Quick multi-view clustering method and system for anchor point diagram decomposition based on logarithm sparse constraint, storage medium and computer equipment

Abstract

The invention discloses a fast multi-view clustering method and system for anchor point diagram decomposition based on logarithm sparse constraint, a storage medium and computer equipment, and belongs to the field of machine learning and data analysis, and the method mainly comprises the following steps: reading a vectorized multi-view data set, and generating anchor points in all views; constructing an anchor point diagram between the original data and an anchor point set formed by the anchor points; performing anchor point diagram decomposition on the anchor point diagram to obtain a basis matrix and a coefficient matrix, performing log norm constraint on the basis matrix, and removing redundant information; and performing K-means on the coefficient matrix to obtain a clustering label, and generating a clustering result. According to the method, the clustering precision and efficiency can be remarkably improved when a large-scale multi-view clustering task is processed, and the method can be widely applied to the field of data analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of cluster analysis in machine learning, and in particular relates to a fast multi-view clustering method and system based on logarithmic sparse non-negative matrix decomposition. Background Art

[0002] With the development of the times, the scale of data is also constantly increasing. Compared with single-view data, multi-view data has attracted widespread attention because it contains information from multiple perspectives. Multi-view clustering is therefore widely used in several disciplines of machine learning, including pattern recognition, computer vision, and data mining, and has been proven to be more successful than single-view clustering in many cases. The introduction of multi-view data, especially large-scale or high-dimensional multi-view data, has put forward great requirements on the efficiency of existing clustering methods. How to improve the efficiency of multi-view clustering has become an important issue in unsupervised learning.

[0003] At present, clustering methods for large-scale multi-view data are mainly divided into two categories: the first category is anchor graph-based methods, that is, a small number of anchor points are first generated for the original data, an anchor graph between the original data and the anchor points is constructed, and then spectral clustering operations are performed. This type of method improves clustering efficiency by constructing an anchor graph to approximate the full sample graph, but the subsequent spectral clustering is still time-consuming; the second category is matrix decomposition-based methods, which directly operate on the original data and decompose it into the product of a small-scale coefficient matrix and a base matrix, and then perform k-means clustering on the obtained coefficient matrix to obtain the clustering result. Compared with traditional multi-view clustering methods, the computational complexity of these methods is significantly reduced, which improves the efficiency of multi-view clustering and enables it to be used for large-scale clustering tasks.

[0004] However, the above two methods still have certain limitations. For the first type of anchor graph-based methods, constructing an anchor graph instead of the traditional full sample graph reduces the computational complexity, but the time and space overhead of spectral clustering of the anchor graph is still high; for the second type of matrix decomposition-based methods, when faced with high-dimensional data, directly decomposing the original data becomes time-consuming, that is, the clustering efficiency is greatly affected by the data dimension. In addition, the basis matrix of this type of method is constrained to be a continuous non-negative matrix, and the redundant information present will lead to a decrease in clustering performance. Therefore, developing a multi-view clustering method that is efficient and not sensitive to data dimension has become an important issue that needs to be solved in the current large-scale multi-view clustering field. Summary of the invention

[0005] The purpose of the present invention is to further improve the clustering accuracy and efficiency, and provide a fast multi-view clustering method and system based on logarithmic sparse non-negative matrix decomposition. This method removes redundant information by imposing log norm constraints, so that the non-negative matrix decomposition based on the anchor graph can obtain a sparse solution that is more in line with the sample category distribution, while ensuring the clustering efficiency. At the same time, the clustering accuracy is greatly improved.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints is proposed. Anchor graphs are used instead of original data for anchor graph decomposition, which reduces the computational complexity and significantly improves the clustering efficiency when processing large-scale multi-view clustering tasks. Log norm constraints are imposed in the process of anchor graph decomposition to remove redundant information and obtain a sparser representation, which can significantly improve the clustering accuracy when processing large-scale multi-view clustering tasks. The method specifically includes the following steps:

[0008] Step 1: Input the multi-view dataset to be clustered, connect the multi-view data to obtain a spliced ​​single view, generate anchor points for all views, and obtain an anchor point set;

[0009] Step 2: Using the sparse graph learning method, construct a multi-view anchor graph B between the anchor set and the multi-view dataset;

[0010] Step 3: Decompose the anchor graph of the multi-view anchor graph, and then optimize iteratively to obtain the basis matrix and corresponding coefficient matrix that can represent the sample category structure;

[0011] Step 4: Perform K-means clustering on the coefficient matrix to obtain cluster labels and generate clustering results.

[0012] The anchor points are generated using the K-means algorithm instead of random sampling, which improves the quality of the anchor points. Step 1 specifically includes:

[0013] Input the multi-view dataset to be clustered, connect all views and perform K-means clustering to obtain anchor points, and then assign anchor points according to the dimensions of different views to obtain a set of anchor points of different views; multi-view dataset to be clustered χ = [X (1) ,X (2) ,...,X (V) ] T , X (i) is the i-th view of the multi-view to be clustered; the anchor point set of all views ε = [E (1) ,E (2) ,...,E (V) ] T , E (i) ∈R n×m ; E(i) is the anchor point set of the i-th view, R n×m Represents the matrix E (i) The dimension is n×m, where n is the number of rows and m is the number of columns.

[0014] It is stipulated is the element of the i-th row and j-th column of the v-th view of the multi-view anchor graph B, and m is the total number of columns of the multi-view anchor graph B. The sum of each row of the multi-view anchor graph B is made to be 1, avoiding the situation where some rows of the multi-view anchor graph B are all 0, ensuring the participation of the data, unifying the scale, simplifying the calculation, and improving the stability of clustering. Step 2 specifically includes:

[0015] Construct a multi-view anchor graph B between the anchor set and the multi-view dataset, using data points The k nearest anchor points of , construct the normalized KNN anchor graph for each view:

[0016]

[0017] in is a sorting function that sorts distances in ascending order, is the Euclidean distance between two arbitrary elements a and b; j′ is the distance from the i-th sample X in the multi-view dataset i The indices of the nearest k anchor points; is the corresponding element of the i-th row and j-th column of the v-th view of the anchor graph B; is the i-th row of the v-th view of the sample view, that is, the data of the i-th data point in the v-th view; is the j-th row of the v-th view of the anchor set.

[0018] Step 3 specifically includes:

[0019] Add self-learning weights to multi-view anchor maps:

[0020]

[0021] where B∈R N×M , R N×M The dimension of the multi-view anchor graph B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the v-th view of the multi-view anchor graph B, α (v) is the self-learning weight of the vth view of the multi-view anchor graph B, v∈{1,2,...,V}, V is the total number of views in the multi-view anchor graph B;

[0022] Apply log norm constraints to the basis matrix obtained by anchor graph decomposition:

[0023]

[0024] G ij is the element in the i-th row and j-th column of the basis matrix G; applying the log norm constraint enables the anchor graph decomposition model to perform more precise sparse constraints on the basis matrix, remove redundant information, and obtain a sparse solution that is more consistent with the sample category distribution;

[0025] The original anchor graph decomposition model is:

[0026]

[0027] By adding the logarithmic sparsity constraint, the model is updated as follows:

[0028]

[0029] Where F is the coefficient matrix, γ>0 is the equilibrium parameter;

[0030] Step 4 specifically includes:

[0031] For the coefficient matrix F, the K-means clustering method is used to extract the discrete categories corresponding to the samples in the multi-view dataset and obtain the clustering results.

[0032] A system for implementing the fast multi-view clustering method based on logarithmic sparsity constrained anchor graph decomposition, the system comprising:

[0033] Data reading module: reads multi-view datasets;

[0034] Data connection module: connects all views together;

[0035] Anchor point generation module: K-means clustering is performed on the connected views to generate anchor points, and they are assigned to each view;

[0036] Anchor graph construction module: constructs an anchor graph using the k nearest anchor points of each data point;

[0037] Anchor graph decomposition module: used to decompose the obtained multi-view anchor graph based on logarithmic sparsity constraints and learn the basis matrix that can represent the sample category structure;

[0038] Clustering module: used to extract clustering results of multi-view datasets from the coefficient matrix using K-means clustering.

[0039] A storage medium includes: the storage medium stores one or more programs, and when the programs are executed by a processor, the fast multi-view clustering method of anchor graph decomposition based on logarithmic sparsity constraints is implemented.

[0040] A computer device comprising a memory and a processor, wherein:

[0041] The memory is used to store computer programs;

[0042] When the processor is used to execute the computer program stored in the memory, the fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints as described in any one of claims 1 to 5 is implemented.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] (1) A multi-view anchor graph is used instead of a multi-view dataset for non-negative matrix factorization, which greatly reduces the computational complexity, effectively improves clustering efficiency, and reduces the sensitivity of efficiency to data dimensions.

[0046] (2) The coefficient matrix of the log norm constrained non-negative matrix decomposition is used to effectively remove redundant information and improve clustering accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is the algorithm flow chart.

[0048] Figure 2 Schematic diagram of the number of steps required for the clustering process.

[0049] Figure 3 This is a visualization of the clustering algorithm effect. DETAILED DESCRIPTION

[0050] The present invention is further described below in conjunction with the accompanying drawings. The specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0051] The flowchart of the specific implementation of the present invention is as follows Figure 1 As shown, the steps are as follows:

[0052] Step 1: Input the multi-view dataset to be clustered, connect the multi-view data to obtain a spliced ​​single view, generate anchor points for all views, and obtain an anchor point set;

[0053] Step 2: Using the sparse graph learning method, a multi-view anchor graph is constructed between the anchor set and the multi-view dataset;

[0054] Step 3: Decompose the anchor graph of the multi-view anchor graph, and then optimize iteratively to obtain the basis matrix and corresponding coefficient matrix that can represent the sample category structure;

[0055] Step 4: Perform K-means clustering on the coefficient matrix to obtain cluster labels and generate clustering results.

[0056] In the example of the present invention, a multi-view dataset is first obtained, and the dataset can be represented by a web page dataset WebKB.

[0057] The specific implementation steps of step 1 are:

[0058] The WebKB multi-view dataset to be clustered connects all views and performs K-means clustering to obtain anchor points, and then distributes the anchor points according to the dimensions of different views to obtain a set of anchor points of different views; the WebKB multi-view dataset to be clustered χ=[X (1) ,X (2) ,...,X (V) ] T , X (i) is the i-th view of the WebKB multi-view to be clustered; the anchor point set of all views ε = [E (1) ,E (2) ,...,E (V) ] T , E (i) ∈R n×m ; E (i) is the anchor point set of the i-th view, R n×m Represents the matrix E (i) The dimension is n×m, where n is the number of rows and m is the number of columns.

[0059] The specific implementation steps of step 2 are:

[0060] Construct a multi-view anchor graph B between the anchor set and the WebKB multi-view dataset, using data points The k nearest anchor points of , construct the normalized KNN anchor graph for each view:

[0061]

[0062] in is a sorting function that sorts distances in ascending order, is the Euclidean distance between two arbitrary elements a and b; j′ is the distance from the i-th sample X in the multi-view dataset i The indices of the nearest k anchor points; is the corresponding element of the i-th row and j-th column of the v-th view of the anchor graph B; is the i-th row of the v-th view of the sample view, that is, the data of the i-th data point in the v-th view; is the j-th row of the v-th view of the anchor set.

[0063] The specific implementation steps of step 3 are:

[0064] Add self-learning weights to multi-view anchor maps:

[0065]

[0066] where B∈R N×M , R N×M The dimension of the multi-view anchor graph B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the v-th view of the multi-view anchor graph B, α (v)

[0067] is the self-learning weight of the vth view of the multi-view anchor graph B, v∈{1,2,...,V}, V is the total number of views in the multi-view anchor graph B;

[0068] Apply log norm constraints to the basis matrix obtained by anchor graph decomposition:

[0069]

[0070] G ij is the element in the i-th row and j-th column of the basis matrix G; applying the log norm constraint enables the anchor graph decomposition model to perform more precise sparse constraints on the basis matrix, remove redundant information, and obtain a sparse solution that is more consistent with the sample category distribution;

[0071] The original anchor graph decomposition model is:

[0072]

[0073] By adding the logarithmic sparsity constraint, the model is updated as follows:

[0074]

[0075] Where F is the coefficient matrix, γ>0 is the equilibrium parameter;

[0076] like Figure 2 As shown, in the process of optimization iteration, it can be observed that the value of the model decreases with each iteration, which shows that the method of the present invention is practical and effective.

[0077] The specific implementation steps of step 4 are:

[0078] For the coefficient matrix F, the K-means clustering method is used to extract the discrete categories corresponding to the samples in the multi-view dataset and obtain the clustering results. Figure 3 shown.

[0079] It should be noted that a large number of comparative experiments were conducted on five different multi-view datasets with seven existing multi-view clustering methods under the three indicators of clustering accuracy (ACC), adjusted Rand index (ARI), and F-score (F-Score), and all achieved excellent performance. The datasets used in the comparative experiments include:

[0080] WebKB is a website dataset containing 1051 samples, including two views: web page content and URL, with data dimensions of 1840 and 3000 respectively.

[0081] NUS is a multi-label web image dataset created by the Media Search Laboratory of the National University of Singapore, including: 2,400 images, 12 specific tags; 6 categories of low-level features, including 64-dimensional color histogram, 144-dimensional color correlation map, 73-dimensional edge histogram, 128-dimensional microwave texture, 225-dimensional block color moment of 5×5 fixed grid partition and 500-dimensional bag of words based on SIFT description.

[0082] The AWA dataset is a widely used standard dataset that contains a large amount of images and attribute information about different animal categories, including 50 categories of pictures, 40 categories as training sets, and 10 categories as test sets. The semantics of each category in the AWA dataset is 85 dimensions, with a total of 30,475 pictures.

[0083] The MSRC dataset contains color images of various natural scenes, covering a variety of objects and backgrounds, such as animals, buildings, vehicles, plants, and roads.

[0084] The CCV dataset contains a large number of consumer videos from the Internet. These videos cover a variety of topics and activities, such as sports, music, animals, news events, etc. Each video has a unique YouTube ID, ground-truth annotations, standard training and testing splits, and multiple views including three audio / visual feature representations.

[0085] The evaluation indicators of the comparative experiments include the clustering accuracy of other comparative methods on different data sets, the adjusted Rand index and the F score, as shown in Table 1.

[0086] From the results in Table 1, we can see that our method has a significant performance advantage over traditional and cutting-edge clustering algorithms. In the three clustering evaluations of different data sets, our method ranks first in most cases, and ranks second in a few cases where it does not reach the optimal index.

[0087] Table 1 Summary of comparative experimental results of different clustering algorithms on multiple real-world datasets

[0088]

[0089]

[0090]

[0091] Table 2 Comparison of running time between the proposed method and existing methods on different real data sets

[0092]

[0093]

[0094] It can be seen that the present invention is a fast multi-view clustering method based on logarithmic sparse non-negative matrix decomposition. By performing anchor graph decomposition on the learned anchor graph, the data scale is reduced, the computational complexity is reduced, and the clustering efficiency is improved. At the same time, a new anchor graph decomposition model based on logarithmic sparsity constraints is proposed, which removes redundant information to generate a decomposition that is more in line with the sample category distribution, thereby improving the clustering accuracy.

[0095] Those skilled in the art will appreciate that the logic and / or steps represented in the flowchart or otherwise described herein, for example, may be considered as an ordered list of executable instructions for implementing logical functions, and may be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" may be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0096] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0097] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints, Features: Anchor graphs are used to replace original data for anchor graph decomposition, which reduces computational complexity and significantly improves clustering efficiency when processing large-scale multi-view clustering tasks. Log norm constraints are imposed during anchor graph decomposition to remove redundant information and obtain a sparser representation, which significantly improves clustering accuracy when processing large-scale multi-view clustering tasks. The specific steps are as follows: Step 1: Input the multi-view dataset to be clustered, connect the multi-view data to obtain a spliced ​​single view, generate anchor points for all views, and obtain an anchor point set; Step 2: Using the sparse graph learning method, construct a multi-view anchor graph B between the anchor set and the multi-view dataset; Step 3: Decompose the anchor graph of the multi-view anchor graph, and then optimize iteratively to obtain the basis matrix and corresponding coefficient matrix that can represent the sample category structure; Step 4: Perform K-means clustering on the coefficient matrix to obtain cluster labels and generate clustering results.

2. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, Features: The anchor points are generated using the K-means algorithm instead of random sampling, which improves the quality of the anchor points. Step 1 specifically includes: Input the multi-view dataset to be clustered, connect all views and perform K-means clustering to obtain anchor points, and then assign anchor points according to the dimensions of different views to obtain a set of anchor points of different views; multi-view dataset to be clustered χ = [X (1) ,X (2) ,...,X (V) ] T , X (i) is the i-th view of the multi-view to be clustered; the anchor point set of all views ε = [E (1) ,E (2) ,...,E (V) ] T , E (i) ∈R n×m ; E (i) is the anchor point set of the i-th view, R n×m Represents the matrix E (i) The dimension is n×m, where n is the number of rows and m is the number of columns.

3. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, Features: It is stipulated is the element of the i-th row and j-th column of the v-th view of the multi-view anchor graph B, and m is the total number of columns of the multi-view anchor graph B. The sum of each row of the multi-view anchor graph B is made to be 1, avoiding the situation where some rows of the multi-view anchor graph B are all 0, ensuring the participation of the data, unifying the scale, simplifying the calculation, and improving the stability of clustering. Step 2 specifically includes: Construct a multi-view anchor graph B between the anchor set and the multi-view dataset, using the data point X i (v) The k nearest anchor points of , construct the normalized KNN anchor graph for each view: in is a sorting function that sorts distances in ascending order, is the Euclidean distance between two arbitrary elements a and b; j′ is the distance from the i-th sample X in the multi-view dataset i The indices of the nearest k anchor points; is the corresponding element of the i-th row and j-th column of the v-th view of the anchor graph B; is the i-th row of the v-th view of the sample view, that is, the data of the i-th data point in the v-th view; is the j-th row of the v-th view of the anchor set.

4. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, Features: Step 3 specifically includes: Add self-learning weights to multi-view anchor maps: where B∈R N×M , R N×M The dimension of the multi-view anchor graph B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the v-th view of the multi-view anchor graph B, α (v) is the self-learning weight of the vth view of the multi-view anchor graph B, v∈{1,2,...,V}, V is the total number of views in the multi-view anchor graph B; Apply log norm constraints to the basis matrix obtained by anchor graph decomposition: G ij is the element in the i-th row and j-th column of the basis matrix G; applying the log norm constraint enables the anchor graph decomposition model to perform more precise sparse constraints on the basis matrix, remove redundant information, and obtain a sparse solution that is more consistent with the sample category distribution; The original anchor graph decomposition model is: Adding the logarithmic sparsity constraint, the model is updated as follows: Where F is the coefficient matrix and γ>0 is the equilibrium parameter.

5. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, Features: Step 4 specifically includes: For the coefficient matrix F, the K-means clustering method is used to extract the discrete categories corresponding to the samples in the multi-view dataset and obtain the clustering results.

6. A system for implementing the fast multi-view clustering method based on logarithmic sparsity constrained anchor graph decomposition according to any one of claims 1 to 5, It is characterized in that The system comprises: Data reading module: reads multi-view datasets; Data connection module: connects all views together; Anchor point generation module: K-means clustering is performed on the connected views to generate anchor points, and they are assigned to each view; Anchor graph construction module: constructs an anchor graph using the k nearest anchor points of each data point; Anchor graph decomposition module: used to decompose the obtained multi-view anchor graph based on logarithmic sparsity constraints and learn the basis matrix that can represent the sample category structure; Clustering module: used to extract clustering results of multi-view datasets from the coefficient matrix using K-means clustering.

7. A storage medium, It is characterized in that include: The storage medium stores one or more programs, which, when executed by a processor, implement the fast multi-view clustering method based on logarithmic sparsity constrained anchor graph decomposition as described in any one of claims 1 to 5.

8. A computer device, It is characterized in that The computer device comprises a memory and a processor, wherein: The memory is used to store computer programs; When the processor is used to execute the computer program stored in the memory, the fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints as described in any one of claims 1 to 5 is implemented.

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