Fast multi-view clustering method, system, storage medium and computer device based on logarithmic sparsity constrained anchor graph decomposition

Abstract

The present invention discloses a fast multi-view clustering method, system, storage medium, and computer device based on logarithmic sparsity-constrained anchor graph decomposition. The method, which belongs to the field of machine learning and data analysis, mainly comprises the following steps: reading a vectorized multi-view dataset and generating anchor points in all views; constructing an anchor graph between the original data and the anchor point set formed by the anchor points; performing anchor graph decomposition on the anchor graph to obtain a basis matrix and a coefficient matrix, and applying log-norm constraints to the basis matrix to remove redundant information; and performing K-means on the coefficient matrix to obtain cluster labels and generate clustering results. The present invention can significantly improve the accuracy and efficiency of clustering when processing large-scale multi-view clustering tasks and can be widely used in 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 constantly increasing. Compared to single-view data, multi-view data has attracted widespread attention because it contains information from multiple perspectives. Multi-view clustering has therefore been 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. However, the introduction of multi-view data, especially large-scale or high-dimensional multi-view data, places great demands on the efficiency of existing clustering methods. How to improve the efficiency of multi-view clustering has become a key issue in unsupervised learning.

[0003] Currently, clustering methods for large-scale multi-view data fall into two main categories: the first is anchor graph-based methods, which first generate a small number of anchor points for the original data, construct an anchor graph between the original data and the anchor points, and then perform spectral clustering. This 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 factorization-based methods, which directly operate on the original data, decomposing it into the product of a small coefficient matrix and a basis matrix. The resulting coefficient matrix is ​​then clustered using k-means clustering. Compared to traditional multi-view clustering methods, these methods significantly reduce computational complexity, improve the efficiency of multi-view clustering, and enable their application to large-scale clustering tasks.

[0004] However, the above two types of methods still have certain limitations. For the first type of methods based on anchor graphs, constructing anchor graphs instead of traditional full-sample graphs reduces the computational complexity, but the time and space overhead of spectral clustering on anchor graphs is still high; for the second type of methods based on matrix decomposition, 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 presence of redundant information 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 problem that needs to be solved urgently in the current field of large-scale multi-view clustering. 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 consistent with the sample category distribution, while ensuring clustering efficiency. It greatly improves clustering accuracy.

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

[0007] A fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints is proposed. This method uses anchor graphs instead of raw data for anchor graph decomposition, reducing computational complexity and significantly improving clustering efficiency when handling large-scale multi-view clustering tasks. Furthermore, a log-norm constraint is imposed during anchor graph decomposition to remove redundant information and obtain a sparser representation, significantly improving clustering accuracy when handling 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 data of multiple views 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 multi-view anchor graph and iterate 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 distribute the anchor points according to the dimensions of different views to obtain a set of anchor points of different views; the 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 stipulates is the element in 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 in 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 neighbor anchors 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 jth row of the vth 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 map B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the vth view of the multi-view anchor map 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] Adding the logarithmic sparsity constraint, the model is updated as follows:

[0028]

[0029] Where F is the coefficient matrix, γ>0 is the balance 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 assign them 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 perform anchor graph decomposition based on logarithmic sparsity constraints on the obtained multi-view anchor graph and learn the basis matrix that can represent the sample category structure;

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

[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 based on anchor graph decomposition with 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 of anchor graph decomposition based on logarithmic sparsity constraints 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) The multi-view anchor graph is used instead of the multi-view dataset for non-negative matrix factorization, which greatly reduces the computational complexity, effectively improves the clustering efficiency and reduces the sensitivity of the efficiency to the data dimension.

[0046] (2) The coefficient matrix of the non-negative matrix decomposition with log norm constraint 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 the visualization result of the clustering algorithm effect. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the accompanying drawings. The specific embodiments described herein are only used to explain the present application and are not intended 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 data of multiple views to obtain a spliced ​​single view, generate anchor points for all views, and obtain an anchor point set;

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

[0054] Step 3: Decompose the multi-view anchor graph and iterate 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 present invention, a multi-view dataset is first obtained. 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 is constructed by connecting all views and performing K-means clustering to obtain anchor points. The anchor points are then assigned according to the dimensions of different views to obtain a set of anchor points for different views. The WebKB multi-view dataset to be clustered is 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 neighbor anchors 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 jth row of the vth 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 map B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the vth view of the multi-view anchor map 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] Adding the logarithmic sparsity constraint, the model is updated as follows:

[0074]

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

[0076] like Figure 2 As shown, during the optimization iteration process, 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, comparing the proposed method with seven existing multi-view clustering methods using three metrics: clustering accuracy (ACC), adjusted Rand index (ARI), and F-score. All methods achieved excellent performance. The datasets used for 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 consisting of 2,400 images with 12 specific labels and 6 types of low-level features, including a 64-dimensional color histogram, a 144-dimensional color correlation map, a 73-dimensional edge histogram, a 128-dimensional microwave texture, a 225-dimensional block color moment partitioned by a 5×5 fixed grid, and a 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. It includes images from 50 categories, 40 of which are used as training sets and 10 as test sets. The semantics of each category in the AWA dataset is 85-dimensional, and the total number of images is 30,475.

[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 collection of consumer videos from the internet. These videos cover a wide range of topics and activities, such as sports, music, animals, and news events. 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, adjusted Rand index and F score of other comparative methods on different datasets, as shown in Table 1.

[0086] From the results in Table 1, it can be seen that the method of the present invention has significant performance advantages over traditional and cutting-edge clustering algorithms. In the three clustering evaluations of different data sets, the method of the present invention 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]

[0092] Table 2 Comparison of running time between the proposed method and existing methods on different real data sets

[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 flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device), or in conjunction with such instruction execution system, apparatus, or device. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by an instruction execution system, apparatus, or device, or in conjunction with such instruction execution system, apparatus, or device.

[0096] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0097] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the embodiments. Those skilled in the art can 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, characterized by: Anchor graphs are used instead of raw data for anchor graph decomposition, which reduces computational complexity and significantly improves clustering efficiency when handling 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 handling large-scale multi-view clustering tasks. The specific steps include the following: Step 1: Input the multi-view dataset to be clustered, connect the data of multiple views 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 multi-view anchor graph and iterate 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; 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 distribute the anchor points according to the dimensions of different views to obtain a set of anchor points of different views; the 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; Step 3 specifically includes: adding self-learning weights to the multi-view anchor map: where B∈R N×M , R N×M The dimension of the multi-view anchor map B is N×M, where N is the number of samples, M is the number of anchor points, and B (v) is the vth view of the multi-view anchor map 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 decomposing the anchor graph: 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 balance parameter.

2. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, characterized in that: It stipulates is the element in 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 in 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 data points The k nearest neighbor anchors 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.

3. The fast multi-view clustering method based on anchor graph decomposition with logarithmic sparsity constraints according to claim 1, characterized in that: 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.

4. 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 3, 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 assign them 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 perform anchor graph decomposition based on logarithmic sparsity constraints on the obtained multi-view anchor graph and learn the basis matrix that can represent the sample category structure; Clustering module: used to use K-means clustering to extract clustering results for multi-view datasets from the coefficient matrix.

5. A storage medium, 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 according to any one of claims 1 to 3.

6. A computer device, 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, it implements the fast multi-view clustering method based on logarithmic sparsity constrained anchor graph decomposition according to any one of claims 1 to 3.

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