Multi-view clustering method and system based on adaptive anchor graph learning and tensor compensation

Abstract

The invention provides a multi-view clustering method and system based on adaptive anchor graph learning and tensor compensation, and belongs to the technical field of machine learning, and the method comprises the steps: obtaining a data matrix of multi-view data; the optimal anchor point number of each view is automatically determined through a layered bipartite neighborhood clustering method, and a specific anchor map of the view is constructed; selecting a view with optimal clustering quality as a reference view, unifying a clustering representation space, and introducing an enhanced tensor rank regularization item to compensate structure information possibly lost in a cross-view alignment process; and constructing a unified similarity matrix fused with multi-view representation, and obtaining a final clustering result through spectral clustering. According to the method, under the condition that the number of anchor points and the number of clusters are not preset, the anchor point diagram structure of each view can be learned in a self-adaptive mode, high-order complementary information among multiple views is captured, the robustness and expandability of clustering performance are improved, and the method can be widely applied to analysis and mining tasks of large-scale complex data.

Description

Technical Field

[0001] This invention belongs to the field of machine learning technology, and more specifically, relates to a multi-view clustering method and system based on adaptive anchor graph learning and tensor compensation. Background Technology

[0002] Multi-view clustering, by integrating information from multiple sources or perspectives, improves the accuracy and robustness of clustering results and has become a key technology for processing complex heterogeneous data. However, traditional multi-view clustering methods face two major challenges; First, there's the dependency on anchor point selection. Most efficient anchor graph learning methods require pre-specifying the number of anchor points for each view. This not only contradicts the nature of unsupervised learning, but also, in real-world scenarios, different views have different data structures, making it difficult for a fixed number of anchor points to optimally represent all views, leading to a decline in clustering performance.

[0003] Second, there is information loss during view alignment. When different views are allowed to have different numbers of anchor points, aligning these anchor maps of varying sizes (e.g., through a permutation matrix) to reach a consensus inevitably results in the loss of structural information within each view. This information loss directly weakens the consistency and discriminative power of the final clustering results.

[0004] While existing technologies have made progress in automatic anchor point selection, they still treat anchor points as static representations and have not effectively solved the information compensation problem during cross-view alignment, thus limiting their performance on complex or large-scale data.

[0005] Therefore, there is an urgent need for a novel multi-view clustering framework that can adaptively learn view-specific anchor maps and effectively compensate for information loss during the alignment process. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a multi-view clustering method and system based on adaptive anchor graph learning and tensor compensation.

[0007] The purpose and effectiveness of the multi-view clustering method and system based on adaptive anchor graph learning and tensor compensation of the present invention are achieved by the following specific technical means: The multi-view clustering method based on adaptive anchor graph learning and tensor compensation includes the following steps: Data matrix for obtaining multi-view data; The optimal number of anchor points for each view is automatically determined by a hierarchical binary neighborhood clustering method, and a view-specific anchor map is constructed. The optimal view is selected as the clustering representation space, and the permutation matrix is ​​learned to align the anchor graphs of other views. An enhanced tensor rank regularization term is introduced to construct a multi-view representation tensor to compensate for information loss during view alignment. The objective function is optimized by using the alternating direction multiplier method to generate a unified similarity matrix. Spectral clustering is then performed on the similarity matrix to obtain the final clustering result.

[0008] According to a preferred embodiment, automatically determining the optimal number of anchor points for each view using a hierarchical binary neighborhood clustering method includes: Randomly select the initial seed sample; Calculate the Euclidean distance between this sample and other samples in the same view, and construct the sorted distance vector; The optimal partitioning boundary is determined by minimizing the objective function, and the samples are recursively partitioned until clustering is complete. The number of anchor points for each view is determined based on the clustering results; The objective function for the optimal boundary partitioning is: ; in, , , , , This represents the number of samples in the optimal cluster.

[0009] According to a preferred embodiment, the step of selecting the optimal view includes: Calculate the intra-cluster variance for each view: ; In the formula, Indicates the first in this cluster One sample, Indicates the first The first view The cluster center of each cluster, Indicates the first Evaluation metrics for each cluster; The view with the minimum intra-cluster variance is selected as the optimal view.

[0010] According to a preferred embodiment, the expression for aligning the learned permutation matrix with the anchor graph of other views is as follows: ; In the formula, The clustering representation matrix represents the clustering matrix. Represents the permutation matrix. This represents an anchor chart.

[0011] According to a preferred embodiment, the enhanced tensor rank regularization term is defined as follows: ; In the formula, This represents a tensor formed by stacked multi-view representation matrices. Indicates the first The singular value matrix of a front slice.

[0012] According to a preferred embodiment, the expression of the objective function is: ; In the formula, This represents a tensor constructed from anchor graphs of various views. The j-cluster representation matrix represents the mapping of each view to the cluster space. This represents the permutation matrix that aligns each view to the optimal view. Anchor diagrams representing each view.

[0013] According to a preferred embodiment, the optimization of the objective function using the alternating direction multiplier method to generate a unified similarity matrix, followed by spectral clustering of the similarity matrix to obtain the final clustering result, includes: By introducing auxiliary variables and Lagrange multipliers, an augmented Lagrange function can be constructed. For anchor point graphs, by fixing other variables, the problem is transformed into a trace maximization problem. By calculating its singular value decomposition, the optimal anchor point graph for each view is obtained. For the permutation matrix, fixing other variables, the problem is transformed into another trace maximization problem, which is also solved by singular value decomposition to obtain the permutation matrix used to align anchor graphs of different sizes; For the anchor representation matrix, by fixing other variables and setting the derivative of the objective function to zero, the anchor representation matrix that can best reconstruct the original data can be obtained directly. For the clustering representation matrix, with other variables fixed, the problem is transformed into a trace maximization problem again, and solved by singular value decomposition to obtain the clustering representation matrix of each view. Then, these matrices are stacked to form the updated core tensor. By fixing all anchor graphs, permutation matrices, anchor representation matrices, cluster representation matrices, and the core tensor formed by their stacking, the auxiliary tensor in the augmented Lagrangian function is updated and solved. This step is transformed into an augmented tensor rank minimization problem, which is solved by the corresponding threshold contraction theorem to obtain the updated auxiliary tensor. Based on the difference between the newly obtained core tensor and auxiliary tensor, the Lagrange multipliers are updated; at the same time, the value of the penalty parameter is increased according to the preset rules to accelerate the convergence process. The iteration terminates when the change in the Lagrange multipliers or the difference between the core tensor and the auxiliary tensor is less than the preset convergence tolerance, and the final optimized anchor point graph, permutation matrix and unified similarity matrix are output. Spectral clustering analysis is performed on the final unified similarity matrix to obtain the final clustering results of the multi-view data.

[0014] According to a preferred embodiment, the method includes: The specific expression for updating the anchor point graph in the model is as follows: ; In the formula, This represents the updated anchor point graph, where ; The specific expression for updating the permutation matrix in the model is shown below: ; In the formula, Let represent the updated permutation matrix, where ; The specific expression for updating the anchor representation matrix in the model is shown below: ; The specific expression for updating the cluster representation matrix in the model is shown below: ; In the formula, This represents the updated anchor representation matrix, where... .

[0015] According to a preferred embodiment, the method further includes: The specific expression for updating the auxiliary tensor in the model is shown below: ; In the formula, This represents the updated auxiliary tensor. Indicates the penalty coefficient. Represents the Lagrange multipliers. Denotes the square of the Frobenius norm; The specific expressions for updating the Lagrange multipliers and penalty parameters in the model are shown below: ; In the formula, and Let these represent the updated Lagrange multipliers and the penalty parameter, respectively. , .

[0016] A multi-view clustering system based on adaptive anchor graph learning and tensor compensation includes: The preprocessing module is used to obtain the multi-view data matrix; Anchor map building module, used to adaptively determine the number of anchor points for each view and build the anchor map; The view alignment module is used to select the optimal view and align it with other views; The tensor compensation module is used to construct multi-view representation tensors and apply enhanced tensor rank regularization. The optimization solution module is used to solve the objective function and generate a similarity matrix; The clustering module is used to perform spectral clustering on the similarity matrix and output the clustering results.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. By acquiring a multi-view data matrix and employing a hierarchical clustering strategy, the optimal number of anchor points for each view is adaptively determined, constructing view-specific anchor maps. Furthermore, an optimal view selection mechanism is introduced to align anchor maps of different sizes to a unified clustering space. To compensate for information loss during alignment, a third-order tensor is constructed using stacked representation matrices, and an enhanced tensor rank regularization term is introduced to effectively mine high-order complementary structural information between views, compensating for information loss during alignment. This tensor compensation mechanism preserves the core structural information of individual views while strengthening consensus features between views, making the final clustering results more consistent and discriminative.

[0018] 2. An objective function integrating adaptive anchor graph learning and tensor compensation is constructed and optimized using the alternating direction multiplier method. Other variables are fixed and the anchor graph, permutation matrix, anchor representation matrix, and cluster representation matrix are updated sequentially. The auxiliary tensor is then solved using the threshold contraction theorem, and the Lagrange multipliers and penalty parameters are updated simultaneously to accelerate convergence. Finally, a unified similarity matrix is ​​generated and spectral clustering is performed to obtain the final clustering result. Through variable splitting and iteration strategies, the solution is ensured to be stable and efficient, avoiding local optima. At the same time, adaptive multi-view clustering without the need to preset the number of anchor points and clusters is realized, improving clustering performance and robustness. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the steps of the multi-view clustering method based on adaptive anchor graph learning and tensor compensation in this invention: Figure 2 This is a structural block diagram of the multi-view clustering system based on adaptive anchor graph learning and tensor compensation of the present invention. Detailed Implementation

[0020] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the technical solutions of the present invention, but should not be used to limit the scope of protection of the present invention.

[0021] Example: As attached Figure 1 As shown: This invention provides a multi-view clustering method based on adaptive anchor graph learning and tensor compensation, comprising the following steps: S1: Obtain the data matrix for multi-view data; Specifically, for publicly available multi-view datasets, the data for each view is first preprocessed, and then... Indicates the first A data matrix of views, where V is the number of views. It is the first The feature dimensions of each view; the purpose of this step is to transform multi-view data from different sources and in different formats into a unified matrix form, providing a standardized data foundation for subsequent operations such as anchor chart construction and view alignment, and ensuring consistency in the processing of each step.

[0022] S2: Automatically determine the optimal number of anchor points for each view using a hierarchical binary neighborhood clustering method, and construct a view-specific anchor map; In this embodiment, for each view in the multi-view data Hierarchical neighborhood clustering algorithms are applied to the corresponding feature data to automatically determine the required number of anchor points for the view, eliminating the need for manual pre-setting of the anchor point number. Based on the determined Anchor points are used to construct the anchor map corresponding to the view by calculating the similarity between the samples and the anchor points. Anchor chart Each row corresponds to a sample, and each column corresponds to an anchor point. The element value represents the correlation strength between the sample and the anchor point. Its function is to approximate the structural information of the entire view with a small number of anchor points, thereby reducing the complexity of subsequent calculations.

[0023] S21: Randomly select the initial seed sample; during operation, an unbiased sample is randomly selected from the n samples of the vth view as the initial seed to avoid bias in the clustering results due to initial selection preference. This seed sample serves as the initial center of the first cluster.

[0024] S22: Calculate the Euclidean distance between this sample and other samples in the same view, and construct the sorted distance vector; Specifically, Euclidean distance is used to quantify the similarity between the seed sample and all other samples. The smaller the distance, the more similar the samples are. All distance values ​​are arranged in ascending order to form a sorted distance vector. Its purpose is to provide a quantitative basis for determining the subsequent boundary and clarify the relationship between samples.

[0025] S23: Determine the optimal partitioning boundary by minimizing the objective function, and recursively partition the samples until clustering is complete; Specifically, the expression for minimizing the objective function to determine the optimal partition boundary is as follows: ; In the formula, , , , , This represents the number of samples in the optimal cluster. When using it, we iterate through all possible values ​​of k to find the k that minimizes the objective function value. This k value is then used as the partition boundary. The k samples closest to the seed sample are grouped into a cluster. We then recursively select a seed sample from the remaining samples and repeat this process until all samples are clustered. The purpose of this process is to minimize the distance difference between samples within a cluster and maximize the difference between clusters, ensuring that the clustering results closely match the natural structure of the data.

[0026] S24: Determine the number of anchor points for each view based on the clustering results.

[0027] Specifically, during operation, the center sample of each cluster is used as the anchor point of the view, and the number of clusters is the optimal number of anchor points for the view. Different views will produce different results due to differences in data structure. The purpose of this step is to achieve adaptive matching of the number of anchor points, avoiding the problem of insufficient adaptability caused by the preset number of anchor points in traditional methods, and allowing the anchor map to more accurately capture the unique structure of each view.

[0028] S3: Select the optimal view as the clustering representation space and learn the permutation matrix to align the anchor graphs of other views; In this embodiment, based on the clustering evaluation criteria of minimizing intra-class divergence and maximizing inter-class divergence, the clustering quality index of the anchor plot corresponding to each view is calculated, and the view with the best clustering quality is selected as the benchmark view; for each of the remaining non-benchmark views... By solving the label alignment optimization problem, the corresponding permutation matrix is ​​obtained. This causes the anchor label of the view to be... After transformation, the anchor point labels are aligned with the base view to obtain the clustering representation matrix of each view. ,in This represents the number of anchor points in the baseline view.

[0029] S31: Calculate the distance between samples in each view and sum them as a quality index for that view; Specifically, the expression for calculating the clustering quality index is as follows: ; In the above formula, Indicates the first in this cluster One sample, Indicates the first The first view The cluster center of each cluster, Indicates the first Evaluation metrics for each cluster. The calculation involves summing the squared Euclidean distances from all samples within each cluster to the cluster center, and then accumulating the sums from all clusters to obtain the view's metric. Its function is to quantify the compactness of clusters within a view. The smaller the value, the more concentrated the samples within the cluster, and the better the clustering structure of the view.

[0030] S32: Clustering evaluation metrics in each view The view with the smallest number of anchor points is selected as the optimal view, and its anchor point count is determined accordingly. As the final number of cluster categories A unified clustering benchmark is established so that the alignment of all subsequent views revolves around this optimal view. This avoids the need for manual pre-setting of the number of clusters and improves the reliability of the overall clustering based on the view with the richest information.

[0031] S33: For each of the remaining views Through the permutation matrix Align the clustering structures of each view to the optimal view to obtain the clustering representation matrix of each view. .

[0032] Specifically, the obtained view permutation matrices are... Clustering representation matrix A trace maximization objective is introduced to enhance the consistency of clustering structure among views, and its specific expression is as follows: ; In the above formula, The clustering representation matrix represents the clustering matrix. Represents the permutation matrix. Represents an anchor chart; When using it, the trace maximization problem is solved to adjust... and The value of makes the anchor plot of the non-base view... After transformation, the clustering structure is made as consistent as possible with the baseline view. The purpose of this step is to eliminate the size differences and structural deviations of anchor diagrams in different views and to achieve a preliminary consensus on the multi-view clustering structure.

[0033] S4: Introduce an enhanced tensor rank regularization term to construct a multi-view representation tensor to compensate for information loss during view alignment. In this embodiment, the specific form of tensor rank enhancement is as follows: ; In the above formula, For tensors formed by stacked multi-view representation matrices, For the first The singular value matrix of each frontal slice. During operation, the clustering representation matrix of each view is first... Stack them according to view dimensions to form a multi-view representation tensor. Then, the tensor is constrained by the enhanced tensor rank regularization term. Its function is to mine the high-order complementary structural information between views, compensate for the loss of the internal structural information of a single view during the view alignment process, and at the same time strengthen the consensus features between multiple views, making the clustering results more discriminative.

[0034] S5: The objective function is optimized by using the alternating direction multiplier method to generate a unified similarity matrix. Spectral clustering is then performed on the similarity matrix to obtain the final clustering result. In this embodiment, S51: Based on the adaptive anchor graph learning and tensor compensation model, Lagrange multipliers and a parameter for controlling the strength of the penalty term are introduced to define the augmented Lagrange function; this function transforms the original constrained optimization problem into an unconstrained optimization problem, which facilitates subsequent step-by-step solution, while the penalty strength is controlled by μ to ensure that the constraint conditions are met.

[0035] S52: Fix the essential tensor in the bipartite graph tensor model, update and solve the variables in the adaptive anchor graph learning and tensor compensation model, and obtain the solution results of each variable; Specifically, the model is solved by alternating direction multipliers, which decomposes the original problem into multiple subproblems and solves them by alternately optimizing variables.

[0036] The augmented Lagrangian function of this method can be expressed in the following form: ; in, It is a parameter that controls the strength of the penalty term. They are Lagrange multipliers. (Through continuous updates) The alternating direction multiplier method gradually approaches the optimal solution of the original optimization problem.

[0037] When other variables are fixed, anchor plot The update calculation is as follows: ; In the formula, This represents the updated anchor point graph, where .

[0038] When other variables are fixed, the permutation matrix The update calculation is as follows: ; In the formula, Let represent the updated permutation matrix, where .

[0039] When other variables are fixed, the update calculation of the anchor representation matrix is ​​as follows: ; When other variables are fixed, the update calculation of the cluster representation matrix is ​​as follows: ; In the formula, This represents the updated anchor representation matrix, where... .

[0040] When other variables are fixed, the update of the auxiliary tensor is calculated as follows: ; In the formula, This represents the updated auxiliary tensor. Indicates the penalty coefficient. Represents the Lagrange multipliers. This represents the square of the Frobenius norm.

[0041] S53: Repeat the solution steps of S52 until the updated Lagrange multipliers meet the preset conditions, and output the final solution result; the purpose of this loop process is to ensure that the optimization result gradually approaches the global optimum and avoids the decline in clustering performance caused by local optimum solutions.

[0042] S54: Perform spectral clustering on the final solution results, transform the similarity matrix into sample category labels, obtain the final clustering results, and transform the unified structural information after multi-view fusion into interpretable and applicable clustering categories to complete the clustering task of multi-view data.

[0043] Please see as follows Figure 2 As shown, the present invention also provides a multi-view clustering system based on adaptive anchor graph learning and tensor compensation, comprising: The preprocessing module is used to obtain the multi-view data matrix; Anchor map building module, used to adaptively determine the number of anchor points for each view and build the anchor map; The view alignment module is used to select the optimal view and align it with other views; The tensor compensation module is used to construct multi-view representation tensors and apply enhanced tensor rank regularization. The optimization solution module is used to solve the objective function and generate a similarity matrix; The clustering module is used to perform spectral clustering on the similarity matrix and output the clustering results.

[0044] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A multi-view clustering method based on adaptive anchor graph learning and tensor compensation, characterized in that, It includes the following steps: Obtain the data matrix of multi-view data; The optimal number of anchor points for each view is automatically determined by a hierarchical binary neighborhood clustering method, and a view-specific anchor map is constructed. The optimal view is selected as the clustering representation space, and the permutation matrix is ​​learned to align the anchor graphs of other views. An enhanced tensor rank regularization term is introduced to construct a multi-view representation tensor to compensate for information loss during view alignment. The objective function is optimized by using the alternating direction multiplier method to generate a unified similarity matrix. Spectral clustering is then performed on the similarity matrix to obtain the final clustering result.

2. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 1, characterized in that, The method of automatically determining the optimal number of anchor points for each view using hierarchical binary neighborhood clustering includes: Randomly select the initial seed sample; Calculate the Euclidean distance between this sample and other samples in the same view, and construct the sorted distance vector; The optimal partitioning boundary is determined by minimizing the objective function, and the samples are recursively partitioned until clustering is complete. The number of anchor points for each view is determined based on the clustering results; The objective function for the optimal boundary partitioning is: ； in, , , , , This represents the number of samples in the optimal cluster.

3. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 1, characterized in that, The steps for selecting the optimal view include: Calculate the intra-cluster variance for each view: ； In the formula, Indicates the first in this cluster One sample, Indicates the first The first view The cluster center of each cluster, Indicates the first Evaluation metrics for each cluster; The view with the minimum intra-cluster variance is selected as the optimal view.

4. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 1, characterized in that, The expression for aligning the anchor graph of other views with the learned permutation matrix is ​​as follows: ； In the formula, The clustering representation matrix represents the clustering matrix. Represents the permutation matrix. This represents an anchor chart.

5. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 1, characterized in that, The definition of the enhanced tensor rank regularization term is: ； In the formula, This represents a tensor formed by stacked multi-view representation matrices. Indicates the first The singular value matrix of a front slice.

6. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 1, characterized in that, The expression for the objective function is: ； In the formula, This represents a tensor constructed from anchor graphs of various views. The j-cluster representation matrix represents the mapping of each view to the cluster space. This represents the permutation matrix that aligns each view to the optimal view. Anchor diagrams representing each view.

7. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 5, characterized in that, The objective function is optimized using the alternating direction multiplier method to generate a unified similarity matrix. Spectral clustering is then performed on the similarity matrix to obtain the final clustering result, including: By introducing auxiliary variables and Lagrange multipliers, an augmented Lagrange function can be constructed. For anchor point graphs, by fixing other variables, the problem is transformed into a trace maximization problem. By calculating its singular value decomposition, the optimal anchor point graph for each view is obtained. For the permutation matrix, fixing other variables, the problem is transformed into another trace maximization problem, which is also solved by singular value decomposition to obtain the permutation matrix used to align anchor graphs of different sizes; For the anchor representation matrix, by fixing other variables and setting the derivative of the objective function to zero, the anchor representation matrix that can best reconstruct the original data can be obtained directly. For the clustering representation matrix, with other variables fixed, the problem is transformed into a trace maximization problem again, and solved by singular value decomposition to obtain the clustering representation matrix of each view. Then, these matrices are stacked to form the updated core tensor. By fixing all anchor graphs, permutation matrices, anchor representation matrices, cluster representation matrices, and the core tensor formed by their stacking, the auxiliary tensor in the augmented Lagrangian function is updated and solved. This step is transformed into an augmented tensor rank minimization problem, which is solved by the corresponding threshold contraction theorem to obtain the updated auxiliary tensor. Based on the difference between the newly obtained core tensor and auxiliary tensor, the Lagrange multipliers are updated; at the same time, the value of the penalty parameter is increased according to the preset rules to accelerate the convergence process. The iteration terminates when the change in the Lagrange multipliers or the difference between the core tensor and the auxiliary tensor is less than the preset convergence tolerance, and the final optimized anchor point graph, permutation matrix and unified similarity matrix are output. Spectral clustering analysis is performed on the final unified similarity matrix to obtain the final clustering results of the multi-view data.

8. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 7, characterized in that, The method includes: The specific expression for updating the anchor point graph in the model is as follows: ； In the formula, This represents the updated anchor point graph, where ; The specific expression for updating the permutation matrix in the model is shown below: ； In the formula, Let represent the updated permutation matrix, where ; The specific expression for updating the anchor representation matrix in the model is shown below: ； The specific expression for updating the cluster representation matrix in the model is shown below: ； In the formula, This represents the updated anchor representation matrix, where... .

9. The multi-view clustering method based on adaptive anchor graph learning and tensor compensation according to claim 7, characterized in that, The method further includes: The specific expression for updating the auxiliary tensor in the model is shown below: ； In the formula, This represents the updated auxiliary tensor. Indicates the penalty coefficient. Represents the Lagrange multipliers. Denotes the square of the Frobenius norm; The specific expressions for updating the Lagrange multipliers and penalty parameters in the model are shown below: ； In the formula, and Let these represent the updated Lagrange multipliers and the penalty parameter, respectively. , .

10. A multi-view clustering system based on adaptive anchor graph learning and tensor compensation, characterized in that, include: The preprocessing module is used to obtain the multi-view data matrix; Anchor map building module, used to adaptively determine the number of anchor points for each view and build the anchor map; The view alignment module is used to select the optimal view and align it with other views; The tensor compensation module is used to construct multi-view representation tensors and apply enhanced tensor rank regularization. The optimization solution module is used to solve the objective function and generate a similarity matrix; The clustering module is used to perform spectral clustering on the similarity matrix and output the clustering results.

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