Multi-view subspace clustering method based on diversity graph fusion
By preprocessing and self-expression learning of multi-view data, combining the consistency and diversity regularization terms of multi-views, and fusing the view similarity matrix, the problem of low performance of multi-view subspace clustering method is solved, and high-accurate clustering results are achieved.
Patent Information
- Application Number
- CN202311207074.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-09-18
- Publication Date
- 2025-08-15
- Estimated Expiration
- 2043-09-18
AI Technical Summary
The existing multi-view subspace clustering method has low clustering performance and it is difficult to obtain the best clustering effect.
By obtaining multi-view data and pre-processing, adding regularization terms for the consistency and diversity of multi-views, introducing self-expression learning, mining the intrinsic structure of multi-view data, and obtaining a high reliability and robust similarity matrix through low-rank and sparse constraints, and then using induced self-weighting to fuse the view similarity matrix to form the ultimate consistent similarity matrix as the input of the spectral clustering algorithm.
The accuracy and robustness of clustering are improved, and high-quality clustering effect is obtained, with an accuracy rate of 90%.
Smart Images
Figure CN117235562B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of machine learning and data mining, and in particular to a multi-view subspace clustering method based on diversity graph fusion. Background Art
[0002] Multi-view data refers to data from different sources or sources, described in different feature spaces. For the same object or thing, different data views may present unique characteristic information. This information may complement or contradict each other, but all provide a more comprehensive and accurate description of the object or thing. For example, a news article or text may be presented in different languages, such as Chinese, English, and Spanish. A website may be presented using video, audio, and text. A car may be viewed from different angles, such as the front, side, and back. For another example, in the field of face recognition, a person's facial image can be represented as different views, such as grayscale, depth, and infrared. Each view can provide different information to help identify and verify the person's identity. Similarly, in the field of social network analysis, user information can be collected and described from multiple perspectives, such as friend lists, posting histories, and user profiles. This information can be combined to form multi-view data for a user.
[0003] Multi-view clustering refers to clustering samples using different data views or data sources. Multi-view clustering is usually used to solve the problems of incomplete data and high data dimensionality in single-view clustering. Its purpose is to obtain the properties and characteristics of samples from different angles and multiple data sources, explore the potential structure of multi-view data, and improve the accuracy and robustness of clustering. Common multi-view clustering methods can be divided into four categories: (1) multi-view clustering based on co-training; (2) multi-view clustering based on multiple kernel learning; (3) multi-view clustering based on graph learning; and (4) multi-view clustering based on subspace learning. The main idea of these multi-view clustering methods is to fuse the information of different views, associate multiple views to form a new view, and then perform cluster analysis on the new view. Multi-view clustering is an important technology in the fields of data mining, image processing, natural language processing, etc., and is widely used in tasks such as text classification, image recognition, and protein function prediction.
[0004] Multi-view subspace clustering (MVSC) is a clustering method that integrates data from multiple views. In the real world, data from multiple views can be obtained from different sensors, different algorithms, or different feature extractors. However, each view may only provide one aspect of the data, so clustering data using only a single view may lead to information loss and inaccurate results. Compared with traditional single-view clustering methods, MVSC can better handle data with complex structures and is more robust and reliable. MVSC leverages the strengths of multiple views, combining them to better represent the data, and preserves the subspace structure within each view to better identify and distinguish data. Because MVSC can provide more comprehensive and accurate clustering results, it has been widely used in many fields, such as computer vision, bioinformatics, and social network analysis.
[0005] However, the existing multi-view subspace clustering methods have low clustering performance and it is difficult to obtain the best clustering effect. Summary of the Invention
[0006] The purpose of the present invention is to provide a multi-view subspace clustering method based on diversity graph fusion, which can improve clustering performance and obtain the best clustering effect.
[0007] To achieve the above object, the present invention provides a multi-view subspace clustering method based on diversity graph fusion, which includes:
[0008] Step 1: Obtain multi-view data and preprocess;
[0009] Step 2: By adding regularization terms for multi-view consistency and diversity, self-expression learning is introduced to explore the intrinsic structure of multi-view data. Low-rank and sparsity constraints are introduced to the consistent expression matrix to obtain a highly reliable and robust similarity matrix.
[0010] Step 3: Use the induced self-weighting method to fuse the view similarity matrix obtained in step 2 to form a final consistent similarity matrix, which serves as the input of the spectral clustering algorithm and outputs the clustering result.
[0011] Preferably, the pre-processing in step 1 includes:
[0012] Step 1.1: Feature extraction: use multiple feature extraction methods to obtain different features for the same batch of multi-view data;
[0013] Step 1.2: Data cleaning: Spline interpolation is used to interpolate the missing parts of the multi-view data, and the average method is used to replace the extremely large or extremely small outliers in the multi-view data.
[0014] Preferably, the similarity matrix corresponding to each view data in the multi-view data obtained in step 2 is:
[0015]
[0016] in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain.
[0017] Preferably, the input and output clustering result of the spectral clustering algorithm in step 3 is:
[0018]
[0019] Preferably, in step 3, according to the Laplace matrix properties, the number of connection points k of the graph U and its Laplace matrix The number of repeated roots of the zero eigenvalues of is the same; because It has the properties of a semi-positive matrix, so its eigenvalue ;if , then the fusion graph U has corresponding k connection points; according to Ky Fan's theorem, the objective function of spectral clustering is obtained:
[0020]
[0021] in, is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix;
[0022] The formula Substitute into the formula In the formula, we get a new expression, that is, Translates to:
[0023]
[0024] in, and is the regularization parameter.
[0025] Preferably, in step 3, by changing the formula and formula Integrating them together, we get the objective function of the diversity-based multi-view fusion subspace clustering method:
[0026]
[0027] in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain; is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix, and is the regularization parameter; the latter two terms use the induced self-weighting method to fuse the previously obtained view similarity matrices to form the final consistent similarity matrix;
[0028] Because the formula There are multiple variables and multiple constraints in the problem. Only one of the variables is solved, and then the problem is solved alternately until the optimal solution for all variables is obtained.
[0029] First, the formula Optimize, fix F1, and solve ,formula Converted into the following form:
[0030]
[0031] make As auxiliary variables, and into the formula In the expression,
[0032]
[0033] Introduce Lagrangian expression to solve the formula , we can get the following expression:
[0034]
[0035] right Taking the derivative and setting it to 0, we get The expression is as follows:
[0036]
[0037] renew The specific expression is as follows:
[0038]
[0039] renew The specific expression is as follows:
[0040]
[0041] renew The specific expression is as follows:
[0042]
[0043] renew The specific expression is as follows:
[0044]
[0045] In the above obtained Afterwards, the dual variables are updated according to the following expressions:
[0046]
[0047] in, is the maximum value of the multiplier coefficient, is the positive coefficient of the multiplier;
[0048] fixed , solve , formula Converted to the following form:
[0049]
[0050] in, It is The degree matrix of the view, It is The adjacency matrix of the view; the formula Converted into the following expression:
[0051]
[0052] Define the matrix ,formula Rewritten as:
[0053]
[0054] formula The corresponding solution is the characteristic matrix Before The eigenvector corresponding to the minimum eigenvalue is calculated by repeating formula (9) to formula (17) 200 times and stopping to obtain the consistency expression matrix. Then, the formula Optimize, fix and ,renew ,in The expression is as follows:
[0055]
[0056] in, It is a very small number used to prevent the denominator from being 0;
[0057] fixed and ,renew ,because yes Function formula Translates to:
[0058]
[0059] Formula Convert it to:
[0060]
[0061] definition ,formula Translates to:
[0062]
[0063] Formula Taking the derivative and making it equal to zero gives the following expression:
[0064]
[0065] fixed and ,renew , the formula Converted into the following expression:
[0066]
[0067] The optimal solution is given by of The corresponding eigenvalues The smallest eigenvectors are composed; repeat the calculation of formula (18) to formula (23) 200 times and stop.
[0068] According to the above technical solution, the present invention first obtains multi-view data and pre-processes the multi-view data. Secondly, by adding regularization terms for the consistency and diversity of multiple views, self-expression learning is introduced to mine the intrinsic structure of the multi-view data, and low-rank and sparse constraints are introduced to the consistency expression matrix, thereby obtaining a highly reliable and robust similarity matrix. Then, the previously obtained view similarity matrix is fused to form a final consistent similarity matrix using an induced self-weighting method. Finally, the fusion graph is used as the input of the spectral clustering algorithm and the clustering result is output. The method provided by the present invention not only generates a consistent similarity matrix but also reveals the potential clustering structure of the data, improves the accuracy and robustness of clustering, and obtains a high-quality clustering effect.
[0069] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS
[0070] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the following detailed description, they are used to explain the present invention but do not constitute a limitation of the present invention. In the accompanying drawings:
[0071] Figure 1 The present invention provides a flowchart of a multi-view subspace clustering method based on diversity graph fusion. DETAILED DESCRIPTION
[0072] The following describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.
[0073] See also Figure 1 The present invention provides a multi-view subspace clustering method based on diversity graph fusion, the method comprising:
[0074] Step 1: Obtain multi-view data and preprocess;
[0075] Step 2: By adding regularization terms for multi-view consistency and diversity, self-expression learning is introduced to explore the intrinsic structure of multi-view data. Low-rank and sparsity constraints are introduced to the consistent expression matrix to obtain a highly reliable and robust similarity matrix.
[0076] Step 3: Use the induced self-weighting method to fuse the view similarity matrix obtained in step 2 to form a final consistent similarity matrix, which serves as the input of the spectral clustering algorithm and outputs the clustering result.
[0077] In one embodiment, the multi-view data acquired in step 1 includes 400 images of 40 different individuals, spanning 40 categories, created by AT&T Labs at the University of Cambridge, UK. Each image is captured with varying lighting, time of day, facial expressions, and details. The experiment primarily uses three types of features: intensity, LBP, and Gabor features to construct a three-view dataset.
[0078] Specifically, the preprocessing in step 1 includes:
[0079] Step 1.1: Feature extraction: use multiple feature extraction methods to obtain different features for the same batch of multi-view data;
[0080] Step 1.2: Data cleaning: Spline interpolation is used to interpolate the missing parts of the multi-view data, and the average method is used to replace the extremely large or extremely small outliers in the multi-view data.
[0081] The similarity matrix corresponding to each view data in the multi-view data obtained in step 2 is:
[0082]
[0083] in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain.
[0084] The input of the spectral clustering algorithm in step 3 and the output clustering result are:
[0085]
[0086] In step 3, according to the Laplace matrix properties, the number of connection points k of the graph U and its Laplace matrix The number of repeated roots of the zero eigenvalues of is the same; because It has the properties of a semi-positive matrix, so its eigenvalue ;if , then the fusion graph U has corresponding k connection points; according to Ky Fan's theorem, the objective function of spectral clustering is obtained:
[0087]
[0088] in, is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix;
[0089] The formula Substitute into the formula In the formula, we get a new expression. Translates to:
[0090]
[0091] in, and is the regularization parameter.
[0092] In step 3, by changing the formula and formula Integrating them together, we get the objective function of the diversity-based multi-view fusion subspace clustering method:
[0093]
[0094] in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain; is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix, and is the regularization parameter; the latter two terms use the induced self-weighting method to fuse the previously obtained view similarity matrices to form the final consistent similarity matrix;
[0095] Because the formula There are multiple variables and multiple constraints in the problem. Only one of the variables is solved, and then the problem is solved alternately until the optimal solution for all variables is obtained.
[0096] First, the formula Optimize, fix F1, and solve ,formula Converted into the following form:
[0097]
[0098] make As auxiliary variables, and into the formula In the expression,
[0099]
[0100] Introduce Lagrangian expression to solve the formula , we can get the following expression:
[0101]
[0102] right Taking the derivative and setting it to 0, we get The expression is as follows:
[0103]
[0104] renew The specific expression is as follows:
[0105]
[0106] renew The specific expression is as follows:
[0107]
[0108] renew The specific expression is as follows:
[0109]
[0110] renew The specific expression is as follows:
[0111]
[0112] In the above obtained Afterwards, the dual variables are updated according to the following expressions:
[0113]
[0114] in, is the maximum value of the multiplier coefficient, is the positive coefficient of the multiplier;
[0115] fixed , solve , formula Converted to the following form:
[0116]
[0117] in, It is The degree matrix of the view, It is The adjacency matrix of the view; the formula Converted into the following expression:
[0118]
[0119] Define the matrix ,formula Rewritten as:
[0120]
[0121] formula The corresponding solution is the characteristic matrix Before The eigenvector corresponding to the minimum eigenvalue is calculated by repeating formula (9) to formula (17) 200 times and stopping to obtain the consistency expression matrix. Then, the formula Optimize, fix and ,renew ,in The expression is as follows:
[0122]
[0123] in, It is a very small number used to prevent the denominator from being 0;
[0124] fixed and ,renew ,because yes Function formula Translates to:
[0125]
[0126] Formula Convert it to:
[0127]
[0128] definition ,formula Translates to:
[0129]
[0130] Formula Taking the derivative and making it equal to zero gives the following expression:
[0131]
[0132] fixed and ,renew , the formula Converted into the following expression:
[0133]
[0134] The optimal solution is given by of The corresponding eigenvalues The smallest eigenvectors are composed; repeat the calculation of formula (18) to formula (23) 200 times and stop.
[0135] In addition, the ORL dataset can be used to evaluate the method, and the clustering results can be compared with the true categories of the samples. The accuracy of the present invention is 90%, indicating that the present invention has high accuracy.
[0136] In summary, the method provided by the present invention first preprocesses the acquired multi-view data, and then introduces self-expression learning to explore the intrinsic structure of the multi-view data by adding regularization terms for the consistency and diversity of the multi-views, and introduces low-rank and sparse constraints on the consistency expression matrix, thereby obtaining a highly reliable and robust similarity matrix; then, the previously obtained view similarity matrices are fused in an induced self-weighted manner to form a final consistent similarity matrix; finally, the fused graph is used as the input of the spectral clustering algorithm to reveal the clustering results of the data and obtain a high-quality clustering effect.
[0137] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the scope of protection of the present invention.
[0138] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any appropriate manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.
[0139] In addition, the various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.
Claims
1. A multi-view subspace clustering method based on diversity graph fusion, characterized in that: The method comprises: Step 1: Obtain multi-view data and preprocess; Step 2: By adding regularization terms for multi-view consistency and diversity, self-expression learning is introduced to explore the intrinsic structure of multi-view data. Low-rank and sparsity constraints are introduced to the consistent expression matrix to obtain a highly reliable and robust similarity matrix. Step 3: Use the induced self-weighting method to fuse the view similarity matrices obtained in step 2 to form a final consistent similarity matrix, which serves as the input of the spectral clustering algorithm and outputs the clustering result; The multi-view data obtained in step 1 includes 400 images of 40 different people, spanning 40 categories, created by AT&T Labs at the University of Cambridge, UK. Each person has ten different images. Each photo is shot with varying lighting, time of day, facial expressions, and details. The experiment primarily uses intensity, LBP, and Gabor features to construct a three-view dataset. The similarity matrix corresponding to each view data in the multi-view data obtained in step 2 is: in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain.
2. The multi-view subspace clustering method based on diversity graph fusion according to claim 1, characterized in that: The preprocessing in step 1 includes: Step 1.1: Feature extraction: use multiple feature extraction methods to obtain different features for the same batch of multi-view data; Step 1.2: Data cleaning: Spline interpolation is used to interpolate the missing parts of the multi-view data, and the average method is used to replace the extremely large or extremely small outliers in the multi-view data.
3. The multi-view subspace clustering method based on diversity graph fusion according to claim 1, characterized in that: The input of the spectral clustering algorithm in step 3 and the output clustering result are:
4. The multi-view subspace clustering method based on diversity graph fusion according to claim 3, characterized in that: In step 3, according to the Laplace matrix properties, the number of connection points k of the graph U and its Laplace matrix The number of repeated roots of the zero eigenvalues of is the same; because It has the properties of a semi-positive matrix, so its eigenvalue ;if , then the fusion graph U has corresponding k connection points; according to Ky Fan's theorem, the objective function of spectral clustering is obtained: in, is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix; The formula Substitute into the formula In the formula, we get a new expression. Translates to: in, and is the regularization parameter.
5. The multi-view subspace clustering method based on diversity graph fusion according to claim 4, characterized in that: In step 3, by changing the formula and formula Integrating them together, we get the objective function of the diversity-based multi-view fusion subspace clustering method: in, and are the parameters of the low-rank constraint and the sparse constraint of the consistency matrix respectively; and is the balance parameter; the third term in the objective function is the diversity regularization term that uses the position-based diversity calculation method, and the fourth term is the consistency regularization term introduced by the consistency indicator matrix To constrain; is the cluster indicator matrix, is the Laplace matrix, represents the rank of the matrix, and is the regularization parameter; the latter two terms use the induced self-weighting method to fuse the previously obtained view similarity matrices to form the final consistent similarity matrix; Because the formula There are multiple variables and multiple constraints in the problem. Only one of the variables is solved, and then the problem is solved alternately until the optimal solution for all variables is obtained. First, the formula Optimize, fix F1, and solve ,formula Converted into the following form: make As auxiliary variables, and into the formula In the expression, Introduce Lagrangian expression to solve the formula , we can get the following expression: right Taking the derivative and setting it to 0, we get The expression is as follows: renew The specific expression is as follows: renew The specific expression is as follows: renew The specific expression is as follows: renew The specific expression is as follows: In the above obtained Afterwards, the dual variables are updated according to the following expressions: in, is the maximum value of the multiplier coefficient, is the positive coefficient of the multiplier; fixed , solve , formula Converted to the following form: in, It is The degree matrix of the view, It is The adjacency matrix of the view; the formula Converted into the following expression: Define the matrix ,formula Rewritten as: formula The corresponding solution is the characteristic matrix Before The eigenvector corresponding to the minimum eigenvalue is calculated by repeating formula (9) to formula (17) 200 times and stopping to obtain the consistency expression matrix. Then, the formula Optimize, fix and ,renew ,in The expression is as follows: in, It is a very small number used to prevent the denominator from being 0; fixed and ,renew ,because yes Function formula Translates to: Formula Convert it to: definition ,formula Translates to: Formula Taking the derivative and making it equal to zero gives the following expression: fixed and ,renew , the formula Converted into the following expression: The optimal solution is given by of The corresponding eigenvalues The smallest eigenvectors are composed; repeat the calculation of formula (18) to formula (23) 200 times and stop.