Bipartite graph-based large-scale multi-view clustering method and system and electronic equipment

Abstract

The invention discloses a large-scale multi-view clustering method and system based on a bipartite graph and electronic equipment, and is applied to the technical field of multi-view clustering, and the method comprises the steps: carrying out the data preprocessing of a multi-view data set, obtaining an anchor point based on the bipartite graph through employing a random non-replacement sampling method, and calculating the anchor graph of each view through employing a kernel method; defining a semi-definite auxiliary matrix of each view based on the anchor map, and loosening binary constraints and rank constraints of the semi-definite auxiliary matrixes and semi-definite constraints of a kernel clustering formula; and based on a kernel clustering formula obtained by processing, fusing all views in combination with a preset fusion threshold to obtain a unified semi-definite auxiliary matrix, and obtaining a final clustering result label by utilizing spectral clustering. According to the method, continuously increasing large-scale data can be effectively handled, the robustness of the algorithm is effectively improved, and the multi-view clustering precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-view clustering, and in particular to a large-scale multi-view clustering method, system and electronic device based on a bipartite graph. Background Art

[0002] Information obtained from different channels and in different ways is heterogeneous and complementary. Multi-view clustering integrates information from different views to pursue consistent clustering results, and often has more potential for application in multiple fields than single-view clustering. In particular, it can be used for large-scale data application scenarios such as commodity classification, face detection, and logistics management. In addition, graph clustering plays an important role in social network analysis, especially in community detection and recommendation systems. Community detection aims to help researchers understand the inherent patterns and functions of community networks. The recommendation system can help the system better understand the user's consumption pattern and the relationship between items, thereby improving the accuracy and personalization of recommendations. In the field of industry and production, safety issues are related to the life and property safety of producers, so in terms of anomaly detection, highly robust algorithms are more needed to reduce the impact of noise data and improve the accuracy of results.

[0003] Existing multi-view clustering can be generally divided into multi-view clustering based on non-negative matrix factorization (NMF), multi-view clustering based on subspace (MKC), and multi-view clustering based on graph or spectrum, depending on the method. Among them, the MKC method learns a consensus kernel matrix from a set of basic kernel matrices, the NMF method applies matrix decomposition to multi-view clustering with a unified latent space, and the graph or spectral clustering method analyzes and optimizes a unified graph structure from the representation of multi-view data. The K-means algorithm is a classic clustering algorithm. Due to its simple implementation and easy-to-understand nature, most of the current clustering algorithms, whether MKC, NMF or spectral clustering, mostly involve using K-means as the last step of the algorithm to obtain clustering results. In order to obtain a low-dimensional representation of the data, a popular method is to use spectral clustering. The last step of the spectral clustering algorithm is to use the K-means clustering algorithm to obtain the result on the first k eigenvectors of the similarity matrix. However, whether it is spectral clustering or simply K-means clustering, its performance will be greatly affected by outliers, resulting in reduced robustness of the algorithm. At the same time, with the rapid development of the times, the amount of data that needs to be processed continues to increase, and many previously proposed clustering algorithms are no longer suitable for processing such large-scale data.

[0004] Therefore, how to provide a large-scale multi-view clustering method, system and electronic device based on bipartite graph that can effectively cope with the increasing large-scale data, effectively improve the robustness of the algorithm, and improve the accuracy of multi-view clustering is an urgent problem that technicians in this field need to solve. Summary of the invention

[0005] In view of this, the present invention proposes a large-scale multi-view clustering method, system and electronic device based on a bipartite graph.

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

[0007] A large-scale multi-view clustering method based on bipartite graph, comprising:

[0008] Step 1: Preprocess the multi-view dataset, obtain anchor points using random sampling without replacement based on the bipartite graph, and calculate the anchor graph of each view using the kernel method;

[0009] Step 2: Based on the anchor graph, define the semidefinite auxiliary matrix of each view, and relax the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula;

[0010] Step 3: Based on the kernel clustering formula obtained in step 2, all views are fused with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix, and spectral clustering is used to obtain the final clustering result label.

[0011] Optionally, in step 1, data preprocessing is performed on the multi-view dataset, specifically:

[0012] The penalty function is used to find a balanced clustering cluster, and each data point has only two cases: it completely belongs to a cluster or it is an outlier. The penalty function is as follows:

[0013]

[0014] Among them, Z (v) is the indicator matrix defined under the vth view, Z (v) ∈{0,1} N×C ; N is the number of data points; C is the number of clusters; is the kernel function of the vth view with parameter σ; σ is the selected scaling parameter; λ (v) ∈(0,1);E N is an N×N matrix of all 1s; T is the transpose.

[0015] Optionally, in step 1, based on the bipartite graph, a random sampling method without replacement is used to obtain anchor points, and the kernel method is used to calculate the anchor graph of each view, then:

[0016]

[0017] Z (v) ∈{0,1} N×C ,

[0018] Z (v) 1C ≤1 N ;

[0019] Among them, Z (v) is the indicator matrix defined under the vth view; N is the number of data points; C is the number of clusters; D (v) ∈R N×m For each data point in the data set and the m anchor points obtained by sampling using the kernel method, then is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; is the indicator matrix of the anchor point; T is the transpose; 1 C is a C-dimensional all-1 vector; 1 N is an N-dimensional vector of all 1s.

[0020] Optionally, a scaling parameter σ is determined as follows:

[0021]

[0022] Where α is the upper α quantile of the Gaussian distribution; {X1,X2,…,X n} is the data set; is a d-dimensional chi-square distribution;

[0023] The parameter λ is determined as follows:

[0024]

[0025] Among them, t α is the 1-α quantile of the d-dimensional chi-square distribution.

[0026] Optionally, the number of anchor points m is determined as follows:

[0027] For N original data For the interval, a total of t candidate m values ​​are drawn from small to large, among which,

[0028] N is the number of data points; α is the upper α quantile of the Gaussian distribution;

[0029] The t candidate m values ​​are sampled m times in a random sampling manner without replacement to obtain the corresponding anchor box and the value of m is determined based on the experimental results.

[0030] Optionally, in step 2, based on the anchor graph, a semidefinite auxiliary matrix for each view is defined:

[0031]

[0032] in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; and C is the number of clusters.

[0033] Optionally, in step 2, the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula are relaxed, and then:

[0034]

[0035] in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; is the element in the i-th row and j-th column of the S matrix.

[0036] Optionally, in step 3, based on the kernel clustering formula obtained in step 2, all views are fused in combination with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix, specifically:

[0037] According to the kernel clustering formula obtained in step 2, the semidefinite auxiliary matrix is ​​simplified to obtain:

[0038]

[0039] in, is the semidefinite adjuvant matrix for each view defined; is the element in row i and column j of D matrix; (v) ∈(0,1);

[0040] Based on the simplified result of the semidefinite auxiliary matrix, all views are fused in combination with the preset fusion threshold to obtain a unified semidefinite auxiliary matrix as follows:

[0041]

[0042] Among them, SMij is a unified semidefinite auxiliary matrix; V is the number of multiple views; is the element in the i-th row and j-th column of the S matrix; Q is the preset fusion threshold.

[0043] The present invention also provides a large-scale multi-view clustering system based on a bipartite graph using a large-scale multi-view clustering method based on a bipartite graph, comprising:

[0044] Data preprocessing and anchor graph calculation module: used to preprocess the multi-view dataset, obtain anchor points based on the bipartite graph using random sampling without replacement, and calculate the anchor graph of each view using the kernel method;

[0045] Semidefinite auxiliary matrix definition and constraint module: used to define the semidefinite auxiliary matrix of each view based on the anchor graph, and relax the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula;

[0046] Multi-view fusion and clustering module: It is used to fuse all views based on the kernel clustering formula obtained by the semidefinite auxiliary matrix definition and constraint module processing, combined with the preset fusion threshold, to obtain a unified semidefinite auxiliary matrix, and use spectral clustering to obtain the final clustering result label.

[0047] The present invention also provides an electronic device, comprising:

[0048] Memory for storing computer programs;

[0049] The processor is used to implement the steps of a large-scale multi-view clustering method based on bipartite graph when executing the computer program.

[0050] It can be seen from the above technical solutions that, compared with the prior art, the present invention proposes a large-scale multi-view clustering method, system and electronic device based on bipartite graphs. The present invention solves the problem of low robustness of multi-view clustering algorithms by using an improved linear kernel method based on semidefinite programming constraints to act on similarity graphs. This method is simple to solve and only requires simple rounding of the kernel matrix to handle abnormal points. Combined with the bipartite graph, it solves the problem that previous clustering methods cannot be applied to large-scale data. The characteristic of the bipartite graph is that after the data points are classified into two categories, a part of the points can be used as representative anchor points. The anchor points can be regarded as signs that approximately represent the distribution structure of the adjacent data points, so that these fixed number of anchor points can be used to explore the relationship with the original sample, thereby achieving the effect of reducing time complexity. In summary, the present invention can effectively cope with the increasing amount of large-scale data, and effectively improve the robustness of the algorithm and the accuracy of multi-view clustering. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0052] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0053] Figure 2 It is a schematic diagram of the histogram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and various algorithms on the data set ProteinFold.

[0054] Figure 3 Schematic diagram of the histogram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and other algorithms on the data set 100Leaves.

[0055] Figure 4 It is a histogram diagram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and other algorithms on the Handwritten data set.

[0056] Figure 5 It is a schematic diagram of the histogram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and other algorithms on the dataset Wiki_fea.

[0057] Figure 6 It is a schematic diagram of the histogram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and various algorithms on the data set Stl10_fea.

[0058] Figure 7 Schematic diagram of the histogram of the three indicators ACC, NMI and PUR of the algorithm of the present invention and other algorithms on the data set Cifar10.

[0059] Figure 8 This is a schematic diagram of the results of 20 samplings on the data set 100Leaves according to the present invention.

[0060] Fig. 9 This is a schematic diagram of the results of 20 samplings on the Handwritten dataset of the present invention.

[0061] Fig.10 This is a schematic diagram of the results of 20 samplings on the Cifar10 dataset according to the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] Embodiment 1:

[0064] Embodiment 1 of the present invention discloses a large-scale multi-view clustering method based on a bipartite graph, such as Figure 1 As shown, including:

[0065] Step 1: Preprocess the multi-view dataset, obtain anchor points using random sampling without replacement based on the bipartite graph, and calculate the anchor graph of each view using the kernel method.

[0066] In order to better illustrate the robustness of the algorithm, we first consider the kernel clustering problem in the ideal case where there is no noise and the clusters are of equal size, and then extend it. Assume a multi-view dataset with V views, the number of clusters is C, and under the vth view, define an indicator matrix Z (v) ∈{0,1} N×C , then for the assumed ideal situation, we have:

[0067]

[0068] Z (v) ∈{0,1} N×C ,

[0069]

[0070] The goal of this formula is to maximize the cohesion of clusters, that is, the similarity between clusters. At the same time, it is constrained by the allocation conditions, requiring that each data point belongs to exactly one cluster and the size of each cluster is

[0071] However, in reality, it is difficult to meet the premise of cluster equality, and the calculation amount of this formula is quite high for large-scale data. Therefore, in order to remove this cardinality constraint, the multi-view dataset is preprocessed, and based on the bipartite graph, random sampling without replacement is used to obtain anchor points, and the kernel method is used to calculate the anchor graph of each view.

[0072] Data preprocessing is performed on the multi-view dataset, specifically:

[0073] The penalty function is used to find a balanced cluster. The essence of this penalty function is to try to find a balanced cluster. In order to take the noise into consideration, we relax the assignment constraints of each data point so that each data point has only two cases: it completely belongs to a cluster or it is an outlier. The penalty function is as follows:

[0074]

[0075] Among them, Z (v) is the indicator matrix defined under the vth view, Z (v) ∈{0,1} N×C ; N is the number of data points; C is the number of clusters; is the kernel function of the vth view with parameter σ; σ is the selected scaling parameter; λ (v) ∈(0,1);E N is an N×N matrix of all 1s; T is the transpose.

[0076] In order to make the algorithm applicable to large-scale data, anchor points are introduced. Based on the bipartite graph, random sampling without replacement is used to obtain anchor points. The kernel method is used to calculate the anchor graph of each view, and then:

[0077]

[0078] Z (v) ∈{0,1} N×C ,

[0079] Z (v) 1 C ≤1 N ;

[0080] Among them, Z (v) is the indicator matrix defined under the vth view; N is the number of data points; C is the number of clusters; D (v) ∈R N×m For each data point in the data set and the m anchor points obtained by sampling using the kernel method, then is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; is the indicator matrix of the anchor point; T is the transpose; 1 C is a C-dimensional all-1 vector; 1 N is an N-dimensional vector of all 1s.

[0081] In the Gaussian kernel function, the correct choice of scaling parameter σ plays an important role in the performance of spectral clustering and kernel clustering algorithms. According to the optimal value of σ in low-dimensional problems, the main idea of ​​​​the value is,

[0082] Using the concept of the upper α quantile of the Gaussian distribution, we ensure that among (1-α)×100% of the data points, at least a small part (about 5%-10%) is within the range of the kernel function. Let this small part be β. Generally speaking, the value of β should be high enough to ensure that the points from the same cluster have a high similarity. Therefore, the method for determining the scaling parameter σ is as follows:

[0083]

[0084] Where α is the upper α quantile of the Gaussian distribution; {X1,X2,…,X n} is the data set; is a d-dimensional chi-square distribution; since there is usually a certain proportion of noise points in the data set, the value of α should be as small as possible so that there will be a higher similarity between non-noise points. In the embodiment of the present invention, α=β=0.5 is selected.

[0085] The value of parameter λ is critical to the robustness of BGR-MVC. If it is arbitrarily close to a number between 0 and 1, the resulting indicator matrix may be a matrix of all 1s or all 0s, which will invalidate the denoising result. Therefore, the parameter λ is determined as follows:

[0086]

[0087] Among them, t α is the 1-α quantile of the d-dimensional chi-square distribution, which is obtained by setting the distance of the Gaussian kernel function to {X1,X2,…,X n} is obtained by taking the 1-α quantile in the equation

[0088] m, as the number of anchor points, is of great significance for controlling the complexity of the algorithm. If it is too large, it loses its necessity. If it is too small, too much data information will be lost.

[0089] For N original data For the interval, a total of t candidate m values ​​are drawn from small to large, among which,

[0090] N is the number of data points; α is the upper α quantile of the Gaussian distribution; when α=0.05, t≤20;

[0091] The t candidate m values ​​are sampled m times in a random sampling manner without replacement to obtain the corresponding anchor box and the value of m is determined based on the experimental results.

[0092] Step 2: Based on the anchor graph, define the semidefinite auxiliary matrix of each view and relax the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula.

[0093] The kernel clustering formula obtained in step 1 involves maximizing a non-convex quadratic objective function on a binary matrix, which is not simple. To avoid this problem, a common method is to increase the dimension. Therefore, based on the anchor graph, a semidefinite auxiliary matrix is ​​defined for each view: By increasing the dimension of the N×C matrix, we have:

[0094]

[0095] in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; and C is the number of clusters.

[0096] From the perspective of linear space, the optimal solution in the above formula is After being decomposed into a specific matrix and then multiplied by a specific orthogonal matrix and rotated, the optimal solution Z in the kernel clustering formula obtained by step 1 can be obtained. (v) , so these two equations are equivalent.

[0097] In the above formula, The zero row vectors in correspond to the noise points in the data, which provides an effective means for identifying the noise points. However, the above formula is still a non-convex optimization problem. Therefore, relaxing the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula, we have:

[0098]

[0099] in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; is the element in the i-th row and j-th column of the S matrix.

[0100] Step 3: Based on the kernel clustering formula obtained in step 2, all views are fused with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix, and spectral clustering is used to obtain the final clustering result label.

[0101] Based on the kernel clustering formula obtained in step 2, all views are fused in combination with the preset fusion threshold to obtain a unified semidefinite auxiliary matrix, which is:

[0102] According to the kernel clustering formula obtained in step 2, the semidefinite auxiliary matrix is ​​simplified to obtain:

[0103]

[0104] in, is the semidefinite adjuvant matrix for each view defined; is the element in row i and column j of D matrix; (v) ∈(0,1);

[0105] Based on the simplified result of the semidefinite auxiliary matrix, all views are fused in combination with the preset fusion threshold to obtain a unified semidefinite auxiliary matrix as follows:

[0106]

[0107] Among them, S Mij is a unified semidefinite auxiliary matrix; V is the number of multiple views; is the element in the i-th row and j-th column of the S matrix; Q is the preset fusion threshold, which is 1 / 2 in the embodiment of the present invention.

[0108] The embodiment of the present invention clusters a given data set through the following specific experiments to verify the beneficial effects of the method of the present invention:

[0109] Implementation Platform:

[0110] The experiments in this embodiment use Win 10 Professional Edition, 64-bit operating system 11th Gen Intel(R) Core(TM) i7-11700K processor (CPU) is x6464GB, and all experiments are run on MATLAB R2021b.

[0111] Dataset:

[0112] Experiments were conducted on six datasets: ProteinFold, 100Leaves, Handwritten, Wiki_fea, Stl10_fea, and Cifar10, as shown in Table 1. The following is a brief introduction:

[0113] Table 1 Datasets for comparative experiments

[0114] Dataset Number of samples Number of views Number of clusters ProteinFold 694 12 27 100Leaves 1600 3 100 Handwritten 2000 6 10 Wiki_fea 2866 2 10 Stl10_fea 13000 3 10 Cifar10 50000 3 10

[0115] ProteinFold: Created by Professor Zhihong Mao's team at the University of California, San Diego. Contains 694 samples, 12 views, and 27 categories of protein data.

[0116] 100Leaves: The full name is One-hundred plant species leaves data set, which means a dataset of 100 plant species leaves with 1,600 samples.

[0117] Handwritten: A digital dataset consisting of 2000 samples, including 6 views including 76-dimensional Fourier coefficients, 64-dimensional Karhunen-Love coefficients, etc.

[0118] Wiki_fea: A text dataset obtained from Wikipedia, containing 2 views and 2866 samples divided into 10 classes.

[0119] Stl10_fea: Adam Coates released an image recognition dataset in 2011 for developing unsupervised feature learning, deep learning, and self-supervised learning algorithms. The images come from ImageNet, with a total of 13,000 RGB images in 3 views.

[0120] Cifar10: A widely used image classification dataset containing 50,000 color images classified into 10 categories: airplanes, cars, birds, cats, etc.

[0121] Evaluation indicators:

[0122] Three evaluation indicators that are widely used in the field of clustering are selected to judge the experimental results, including accuracy (ACC), normalized mutual information (NMI), and purity (PUR).

[0123] Multi-view clustering comparison algorithm:

[0124] GMC: Use a unified graph matrix to fuse the data matrices from each view, and then directly extract the feature vector of the unified graph as the clustering result.

[0125] MVCC: A clustering method based on local shape regularization concept decomposition is proposed.

[0126] BMVC: Multi-view data is represented by binary encoding, and then the binary matrix is ​​decomposed for clustering.

[0127] AMGL: A parameter-free weighted self-learning multi-view clustering method.

[0128] LMVSC: A linear-time multi-view subspace clustering algorithm for large-scale data.

[0129] OPMC: A one-step multi-view clustering approach for large-scale data.

[0130] For the above algorithms, their public Matlab codes were downloaded for implementation. The parameters of the comparison methods set in the experiment were consistent with those recommended in the corresponding literature of the algorithm. All algorithms took the best experimental results in all iterations. In terms of running time, the average time of 20 samplings was taken.

[0131] The best clustering accuracy (ACC), normalized mutual information (NMI) and purity (PUR) of each algorithm and the algorithm of the present invention (BGR-MVC) on multiple data sets are shown in Table 2, Table 3 and Table 4, respectively. Among them, the best result is indicated by bold, the suboptimal result is indicated by underline, and "-" indicates that the operation exceeds the running memory.

[0132] Table 2 Clustering accuracy results

[0133]

[0134] Table 3 Normalized mutual information results

[0135]

[0136] Table 4 Purity results

[0137]

[0138]

[0139] The running time of each algorithm and the algorithm of the present invention (BGR-MVC) on multiple data sets is shown in Table 5.

[0140] Table 5. Running time results

[0141] Algorithm ProteinFold 100Leaves Handwritten Wiki_fea Stl10_fea Cifar10 GMC 2.0112 2.5419 7.4184 10.6348 256.3992 - MVCC 44.8305 47.8388 77.8863 19.3212 208.42 14328 BMVC 0.0511 0.2007 0.2855 0.2638 2.8047 31.4222 AMGL 0.7637 7.5917 15.3566 154.2672 10525 - LMVSC 1.4423 0.8756 1.9289 0.6379 6.0806 20.039 OPMC 0.0982 0.1891 0.3461 0.0432 6.6569 14.0012 OURS 0.0632 0.4235 0.0802 0.1832 26.6603 308.2453

[0142] The histogram forms of the three indicators of ACC, NMI and PUR of each algorithm and the algorithm of the present invention (BGR-MVC) on the datasets ProteinFold, 100Leaves, Handwritten, Wiki_fea, Stl10_fea, and Cifar10 are shown in the figure below. Figure 2 ,like Figure 3 ,like Figure 4 ,like Figure 5 ,like Figure 6 ,like Figure 7 shown.

[0143] The anchor points were sampled 20 times. The results of 20 samplings on the datasets 100Leaves, Handwritten and cifar10 are as follows: Figure 8 ,like Fig. 9 ,like Fig.10 shown.

[0144] Experimental results: On most data sets, the algorithm of the present invention achieves the best performance in all three indicators. Taking LMVC as an example, as an algorithm also inspired by anchor graphs, BGR-MVC has a higher ACC than LMVC on all data sets. On small data sets represented by ProteinFold and WebKB, the ACC value of BGR-MVC is 5.05%, 21.37% and 18.05% higher than that of LMVC, respectively. On large data sets represented by Cifar10, the ACC value of BGR-MVC is also 0.01% higher than that of LMVC.

[0145] This shows the effectiveness of the BGR-MVC algorithm as an anchor graph improvement algorithm. In this group of experiments, the BGR-MVC algorithm has a greater advantage in running time in most cases. Take the experimental results of the Handwritten dataset as an example. Among the operation times of other comparison algorithms, the shortest running time is about 3.5 times that of the BGR-MVC algorithm, and the longest running time is about 971 times that of the BGR-MVC algorithm. For different data sets, the sampling results tend to be stable after 10 times.

[0146] Embodiment 2:

[0147] Embodiment 2 of the present invention discloses a large-scale multi-view clustering system based on a bipartite graph using a large-scale multi-view clustering method based on a bipartite graph, comprising:

[0148] Data preprocessing and anchor graph calculation module: used to preprocess the multi-view dataset, obtain anchor points based on the bipartite graph using random sampling without replacement, and calculate the anchor graph of each view using the kernel method;

[0149] Semidefinite auxiliary matrix definition and constraint module: used to define the semidefinite auxiliary matrix of each view based on the anchor graph, and relax the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula;

[0150] Multi-view fusion and clustering module: It is used to fuse all views based on the kernel clustering formula obtained by the semidefinite auxiliary matrix definition and constraint module, combined with the preset fusion threshold, to obtain a unified semidefinite auxiliary matrix, and use spectral clustering to obtain the final clustering result label.

[0151] Embodiment 3:

[0152] Embodiment 3 of the present invention discloses an electronic device, including:

[0153] Memory for storing computer programs;

[0154] The processor is used to implement the steps of a large-scale multi-view clustering method based on bipartite graph when executing the computer program.

[0155] The embodiment of the present invention discloses a large-scale multi-view clustering method, system and electronic device based on a bipartite graph. The present invention solves the problem of low robustness of the multi-view clustering algorithm by using an improved linear kernel method based on semidefinite programming constraints to act on a similarity graph. The method is simple to solve and only requires a simple rounding of the kernel matrix to handle abnormal points. Combined with the bipartite graph, the problem that the previous clustering method cannot be applied to large-scale data is solved. The characteristic of the bipartite graph is that after the data points are classified into two categories, a part of the points can be used as representative anchor points. The anchor points can be regarded as signs that approximately represent the distribution structure of the adjacent data points, so that these fixed number of anchor points can be used to explore the relationship with the original sample, thereby achieving the effect of reducing time complexity. In summary, the present invention can effectively cope with the increasing amount of large-scale data, and effectively improve the robustness of the algorithm and the accuracy of multi-view clustering.

[0156] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0157] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A large-scale multi-view clustering method based on bipartite graph, characterized in that: include: Step 1: Preprocess the multi-view dataset, obtain anchor points using random sampling without replacement based on the bipartite graph, and calculate the anchor graph of each view using the kernel method; Step 2: Based on the anchor graph, define a semidefinite auxiliary matrix for each view, and relax the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula; Step 3: Based on the kernel clustering formula obtained in step 2, all views are fused with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix, and spectral clustering is used to obtain the final clustering result label.

2. A large-scale multi-view clustering method based on bipartite graph according to claim 1, characterized in that: In step 1, data preprocessing is performed on the multi-view dataset, specifically: A penalty function is used to find a balanced clustering cluster, and each data point has only two cases: completely belonging to a cluster or being an outlier. The penalty function is as follows: Among them, Z (v) is the indicator matrix defined under the vth view, Z (v) ∈{0,1} N×C ; N is the number of data points; C is the number of clusters; is the kernel function of the vth view with parameter σ; σ is the selected scaling parameter; λ (v) ∈(0,1);E N is an N×N matrix of all 1s; T is the transpose.

3. The large-scale multi-view clustering method based on bipartite graph according to claim 1, characterized in that: In step 1, based on the bipartite graph, the random sampling without replacement method is used to obtain anchor points, and the kernel method is used to calculate the anchor graph of each view, then: s.tZ (v) ∈{0,1} N×C , Z (v) 1 C ≤1 N ； Among them, Z (v) is the indicator matrix defined under the vth view; N is the number of data points; C is the number of clusters; D (v) ∈R N ×m For each data point in the data set and the m anchor points obtained by sampling using the kernel method, then is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; is the indicator matrix of the anchor point; T is the transpose; 1 C is a C-dimensional all-1 vector; 1 N is an N-dimensional vector of all 1s.

4. The large-scale multi-view clustering method based on bipartite graph according to claim 3, characterized in that: The scaling parameter σ is selected as follows: Where α is the upper α quantile of the Gaussian distribution; {X1,X2,…,X n } is the data set; is a d-dimensional chi-square distribution; The parameter λ is determined as follows: Among them, t α is the 1-α quantile of the d-dimensional chi-square distribution.

5. The large-scale multi-view clustering method based on bipartite graph according to claim 3, characterized in that: The number of anchor points m is determined as follows: For N original data For the interval, a total of t candidate m values ​​are drawn from small to large, among which, N is the number of data points; α is the upper α quantile of the Gaussian distribution; The t candidate m values ​​are sampled m times in a random sampling manner without replacement to obtain the corresponding anchor box and the value of m is determined based on the experimental results.

6. The large-scale multi-view clustering method based on bipartite graph according to claim 1, characterized in that: In step 2, based on the anchor graph, the semidefinite auxiliary matrix of each view is defined: in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; and C is the number of clusters.

7. The large-scale multi-view clustering method based on bipartite graph according to claim 1, characterized in that: In step 2, the binary constraints and rank constraints of the semidefinite auxiliary matrix and the semidefinite constraints of the kernel clustering formula are relaxed, and then: in, is the semidefinite adjuvant matrix for each view defined, is the element in the i-th row and j-th column of matrix x; is the element in the i-th row and j-th column of matrix a; σ is the selected scaling parameter; λ (v) ∈(0,1);E Nm is an N×m matrix of all 1s; N is the number of data points; m is the number of anchor points; is the element in the i-th row and j-th column of the S matrix.

8. The large-scale multi-view clustering method based on bipartite graph according to claim 1, characterized in that: In step 3, based on the kernel clustering formula obtained in step 2, all views are fused in combination with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix, which is: According to the kernel clustering formula obtained in step 2, the semidefinite auxiliary matrix is ​​simplified to obtain: in, is the semidefinite adjuvant matrix for each view defined; is the element in row i and column j of D matrix; (v) ∈(0,1); Based on the simplified result of the semidefinite auxiliary matrix, all views are fused in combination with a preset fusion threshold to obtain a unified semidefinite auxiliary matrix as follows: Among them, S Mij is a unified semidefinite auxiliary matrix; V is the number of multiple views; is the element in the i-th row and j-th column of the S matrix; Q is the preset fusion threshold.

9. A large-scale multi-view clustering system based on bipartite graphs using a large-scale multi-view clustering method based on bipartite graphs according to any one of claims 1 to 8, characterized in that: include: Data preprocessing and anchor graph calculation module: used to preprocess the multi-view dataset, obtain anchor points based on the bipartite graph using random sampling without replacement, and calculate the anchor graph of each view using the kernel method; A semidefinite auxiliary matrix definition and constraint module: used to define a semidefinite auxiliary matrix of each view based on the anchor graph, and relax the binary constraint and rank constraint of the semidefinite auxiliary matrix and the semidefinite constraint of the kernel clustering formula; Multi-view fusion and clustering module: It is used to fuse all views based on the kernel clustering formula obtained by the semidefinite auxiliary matrix definition and constraint module, combined with the preset fusion threshold, to obtain a unified semidefinite auxiliary matrix, and use spectral clustering to obtain the final clustering result label.

10. An electronic device, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of a large-scale multi-view clustering method based on a bipartite graph as described in any one of claims 1 to 8 when executing the computer program.

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