Multi-view clustering method based on granular ball representation and weighted anchor points

Abstract

The invention belongs to the technical field of clustering methods, and relates to a multi-view clustering method based on granular ball representation and weighted anchor points, which comprises the following steps: acquiring a multi-view image data set, respectively regarding the image data set of each view as a granular ball, and executing a granular ball splitting process on the granular ball of each view to obtain an anchor point set of each view; a weighted anchor point discrimination mechanism and a multi-view structure alignment fusion mechanism are adopted to construct an optimization objective function of a consistent embedded matrix by taking minimization of a sample reconstruction error as a target; solving the optimization objective function by adopting an alternating optimization algorithm according to the image data set and the anchor point set of each view to obtain an optimal consistent embedding matrix of the multi-view image data set; clustering the optimal consistent embedding matrix of the multi-view image data set to obtain a clustering result; according to the self-adaptive anchor point generation algorithm provided based on granular ball calculation, the number of anchor points can be determined according to data density distribution, the representativeness of the anchor points and the difference of multiple views are guaranteed, and therefore the clustering effect of the multiple views is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of clustering methods, and relates to a multi-view clustering method based on particle ball representation and weighted anchor points. BACKGROUND

[0002] With the rapid growth of multi-source data, how to efficiently discover the potential structure of data under different modalities or feature perspectives has become an important research topic in the field of machine learning and data mining. As an unsupervised learning method that can fuse multi-source heterogeneous information, multi-view clustering (MVC) is widely used in image retrieval, social networks, bioinformatics and other fields. By mining the consistency and complementarity between different views, this method can more comprehensively reveal the potential structure of data, and has stronger robustness and accuracy than single-view clustering.

[0003] In the multi-view clustering method, clustering based on graph structure has attracted widespread attention due to its ability to effectively describe complex relationships between samples. Traditional multi-view graph clustering methods usually consist of two stages: (1) constructing a sample-sample similarity graph for each view; (2) fusing the similarity graphs of multiple views to obtain a consensus graph, and then using spectral clustering algorithms to obtain the clustering results. However, this method has a significant computational bottleneck: constructing a complete n x n similarity matrix requires O(n²) space complexity, and the time complexity of the spectral decomposition process reaches O(n³), which is difficult to apply in large-scale data scenarios.

[0004] To alleviate the computational complexity problem, the anchor graph (Anchor Graph) idea is introduced into multi-view clustering. This method approximates the complete similarity graph by selecting a small number of representative sample points (i.e. anchors), and converts the relationship between samples into a "sample-anchor" relationship, thereby reducing the complexity from quadratic to linear. Current anchor selection methods mainly fall into two categories: heuristic sampling methods (such as random sampling or k-means clustering) and learning-driven methods. The former is computationally efficient but cannot adapt to the differences in data distribution between different views, easily missing important structural information; the latter improves robustness by jointly optimizing anchors and graph structures, but often introduces additional optimization variables and high computational costs.

[0005] Although the anchor mechanism significantly improves the scalability of multi-view clustering, existing technologies still have the following outstanding problems:

[0006] (1) Fixed number of anchors, lack of adaptability: existing methods usually preset the same number of anchors for each view, ignoring the differences in data distribution and complexity between different views. This "one-size-fits-all" structural constraint results in too many or too few anchors for some views, making it difficult to accurately reflect the data characteristics of that view.

[0007] (2) Anchor quality is not high, and noise is difficult to remove: The anchor generation method based on heuristic sampling is easily affected by noise samples, especially in high-dimensional or heterogeneous views. Noise anchors can reduce the discriminability of the overall graph structure, leading to a decline in clustering performance. Although some methods dynamically update anchors through end-to-end learning, they increase the complexity and training cost of the model.

[0008] (3) Lack of anchor importance differentiation mechanism: Existing methods generally treat all anchors as equivalent units and fail to distinguish the importance difference between high-quality anchors and redundant anchors. This can weaken the discriminative information of a few key anchors and make it difficult to highlight representative structural features.

[0009] (4) The structure of the multi-view fusion stage is rigid: The mainstream anchor graph fusion method usually assumes that the anchor graph structure of each view is consistent, or merges them through simple weighted summation, ignoring the heterogeneity of different views at the structural level. This uniform structure assumption violates the essential difference of multi-view data and weakens the utilization of complementary information.

[0010] To solve the above problems, in recent years, some research has tried to introduce adaptive anchor selection and weighted anchor mechanism. For example, some works use low-rank constraints to achieve dynamic update of anchors, or use attention mechanisms to improve the weight of high-quality anchors. However, these methods still have problems such as optimization complexity, high computational cost, and easy to fall into local optimum, and most of them still need to manually set the number of anchors. In addition, existing research often ignores the "coarse-grained priority" feature in human cognition. Granular-Ball Computing (GBC) as a multi-granularity representation method based on granular computing theory, can abstract coarse-grained while ensuring structural accuracy, effectively improving computational efficiency and noise resistance. The granular ball describes the data subset through the center and radius, and can adaptively split and form a multi-level structure representation, providing natural theoretical support for anchor generation.

[0011] In summary, the existing multi-view anchor clustering method still has obvious deficiencies in anchor adaptability, quality control and structure fusion, and lacks a unified framework that can simultaneously realize "high-quality anchor generation-differentiated weighting-structure alignment fusion" in a multi-view heterogeneous environment. Therefore, it is urgent to develop a multi-view adaptive anchor clustering method that combines the ideas of granular ball computing and weighted learning mechanism to improve the discriminability, noise resistance and overall clustering performance of anchors. SUMMARY

[0012] To solve the above problems of the prior art, the present application adopts a multi-view clustering method based on granular ball representation and weighted anchors, comprising:

[0013] S1, obtain a multi-view image data set, regard the image data set of each view v as a particle ball respectively, perform a particle ball splitting process on the particle ball of each view v respectively to obtain an anchor point set of each view v;

[0014] S2, adopt a weighted anchor point discrimination mechanism and a multi-view structure alignment fusion mechanism to construct an optimization objective function of a consistent embedding matrix with the aim of minimizing sample reconstruction error;

[0015] S3, adopt an alternating optimization algorithm to solve the optimization objective function according to the image data set and the anchor point set of each view v to obtain an optimal consistent embedding matrix of the multi-view image data set;

[0016] S4, perform clustering on the optimal consistent embedding matrix of the multi-view image data set to obtain a clustering result of the multi-view image data set.

[0017] Beneficial effects:

[0018] 1, the adaptive anchor point generation algorithm based on particle ball calculation proposed in the present application can automatically determine the number of anchor points according to the data density distribution, eliminate noise points, and does not need to manually set parameters, so that the representativeness and multi-view difference of the anchor points are guaranteed, thereby improving the clustering effect of the multi-view; 2, the present application introduces an anchor point weight matrix and an anchor point correlation matrix by adopting a weighted anchor point discrimination mechanism, realizes anchor point weight self-learning through joint optimization, highlights high-quality anchor points and suppresses the interference of redundant anchor points on the graph structure, thereby improving the clustering effect of the multi-view; 3, aiming at the problem that the number of anchor points of each view is inconsistent, the present application introduces an orthogonal mapping matrix to map the heterogeneous anchor point graph to a unified latent space by adopting a multi-view structure alignment fusion mechanism, realizes structure alignment and fusion, and effectively retains the intra-view consistency and cross-view complementarity; 4, the overall optimization framework of the present application adopts an alternating optimization strategy, each sub-problem has a closed-form solution or a convex form, global convergence is ensured, and the time complexity is approximately linear O(n), so the present application can be applied to large-scale multi-view data. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of a multi-view clustering method based on particle ball representation and weighted anchor points provided for the embodiments of the present application. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0021] As Figure 1As shown, the embodiment of the present application adopts a multi-view clustering method based on particle representation and weighted anchor points, which is characterized by comprising:

[0022] S1, acquiring a multi-view image dataset, regarding the image dataset of each view v as a particle ball respectively, performing a particle ball splitting process on the particle ball of each view v to obtain an anchor point set of each view v;

[0023] The multi-view image dataset , wherein, represents the image dataset of the vth view, n is the number of images in the image dataset of each view, and d is the feature dimension of the image. The multi-view image dataset further comprises the number of clusters k, which represents the number of categories contained in the multi-view image dataset.

[0024] In one embodiment, the multi-view image dataset X={ }; is the image dataset of the black-and-white image and the color image of the portrait respectively; k is the number of people contained in the multi-view image dataset.

[0025] Regarding the image dataset of view v as a particle ball comprises: regarding the images in the image dataset of view v as the points in the particle ball of view v.

[0026] Performing a particle ball splitting process on the particle ball of view v comprises:

[0027] S11, judging whether the particle ball of view v satisfies the splitting condition, if yes, splitting the particle ball of view v into two sub-particle balls , ; otherwise, stopping splitting the particle ball ; ; otherwise, stopping splitting the particle ball ;

[0028] S12, judging whether each sub-particle ball , satisfies the splitting condition respectively, splitting the sub-particle ball satisfying the splitting condition into two sub-particle balls, and stopping splitting the sub-particle ball not satisfying the splitting condition;

[0029] S13, acquiring the sub-particle balls that have not stopped splitting currently, judging whether each sub-particle ball satisfies the splitting condition respectively, splitting the sub-particle ball satisfying the splitting condition into two sub-particle balls, and stopping splitting the sub-particle ball not satisfying the splitting condition; wherein, l is the index of the sub-particle ball;

[0030] Judging whether the sub-particle ball satisfies the splitting condition comprises:

[0031] S131, Calculation of sub-spheres Select the sub-sphere at the center. The farthest point pair, based on the farthest point pair and the sub-sphere Two sub-centers are generated from the center, and sub-spheres are generated based on the two sub-centers. Two sub-granules;

[0032] The farthest point pair refers to the pair of points in a grain that are farthest apart (i.e., the two images with the lowest similarity); subcenter Sub-center ;in, These are the two points that are furthest from each other.

[0033] Sub-spheres are generated based on the two subcenters. The two sub-spheres include: sub-spheres Each point in the matrix is ​​assigned to the nearest sub-center, resulting in a sub-sphere. The two sub-spheres.

[0034] S132, Calculate the number of sub-particles respectively The center of the two sub-spheres; according to the sub-spheres The centers of the two sub-spheres are calculated separately. The density and volume of its two sub-spheres;

[0035] For each sphere, the formula for its center and radius is as follows:

[0036]

[0037]

[0038] in, Let c be the i-th point in the sphere, c be the center of the sphere, r be the radius of the sphere, and k be the number of points in the sphere.

[0039] Particles density volume for:

[0040] Where k is the number of sub-spheres The number of midpoints For sub-spheres The i-th point in the array, where c is a sub-sphere. The center.

[0041] Particles The density-volume ratio of the two sub-spheres , Similarly, we can obtain the following.

[0042] S133, granules the weighted density volume of the two child granules is greater than the density volume of the parent granule the density volume of the two child granules is greater than the density volume of the parent granule satisfies the splitting condition; otherwise, the splitting condition is not satisfied.

[0043] the child granule the weighted density volume of the two child granules ; if the weighted density of the child granule is better than that of the parent granule, it indicates that the child granule satisfies the splitting condition, and subsequent recursive partitioning is required until the splitting condition is no longer satisfied.

[0044] S14, repeating step S13 until all child granules stop splitting; taking the centers of all current child granules as anchor points to obtain an anchor point set of the view v .

[0045] Isolated samples (i.e., |GB|=1, indicating that there is only one sample point in the child granule) are automatically removed to form a high-quality anchor point set.

[0046] The object of the present application is to perform structural alignment and fusion on anchor graphs of different views to obtain consistent low-dimensional representations and output the final clustering result; wherein k is the number of clusters, i.e., the number of categories contained in the image data set.

[0047] S2, using a weighted anchor point discrimination mechanism and a multi-view structural alignment and fusion mechanism to construct an optimization objective function of a consistent embedding matrix with the objective of minimizing sample reconstruction error;

[0048] The weighted anchor point discrimination mechanism of the present application introduces an anchor point weight matrix and an inter-anchor correlation matrix, realizes anchor point weight self-learning through joint optimization, highlights high-quality anchor points and suppresses the interference of redundant anchor points on the graph structure, thereby improving the clustering effect of multi-views; the multi-view structural alignment and fusion mechanism of the present application introduces an orthogonal mapping matrix to map heterogeneous anchor graphs to a unified latent space, realizes structural alignment and fusion, and effectively preserves the consistency within the view and the complementarity across views.

[0049] Specifically, the optimization objective function of the consistent embedding matrix includes:

[0050] S21, constructing an anchor point weight matrix and an inter-anchor correlation matrix, and constructing an objective function of an anchor graph based on the anchor point weight matrix and the inter-anchor correlation matrix with the objective of minimizing sample reconstruction error;

[0051] the objective function of the anchor graph is:

[0052] wherein, is the anchor point weight matrix of the view v, and the anchor point weight matrix is a diagonal matrix, Anchors weight matrix of view v Vector of weights on the diagonal, Anchors interrelation matrix of view v, used to suppress the repeated contribution of highly similar anchors.

[0053] Anchors graph is a mapping representation of data of view v, which linearly represents each data sample point in data of view v with all anchors in anchors set , i.e. each row in anchors graph linearly represents each data sample i in data of view v with all anchors in anchors set in corresponding proportion.

[0054] S22, constructing an orthogonal alignment matrix, projecting the objective function of anchors graph to a consistent latent space by using the orthogonal alignment matrix, to obtain an optimized objective function of consistent embedding matrix E.

[0055] Due to the inconsistency of the number of anchors generated by different views ≠ , it is necessary to project each anchors graph to the same latent space by using an orthogonal alignment matrix to realize structural alignment; then the optimized objective function is as follows:

[0056]

[0057] wherein, is the weight, is the weight of view v.

[0058] S3, solving the optimized objective function according to the image data set and anchors set of each view v by using an alternating optimization algorithm, to obtain the optimal consistent embedding matrix of the multi-view image data set;

[0059] Solving the optimized objective function includes:

[0060] S31, initializing the anchors weight matrix of each view v, anchors graph , orthogonal alignment matrix , view weight and consistent embedding matrix ;

[0061] Initializing the anchors weight matrix: ← ; wherein, is the unit matrix of , and is the number of anchors in anchors set of view v.

[0062] Initialize anchor graph: ; wherein, represents randomly generating a matrix with row number and column number n;

[0063] Initialize consistent embedding matrix: = , wherein, , P is a label matrix with the first k (cluster number) columns being unit matrices and the rest elements being 0, represents SVD decomposition, are respectively left singular vector matrix, singular value matrix and right singular vector matrix of matrix ;

[0064] Initialize orthogonal alignment matrix: , which is obtained by ;

[0065] Initialize view weight: .

[0066] S32, based on the optimization objective function, updating the current anchor weight matrix , anchor graph and orthogonal alignment matrix of each view v according to image data set and anchor set of each view v, obtaining the updated anchor weight matrix , anchor graph and orthogonal alignment matrix of each view v;

[0067] Updating the current orthogonal alignment matrix of each view v includes:

[0068] Based on the optimization objective function, deriving the trace maximization problem of the orthogonal alignment matrix:

[0069]

[0070] Based on the current consistent embedding matrix and the current anchor graph of each view v, solving the trace maximization problem of the orthogonal alignment matrix, obtaining the updated orthogonal alignment matrix .

[0071] In this embodiment, the updated orthogonal alignment matrix may be obtained by performing SVD singular value decomposition on .

[0072] updating the anchor weight matrix of each view v current comprising:

[0073] deriving the minimization problem of the anchor weight matrix based on the optimization objective function:

[0074]

[0075] where the intermediate variable = + , the intermediate variable diag( ), is the weight vector on the diagonal of the anchor weight matrix.

[0076] solving the minimization problem of the anchor weight matrix based on the image dataset of each view v , the anchor set , the anchor graph current and the view weight current to obtain the updated anchor weight matrix .

[0077] The objective function of the above minimization problem is convex with respect to , so it is a convex quadratic programming problem with linear constraints, which can be optimally solved by using the mature quadratic programming algorithm.

[0078] updating the anchor graph of each view v current comprising:

[0079] deriving the minimization problem of the anchor graph based on the optimization objective function:

[0080]

[0081] wherein indicates that each element in the anchor graph is greater than or equal to 0, indicates that the sum of the elements in each row of the anchor graph is equal to 1, i.e. for each data sample i in the data of the view v, the sum of the proportions between it and all anchors in the anchor set is 1, is a full 1 column vector.

[0082] solving the minimization problem of the anchor graph based on the image dataset of each view v , the anchor set , the anchor weight matrix current , the anchor graph current , the view weight current and the current consistent embedding matrix Solve the problem of minimizing the anchor graph to obtain the updated anchor graph. .

[0083] The minimization problem here can also be optimally solved using the currently mature quadratic programming algorithm.

[0084] S33. Update the anchor weight matrix based on each view v. Anchor point diagram and orthogonal alignment matrix Update the current consistent embedding matrix and the current view weight of each view v The updated consistent embedding matrix is ​​obtained. and the updated view weights for each view v ;

[0085] Update the current consistent embedding matrix include:

[0086] The problem of maximizing the trace of a consistent embedding matrix is ​​derived based on the optimization objective function:

[0087] in, for The identity matrix;

[0088] Based on the updated orthogonal alignment matrix for each view v and anchor point diagram Solve the trace maximization problem of the consistent embedding matrix to obtain the updated consistent embedding matrix. .

[0089] In this embodiment, solving the trace maximization problem of the consistent embedding matrix includes: for Performing SVD decomposition yields left and right singular matrices U and V. The updated consistent embedding matrix is ​​then... = .

[0090] Update the current view weight for each view v include:

[0091]

[0092] S34. Repeat steps S32 to S3 until the iteration stopping condition is met, and obtain the optimal consistent embedding matrix of the multi-view image dataset. .

[0093] Optimal consistent embedding matrix Each column in the image represents the image in a low-dimensional semantic space.

[0094] S4. Cluster the optimal consistent embedding matrix of the multi-view image dataset to obtain the clustering results of the multi-view image dataset.

[0095] Consistent embedding matrix Each column represents the representation of each image in the low-dimensional semantic space, and the consistent embedding matrix is ​​used. Each column is treated as an independent data sample. K-means clustering is performed on all columns of the consistent embedding matrix to obtain the clustering results of the multi-view image dataset.

[0096] The method of this invention can be widely applied to multi-source heterogeneous data clustering scenarios, and is especially suitable for multi-view tasks that require efficient structure fusion and noise suppression.

[0097] In one embodiment, the method of the present invention is applied to the field of unsupervised image clustering to obtain a portrait classification method based on multi-view anchor point clustering, including:

[0098] Obtain a portrait library and number of people containing multiple view types. Perform steps S1 to S4 on the feature dataset extracted from each view in the portrait library to obtain the portrait clustering results of the portrait library. The clustering results include multiple semantically consistent clusters. Each cluster can be used as a "semantic index unit" of the portrait library for fast classification.

[0099] Compared with traditional single-modal unsupervised clustering, this example has: stronger robustness: multi-view complementarity reduces the impact of noise, higher clustering accuracy: weighted anchor points can highlight key features.

[0100] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-view clustering method based on sphere representation and weighted anchor points, characterized in that, include: S1. Obtain the multi-view image dataset. Treat the image dataset of each view v as a sphere. Perform a sphere splitting process on each sphere of view v to obtain the anchor point set of each view v. S2. An optimization objective function for the consistent embedding matrix is ​​constructed by adopting a weighted anchor point discrimination mechanism and a multi-view structure alignment and fusion mechanism to minimize the sample reconstruction error. S3. The alternating optimization algorithm is used to solve the optimization objective function based on the image dataset and anchor point set of each view v, so as to obtain the optimal consistent embedding matrix of the multi-view image dataset. S4. Cluster the optimal consistent embedding matrix of the multi-view image dataset to obtain the clustering results of the multi-view image dataset.

2. The multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 1, characterized in that, The process of splitting the spheres in view v includes: S11. Determine the spheres in view v. Does the splitting condition meet? If so, then the sphere in view v will be... It splits into two daughter spheres. , Otherwise, stop splitting the granules. ; S12. Determine the characteristics of each sub-particle ball. , If the splitting condition is met, the sub-sphere that meets the splitting condition will split into two sub-spheres, and the splitting of sub-spheres that do not meet the splitting condition will be stopped. S13. Obtain the currently non-stop dividing sub-spheres. Determine each sub-sphere separately Whether the splitting condition is met, the daughter spheres that meet the splitting condition will be... The grain splits into two daughter grains; the splitting stops when the daughter grains no longer meet the splitting conditions. Where l is the index of the sub-sphere; S14. Repeat step S13 until all child spheres stop splitting; use the center of all current child spheres as anchor points to obtain the anchor point set.

3. The multi-view clustering method based on sphere representation and weighted anchor points according to claim 1, characterized in that, The images in the image dataset of view v are the points in the spheres of view v; determine the subspheres. Whether the conditions for splitting are met includes: S131, Calculation of sub-spheres Select the sub-sphere at the center. The farthest point pair, based on the farthest point pair and the sub-sphere Two sub-centers are generated from the center, and sub-spheres are generated based on the two sub-centers. Two sub-granules; S132, Calculate the number of sub-particles respectively The center of the two sub-spheres; according to the sub-spheres The centers of the two sub-spheres are calculated separately. The density and volume of its two sub-spheres; S133, granules The weighted density volume of the two subspheres is greater than that of the subsphere. The density and volume of the sub-particle sphere The conditions for splitting must be met; otherwise, the conditions for splitting must not be met.

4. The multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 3, characterized in that, Particles density volume for: ； Where k is the number of sub-spheres The number of midpoints For sub-spheres The i-th point in the array, where c is a sub-sphere. The center.

5. The multi-view clustering method based on sphere representation and weighted anchor points according to claim 1, characterized in that, The objective function to be optimized is: ； in, Here is the anchor weight matrix for view v. This is an anchor point diagram for view v, where V is the number of views. The weight of view v, For the data in view v, For the set of anchor points of view v, Anchor weight matrix The weight vector on the diagonal, This is the correlation matrix between anchor points in view v. As weight, Let V be the orthogonal alignment matrix of view v, and E be the consistent embedding matrix.

6. The multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 5, characterized in that, Solving the optimization objective function includes: S31. Initialize the anchor weight matrix for each view v. Anchor point diagram Orthogonal alignment matrix View weight and consistent embedding matrix ; S32. Based on the optimization objective function, according to the image dataset of each view v and anchor set Update the current anchor weight matrix for each view v. Anchor point diagram and orthogonal alignment matrix Obtain the updated anchor weight matrix for each view v. Anchor point diagram and orthogonal alignment matrix ; S33. Update the anchor weight matrix based on each view v. Anchor point diagram and orthogonal alignment matrix Update the current consistent embedding matrix and the current view weight of each view v The updated consistent embedding matrix is ​​obtained. and the updated view weights for each view v ; S34. Repeat steps S32-S33 until the iteration stopping condition is met, and obtain the optimal consistent embedding matrix. .

7. The multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 6, characterized in that, Update the current orthogonal alignment matrix for each view v. include: The problem of maximizing the trace of an orthogonal alignment matrix is ​​derived based on the optimization objective function: Based on the current consistent embedding matrix and the current anchor point graph for each view v Solve the trace maximization problem of the orthogonal alignment matrix to obtain the updated orthogonal alignment matrix. .

8. The multi-view clustering method based on sphere representation and weighted anchor points according to claim 6, characterized in that, Update the current anchor weight matrix for each view v. include: The problem of minimizing the anchor weight matrix is ​​derived based on the optimization objective function: ； in, = + , diag( ), The weight vectors on the diagonal of the anchor weight matrix; Image dataset based on each view v Anchor set Current anchor point diagram Current view weight Solve the problem of minimizing the anchor weight matrix to obtain the updated anchor weight matrix. .

9. The multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 6, characterized in that, Update the current anchor point graph for each view v. include: The problem of minimizing the anchor graph is derived based on the optimization objective function: ； in, Anchor point diagram Each element in the array is greater than or equal to 0. Anchor point diagram The sum of the elements in each row is equal to 1. It is a column vector consisting entirely of 1s; Image dataset based on each view v Anchor set The current anchor weight matrix Current anchor point diagram Current view weight and the current consistent embedding matrix Solve the problem of minimizing the anchor graph to obtain the updated anchor graph. .

10. A multi-view clustering method based on particle sphere representation and weighted anchor points according to claim 6, characterized in that, Update the current consistent embedding matrix include: The problem of maximizing the trace of a consistent embedding matrix is ​​derived based on the optimization objective function: ； in, for The identity matrix, where k is the number of categories contained in the multi-view image dataset; Based on the current orthogonal alignment matrix of each view v and anchor point diagram Solve the trace maximization problem of the consistent embedding matrix to obtain the updated consistent embedding matrix. .

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