, Represents the original data of the v-th view, containing dimensions d v n data points, is the projection matrix that maps the data to the anchor space, represents the anchor matrix, is a bipartite graph connecting the anchor points and the original data points.

3. The multi-view clustering method according to claim 1, wherein: The dynamic learning is achieved through an alternating optimization strategy, which includes: Fixed projection matrix W (v) and anchor matrix A (v) , optimize the bipartite graph G through singular value decomposition (SVD) (v) ; Fixed bipartite graph G (v) and anchor matrix A (v) , optimize the projection matrix W by minimizing the Frobenius norm (v) ; Fixed bipartite graph G (v) and the projection matrix W (v) , optimize the anchor matrix A through quadratic programming (QP) (v) .

4. The multi-view clustering method according to claim 3, wherein: In the step of calculating the graph Laplacian matrix based on the similarity matrix of each view and extracting the spectral embedding, the graph Laplacian matrix is ​​defined as: L (v) =I n -D -1 / 2 S (v) D -1 / 2 , Among them, I n is an n×n identity matrix, D is S (v) The degree matrix is ​​a diagonal matrix where each diagonal element d i It's S (v) The sum of the i-th row of .

5. The multi-view clustering method according to claim 1, wherein: In the step of stacking the spectral embeddings of multiple views into a third-order tensor and extracting shared information across views using a low-rank tensor constraint, the low-rank tensor constraint is implemented by minimizing the tensor nuclear norm: s.t.(H (v) ) T H (v) =I k ,(R (v) ) T R (v) =I k , Among them, the parameters α and β are the trade-off coefficients of different terms in the balance objective function, F represents the result of multi-view spectral embedding fusion, and the spectral rotation matrix of the vth view is expressed as The function f(·) represents the operation for multi-view spectral embedding fusion.

6. The multi-view clustering method according to claim 1, wherein: In the step of aligning the multi-view spectral embeddings by the spectral rotation technology and directly outputting the discrete cluster indicator matrix, the spectral rotation technology is implemented by optimizing the discrete cluster indicator matrix Y, including: Where Y is the cluster assignment matrix containing only 0 or 1 elements; The final objective function is expressed as:

7. The multi-view clustering method according to claim 1, wherein: The low-rank tensor constraint and spectral rotation need to be implemented through the alternating direction multiplier method (ADMM) framework, which includes: Decompose the augmented Lagrangian function into four subproblems, namely, tensor variables Spectral rotation matrix Cluster indicator matrix Y and Lagrange multiplier J; Fixed update of tensor variables Spectral rotation matrix and Lagrange multiplier J, solve the cluster indicator matrix Y; Fixed update of tensor variables Cluster indicator matrix Y and Lagrange multiplier J, solve the spectral rotation matrix Fixed, spectral rotation matrix Cluster indicator matrix Y and Lagrange multiplier J, solve for tensor variables Fixed update of tensor variables Spectral rotation matrix and the cluster indicator matrix Y, solve the Lagrange multiplier J.

8. The multi-view clustering method according to claim 8, wherein: The solutions to the four sub-problems include: The cluster indicator matrix Y selects the best non-zero element in each row through an incremental mechanism and optimizes row by row; The spectral rotation matrix Updated by singular value decomposition (SVD); The tensor variable Updated via the generalized power iteration (GPI) algorithm; The Lagrange multiplier J is updated according to the current variable residual.

9. The multi-view clustering method according to claim 1, wherein: The evaluation indicators of the clustering results include: Accuracy (ACC): the proportion of correctly clustered samples; Normalized Mutual Information (NMI): the consistency between the predicted clusters and the true labels; Purity: the proportion of dominant categories in the cluster; F-score: A comprehensive indicator that balances precision and recall.

10. A multi-view clustering device, characterized in that: include: A building module that dynamically learns the anchor matrix and projection matrix for each view and constructs a bipartite graph to generate a similarity matrix; The extraction module is used to calculate the graph Laplacian matrix based on the similarity matrix of each view and extract the spectral embedding; The stacking module is used to stack the spectral embeddings of multiple views into a third-order tensor and extract shared information across views using low-rank tensor constraints; The output module is used to align multi-view spectral embeddings through spectral rotation techniques and directly output discrete cluster indicator matrices.

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