Multi-view subspace clustering method combining independence criterion and low-rank tensor

Abstract

The invention discloses a multi-view subspace clustering method combining an independence criterion and a low-rank tensor. According to the method, firstly, features of multi-view data are mapped to a regeneration kernel Hilbert space, and the dependency relationship between the data is estimated under the condition that joint distribution of random variables is not explicitly estimated; and then effectively processing and fusing the data from different angles by using a low-rank tensor, iterating the features of the multi-view data, and promoting low-rank representation and consistent learning. Finally, projection matrixes obtained through iteration are added to serve as input of a clustering algorithm, and multi-view subspace clustering is achieved. According to the method, diversity and consistency of multi-view data information are fully utilized, data comparison in views is realized, data comparison information among different views is further supplemented, redundant information is removed by utilizing a Hilbert-Schmidt independence criterion, and clustering performance is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning and relates to a multi-view subspace clustering method combining an independence criterion and a low-rank tensor. Background Art

[0002] To make descriptions more accurate, data from different sources can be used to describe the same subject. For example, for a face, there are frontal and side views, and for a news report, there are different languages. Multi-view clustering was first proposed by Steffen Bickel in "Multi-view Clustering." By learning an adjacency matrix or performing subspace projections on each view, the data matrix used for clustering is finally integrated. Unsupervised classification is then performed based on the features of this transformed data matrix. Compared to single-view clustering, the extensive information provided by multi-view features can better represent data characteristics, making multi-view clustering more likely to achieve satisfactory results.

[0003] However, existing multi-view clustering methods are still limited to data comparison within views, lack vertical comparison between data, and do not truly utilize the diversity characteristics of multi-view data, resulting in less than ideal clustering effects. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention proposes a multi-view subspace clustering method that combines the independence criterion and low-rank tensor. First, the Hilbert-Schmidt independence criterion is used to measure the degree of dependence between data, explore the complementarity of multi-view representation, and then the low-rank tensor is used to effectively process and fuse data from different perspectives, promote low-rank representation and consistency learning, and achieve better clustering effect.

[0005] A multi-view subspace clustering method combining independence criteria and low-rank tensor is proposed. The specific steps are as follows: Step S1: Get multi-view data of a single object X = {X (1) ,X (2) ,X (3) ,…,X (V)}, Represents the vth view of the object, v=1,2,…V, V represents the number of views, n is the number of samples, m v is the dimension of the v-th view.

[0006] Step S2: Superimpose the multi-view data X to obtain the full data view X (V+1) , and added to the multi-view data X.

[0007] Step S3: Joint low-rank tensor pair matrix set X = {X (1) ,X(2) ,X (3) ,…,X (V+1)} perform subspace reconstruction and iteratively obtain the projection matrix Z corresponding to the multi-view data X = { Z (1) ,Z (2) ,Z (3) ,…,Z (V+1)}: s3-1: Introducing the Hilbert-Schmidt independence criterion to calculate the projection matrix Z (v) and Z (w) Dependencies between:

[0008] Where tr() represents the trace of the matrix and the superscript T represents the matrix transpose. , ,matrix , the element in row i and column j , is the identity matrix.

[0009] s3-2: Establish a multi-view clustering method based on the Hilbert-Schmidt independence criterion and low-rank tensor objective function:

[0010] in, denote the nuclear norm and 21 norm respectively, and λ1 and λ2 are regularization parameters.

[0011] For the convenience of solving, use G instead of Z to obtain the following function:

[0012] s3-3: Using the augmented Lagrange multiplier Y (v) , W solves the objective function:

[0013] in, represents the F norm, m and r is the penalty parameter.

[0014] s3-4: Process the objective function and obtain the following iterative formula:

[0015]

[0016]

[0017] in , Represents the j-th column element of Q.

[0018] s3-5: Yes Perform singular value decomposition to obtain the left singular vector , are the singular values O and right singular vectors , iteratively solve G:

[0019]

[0020] in, ,constant , used to accelerate convergence.

[0021] Step S4: The iterative projection matrix Z (v) The sum is used as the input of the clustering algorithm to achieve the final clustering.

[0022] Preferably, the clustering algorithm is spectral clustering or K-means clustering.

[0023] The present invention has the following beneficial effects: Compared with traditional multi-view clustering methods, the multi-view subspace clustering method of the present invention combines the Hilbert-Schmidt independence criterion and the low-rank tensor, which fully utilizes the diversity and consistency of multi-view data information. It not only realizes data comparison within the view, but also further supplements the data comparison information between different views. While retaining more available information, the Hilbert-Schmidt independence criterion can be used to measure the degree of dependence between data, remove redundant information, and improve clustering performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Flowchart of the multi-view subspace clustering method for joint independence criterion and low-rank tensor. DETAILED DESCRIPTION

[0025] The present invention will be further explained below with reference to the accompanying drawings; A multi-view subspace clustering method that combines the independence criterion and low-rank tensor. Based on the multi-view clustering based on low-rank tensor, the Hilbert-Schmidt independence criterion is introduced to measure the degree of dependence between data and realize the subspace reconstruction of data. The specific steps are as follows: Step S1: Download the bbcsport2view dataset as the source of multi-view data. The bbcsport2view dataset contains 544 sports news articles corresponding to five categories: athletics, cricket, football, rugby, and tennis. Convert the original data into the Mat format recognized by MATLAB and obtain the multi-view data matrix set X = {X(1) ,X (2) ,X (3) ,…,X (V)},in represents the vth language version of a sports news article, v=1,2,…V, and n=544 is the number of samples.

[0026] Step S2: Superimpose the multi-view data X to obtain the full data view X (V+1) , and added to the multi-view data X, X={X (1) ,X (2) ,X (3) ,…,X (V+1)}.

[0027] Step S3: Figure 1 As shown, the joint low-rank tensor pair matrix set X={X (1) ,X (2) ,X (3) ,…,X (V+1)} Perform subspace reconstruction to obtain the projection matrix Z corresponding to the multi-view data X = { Z (1) ,Z (2) ,Z (3) ,…,Z (V+1)}: s3-1: Introducing the Hilbert-Schmidt independence criterion to calculate the projection matrix Z (v) and Z (w) Dependencies between:

[0028] Where tr() represents the trace of the matrix and the superscript T represents the matrix transpose. , ,matrix , the element in row i and column j , is the identity matrix.

[0029] s3-2: Establish a multi-view clustering method based on the Hilbert-Schmidt independence criterion and low-rank tensor objective function:

[0030] in, denote the nuclear norm and 21 norm respectively, and λ1 and λ2 are regularization parameters.

[0031] Using G instead of Z gives the following function:

[0032] s3-3: Using the augmented Lagrange multiplier Y (v), W solves the objective function:

[0033] in, represents the F norm, m and r is the penalty parameter.

[0034] s3-4: Process the objective function and obtain the iterative formula: s3-4-1: Extract items related to Z:

[0035] Taking the derivative with respect to Z and setting it equal to 0:

[0036] in , after separation, Z (v) The iterative formula is:

[0037] s3-4-2: Extract items related to E:

[0038] therefore:

[0039] in , represents the j-th column of Q.

[0040] s3-4-3: Extract items related to G:

[0041] right Perform singular value decomposition to obtain the left singular vector , are the singular values O and right singular vectors ,but:

[0042]

[0043] in, .

[0044] s3-4-4: Update Lagrange multipliers:

[0045] Set to 2 to accelerate convergence.

[0046] Step S4: The iterative projection matrix Z(v) The sum of the two sets of data is used as the input for spectral clustering to achieve the final clustering. Clustering results show that this method achieves a clustering accuracy (ACC) of 99.8% on the BBC Sport 2 View dataset, a significant improvement of 20% to 40% over traditional multi-view clustering. This indicates that this method can accurately classify data in clustering domains such as text or images and determine the category to which the data belongs.

Claims

1. A multi-view subspace clustering method combining independence criteria and low-rank tensor, characterized by: The specific steps include: Step S1: Get the multi-view data X = {X (1) ,X (2) ,X (3) ,…,X (V) }, Represents the v-th view of the object, v=1,2,…V, V represents the number of views; Step S2: Overlay the multi-view data to obtain the full data view X (V+1) ; Step S3: Joint low-rank tensor pair matrix set X = {X (1) ,X (2) ,X (3) ,…,X (V+1) } perform subspace reconstruction and iteratively obtain the projection matrix Z corresponding to the multi-view data X = { Z (1) ,Z (2) ,Z (3) ,…,Z (V+1) }: s3-1: Introducing the Hilbert-Schmidt independence criterion to calculate the projection matrix Z (v) and Z (w) Dependencies between ; s3-2: Establish a multi-view clustering method based on the Hilbert-Schmidt independence criterion and low-rank tensor objective function: in, denote the nuclear norm and 21 norm respectively, λ1 and λ2 are regularization parameters; s3-3: Solve the objective function and iterate to obtain the projection matrix Z (v) ; Step S4: The iterative projection matrix Z (v) The sum is used as the input of the clustering algorithm to achieve multi-view subspace clustering.

2. The multi-view subspace clustering method combining the independence criterion and the low-rank tensor as claimed in claim 1, characterized in that: Projection matrix Z (v) and Z (w) The dependencies are: Where tr() represents the trace of the matrix and the superscript T represents the matrix transpose; , ,matrix , the element in row i and column j , is the identity matrix; n represents the number of samples of the multi-view data X.

3. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 1, characterized in that: Using G instead of Z gives the following objective function: Using the augmented Lagrange multiplier Y (v) , W solves the objective function: in, represents the F norm, μ and ρ is the penalty parameter.

4. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 3, characterized in that: Extract the Z (v) 、E (v) , G related items, update the Lagrange multiplier, and update Z in turn (v) 、E (v) , G, and make Z approach G continuously.

5. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 4, characterized in that: Extraction and Z (v) Related items: Taking the derivative with respect to Z and setting it equal to 0: in , after separation, Z (v) The iterative formula is: 。 6. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 4, characterized in that: Extraction and E (v) Related items: therefore: in , represents the j-th column of Q.

7. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 4, characterized in that: Extract terms related to G: right Perform singular value decomposition to obtain the left singular vector , are the singular values O and right singular vectors ,but: in, .

8. The multi-view subspace clustering method combining independence criterion and low-rank tensor as claimed in claim 1, characterized in that: The clustering algorithm is spectral clustering or K-means clustering.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 8.

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