Multi-view clustering method and system for adaptively fusing similar images

Abstract

The invention discloses a multi-view clustering method for adaptively fusing similar graphs, which comprises the following steps of: performing non-negative matrix factorization on an original data matrix, and introducing the constraint of the similarity of data points on a non-negative embedded matrix by utilizing the consistency and complementarity of each view of data to obtain a common matrix capable of directly outputting a clustering result; and the clustering result is evaluated by using four evaluation indexes, namely accuracy, an adjustment Lam coefficient, a purity index and normalized mutual information. On the basis of non-negative matrix factorization, the weight of each view is adaptively adjusted according to the contribution of the common view, the difficulty of hyper-parameter determination is avoided, meanwhile, the constraint of the similarity graph on the non-negative matrix is introduced, and the non-negative matrix factorization of the common regularization consistent constraint view based on the center is utilized, so that the non-negative matrix factorization is realized. And finally, a common matrix containing clustering result information is obtained, and the clustering performance is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of cluster analysis, and in particular to a multi-view clustering method and system for adaptively fusion similarity graphs. Background Art

[0002] Clustering is a powerful data analysis tool that can discover the inherent structure and regularity of data. It has a wide range of applications in data mining, pattern recognition, image analysis, information retrieval, and bioinformatics. For example, in the field of data mining, clustering is used for user behavior analysis, product positioning, market segmentation, etc.; in the field of image processing, clustering is used for image segmentation, target detection, image compression, etc.; in the field of natural language processing, clustering is used for text clustering and topic models, such as news classification, sentiment analysis, and text recommendation; in the field of bioinformatics, clustering is used for clustering and classification of gene expression data, which can be used for gene function prediction, new drug development, etc. Clustering algorithms are widely used in various fields and can help solve the classification and analysis problems of large-scale data and improve the efficiency and accuracy of data processing.

[0003] Traditional clustering algorithms are mainly used for single-view data. Although they perform well, they are still insufficient in processing multi-view data. Multi-view data is consistent and complementary: since different views of multi-view data describe the same object, some of the underlying features learned by different views are shared; at the same time, each view also contains information that is unique to the view and not available in other views. This specific information can correctly divide certain samples. Therefore, clustering by rationally utilizing the characteristics of multi-view data can achieve better results than single-view data.

[0004] Matrix decomposition is widely used in data clustering due to its powerful data dimension reduction and feature extraction capabilities. Researchers hope to obtain a low-dimensional representation of the data through matrix decomposition to facilitate subsequent clustering operations. The multi-view clustering algorithm (MvNMF) with joint non-negative matrix factorization finds the potential common structure shared by multiple views by factorizing constraints, and then obtains the clustering results of multi-view data through methods such as k-means. Due to the effective use of the consistency and complementarity of multi-view data, this method achieves better clustering results than single view. Multi-view clustering method based on local manifold regularized concept decomposition (MvCC) Based on the joint non-negative matrix factorization multi-view clustering algorithm (MvNMF), it uses the principle of local consistency, maintains the local structural characteristics of the data well, and obtains high-quality low-dimensional representation, which is more conducive to subsequent clustering operations.

[0005] The above algorithms generally go through two steps to complete the clustering process. First, the common matrix is ​​obtained, and then the clustering algorithm such as Kmeans is run. Since the common matrix in the first step is to achieve the similarity metric design, a high-quality common matrix cannot be obtained. The multi-view spectral clustering algorithm (NESE) based on non-negative embedding and spectral embedding directly solves the final clustering indicator matrix without the need for subsequent clustering algorithms to process clustering. However, this algorithm does not fully integrate the similarity matrix learning and matrix decomposition of each view, ignores the co-regularization constraint of the view similarity matrix, and thus affects the clustering performance. Summary of the invention

[0006] The present invention discloses a multi-view clustering method of adaptively fused similarity graphs. The present invention is based on non-negative matrix decomposition. It not only adaptively adjusts the weight of each view according to its contribution to a common view, thus avoiding the difficulty of determining hyper-parameters, but also introduces constraints of the similarity graph on the non-negative matrix. It utilizes the center-based co-regularized consistent constraint view similarity matrix decomposition to obtain a common matrix containing clustering result information, thereby greatly improving the clustering performance.

[0007] The present invention provides a multi-view clustering method for adaptively fusion similarity graphs, comprising the following steps:

[0008] S1: Construct a similarity matrix based on a given data set.

[0009] The given dataset is represented as:

[0010]

[0011] in, Represents all samples Views;

[0012] Indicates The sample Views;

[0013] n represents the total number of samples in the data set;

[0014] m represents the number of views of each sample in the dataset;

[0015] Represents the first The dimension of the view;

[0016] The similarity matrix is ​​expressed as:

[0017]

[0018] in, Indicates Similarity matrix of views;

[0019] represents the i-th sample and the j-th sample Similarity measure of views;

[0020] S2: Construction degree matrix :

[0021]

[0022]

[0023]

[0024] in, represents the degree coefficient of the i-th sample;

[0025] represents the mean of the similarity measures of each view between the i-th sample and the j-th sample;

[0026] Constructing a consistent similarity embedding matrix ,in, The element in the i-th row and j-th column of is ;

[0027] Constructing a consistent embedding matrix ,in, , Is Before The eigenvector corresponding to the smallest eigenvalue is composed;

[0028] is the preset number of clusters;

[0029] Intermediate Matrix Calculated by the following formula:

[0030]

[0031] S3: Solve the objective function to obtain , the objective function is:

[0032]

[0033] in, Represents a public matrix containing information about the optimal clustering results;

[0034] Indicates The weight of each view;

[0035] express The i-th dimension column vector of ;

[0036] The clustering of the i-th sample is given by The maximum value of the i-th row is specified.

[0037] Preferably, the method for solving the objective function is to repeat the following steps in sequence for iteration until convergence or a preset maximum number of iterations is reached:

[0038] S3.1: Update using the following formula :

[0039]

[0040] S3.2: Update using the following formula :

[0041]

[0042] in, , Depend on The SVD decomposition of is obtained, namely: ;

[0043] S3.3: Solve the following problem to obtain The update formula of :

[0044]

[0045] S3.4: Updated by the following formula :

[0046] .

[0047] The present invention also provides a multi-view clustering system for adaptively fusion similarity graphs, comprising the following modules:

[0048] The first construction module: used to construct a similarity matrix based on a given data set.

[0049] The given dataset is represented as:

[0050]

[0051] in, Represents all samples Views;

[0052] Indicates The sample Views;

[0053] n represents the total number of samples in the data set;

[0054] m represents the number of views of each sample in the dataset;

[0055] Represents the first The dimension of the view;

[0056] The similarity matrix is ​​expressed as:

[0057]

[0058] in, Indicates Similarity matrix of views;

[0059] represents the i-th sample and the j-th sample Similarity measure of views;

[0060] The second construction module: used to construct the degree matrix :

[0061]

[0062]

[0063]

[0064] in, represents the degree coefficient of the i-th sample;

[0065] represents the mean of the similarity measures of each view between the i-th sample and the j-th sample;

[0066] Constructing a consistent similarity embedding matrix ,in, The element in the i-th row and j-th column of is ;

[0067] Constructing a consistent embedding matrix ,in, , Is Before The eigenvector corresponding to the smallest eigenvalue is composed;

[0068] is the preset number of clusters;

[0069] Intermediate Matrix Calculated by the following formula:

[0070]

[0071] Result output module: used to solve the objective function , the objective function is:

[0072]

[0073] in, Represents a public matrix containing information about the optimal clustering results;

[0074] Indicates The weight of each view;

[0075] express The i-th dimension column vector of ;

[0076] The clustering of the i-th sample is given by The maximum value of the i-th row is specified.

[0077] Preferably, the method for solving the objective function is to repeat the following steps in sequence for iteration until convergence or a preset maximum number of iterations is reached:

[0078] S3.1: Update using the following formula :

[0079]

[0080] S3.2: Update using the following formula :

[0081]

[0082] in, , Depend on The SVD decomposition of is obtained, namely: ;

[0083] S3.3: Solve the following problem to obtain The update formula of :

[0084]

[0085] S3.4: Updated by the following formula :

[0086] .

[0087] Beneficial effects:

[0088] The present invention provides a multi-view clustering method of adaptive fusion similarity graph, which performs non-negative matrix decomposition on the original data matrix, utilizes the consistency and complementarity of each view of the data, introduces the similarity of the data points to constrain the non-negative embedding matrix, and obtains a common matrix that can directly output the clustering results; the clustering results are evaluated using four evaluation indicators: accuracy, adjusted Rand coefficient, purity index, and normalized mutual information. Based on non-negative matrix decomposition, the present invention not only adaptively adjusts the weight of each view according to the contribution size to the public view, avoiding the difficulty of determining the hyperparameter, but also introduces the constraint of the similarity graph on the non-negative matrix, utilizes the center-based co-regularization consistent constraint view similarity matrix decomposition, and calculates the public matrix containing the clustering result information, which greatly improves the clustering performance. DETAILED DESCRIPTION

[0089] In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of them. 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.

[0090] A multi-view clustering method for adaptively fusion similarity graphs, comprising the following steps:

[0091] S1: Construct a similarity matrix based on a given data set.

[0092] The given dataset is represented as:

[0093]

[0094] in, Represents all samples Views;

[0095] Indicates The sample Views;

[0096] n represents the total number of samples in the data set;

[0097] m represents the number of views of each sample in the dataset;

[0098] Represents the first The dimension of the view;

[0099] The similarity matrix is ​​expressed as:

[0100]

[0101] in, Indicates Similarity matrix of views;

[0102] represents the i-th sample and the j-th sample Similarity measure of views;

[0103] S2: Construction degree matrix :

[0104]

[0105]

[0106]

[0107] in, represents the degree coefficient of the i-th sample;

[0108] represents the mean of the similarity measures of each view between the i-th sample and the j-th sample;

[0109] Constructing a consistent similarity embedding matrix ,in, The element in the i-th row and j-th column of is ;

[0110] Constructing a consistent embedding matrix ,in, , Is Before The eigenvector corresponding to the smallest eigenvalue is composed;

[0111] is the preset number of clusters;

[0112] Intermediate Matrix Calculated by the following formula:

[0113]

[0114] S3: Solve the objective function to obtain , the objective function is:

[0115]

[0116] in, Represents a public matrix containing information about the optimal clustering results;

[0117] Indicates The weight of each view;

[0118] express The i-th dimension column vector of ;

[0119] The clustering of the i-th sample is given by The maximum value of the i-th row is specified.

[0120] In this embodiment, the method for solving the objective function is to repeat the following steps in sequence to iterate until convergence or a preset maximum number of iterations is reached:

[0121] S3.1: Update using the following formula :

[0122]

[0123] Derivation process:

[0124] In the objective function, Removing irrelevant terms, we get the equivalent problem:

[0125]

[0126] Solving it yields:

[0127]

[0128] S3.2: Update using the following formula :

[0129]

[0130] in, , Depend on The SVD decomposition of is obtained, namely:

[0131] Derivation process:

[0132] In the objective function, Removing irrelevant terms, we get the equivalent problem:

[0133]

[0134] Using the properties of matrix trace , , ,have ,question Equivalent to ,right Perform SVD decomposition and finally get ;

[0135] S3.3: Solve the following problem to obtain The update formula of :

[0136]

[0137] Derivation process:

[0138] In the objective function, Removing irrelevant terms, we get the equivalent problem:

[0139]

[0140] Further simplification, we get the equivalent problem , using the Lagrange formula and KKT conditions, we can get The update formula of ;

[0141] S3.4: Updated by the following formula :

[0142]

[0143] Derivation process:

[0144] In the objective function, Removing irrelevant terms, we get the equivalent problem:

[0145]

[0146] Then get The update formula is:

[0147]

[0148] In order to better illustrate the beneficial effects of the present invention, a clustering test is performed on the image dataset 100leaves in the UCI repository. The 100leaves dataset contains 100 kinds of leaves, each of which contains 16 images, a total of 1600 images, and each image is described by three features: shape continuous descriptor, internal texture histogram, and fine-scale edge histogram. For each feature, a 64-dimensional vector description is given for each leaf sample.

[0149] The clustering results are evaluated by four evaluation indicators: accuracy, adjusted Rand coefficient, purity index, and normalized mutual information. The clustering results are run on the same data set HW with algorithms SK-means, MvCC, and NESE. The results are shown in Table 1:

[0150] Table 1 Comparison of clustering performance among SK-means, MvCC, NESE and the proposed method

[0151]

[0152] The experimental results show that the clustering effect of the present invention on multi-view data is obviously better than other methods.

[0153] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-view clustering method for adaptive fusion similarity graphs, characterized in that: The following steps are involved: S1: Construct a similarity matrix based on a given data set. The given dataset is represented as: ； in, Represents all samples Views; Indicates The sample Views; n represents the total number of samples in the data set; m represents the number of views for each sample in the dataset; Represents the first The dimension of the view; The similarity matrix is ​​expressed as: ； in, Indicates Similarity matrix of views; represents the i-th sample and the j-th sample Similarity measure of views; S2: Construction degree matrix : ；； ； ； in, represents the degree coefficient of the i-th sample; represents the mean of the similarity measures of each view between the i-th sample and the j-th sample; Constructing a consistent similarity embedding matrix ,in, The element in the i-th row and j-th column of is ; Constructing a consistent embedding matrix ,in, , Is Before The eigenvector corresponding to the smallest eigenvalue is composed; is the preset number of clusters; Intermediate Matrix Calculated by the following formula: ； S3: Solve the objective function to obtain , the objective function is: ； in, Represents a public matrix containing information about the optimal clustering results; Indicates The weight of each view; express The i-th dimension column vector of ; The clustering of the i-th sample is given by The maximum value of the i-th row is specified.

2. The multi-view clustering method of adaptive fusion similarity graph according to claim 1, characterized in that: The method for solving the objective function is to repeat the following steps in sequence until convergence or the preset maximum number of iterations is reached: S3.1: Update using the following formula : ； S3.2: Update using the following formula : ； in, , Depend on The SVD decomposition of is obtained, namely: ; S3.3: Solve the following problem to obtain The update formula of : ； S3.4: Updated by the following formula : 。 3. A multi-view clustering system with adaptive fusion similarity graphs, characterized in that: Includes the following modules: The first construction module: used to construct a similarity matrix based on a given data set. The given dataset is represented as: ； in, Represents all samples Views; Indicates The sample Views; n represents the total number of samples in the data set; m represents the number of views for each sample in the dataset; Represents the first The dimension of the view; The similarity matrix is ​​expressed as: ； in, Indicates Similarity matrix of views; represents the i-th sample and the j-th sample Similarity measure of views; The second construction module: used to construct the degree matrix : ； ； ； in, represents the degree coefficient of the i-th sample; represents the mean of the similarity measures of each view between the i-th sample and the j-th sample; Constructing a consistent similarity embedding matrix ,in, The element in the i-th row and j-th column of is ; Constructing a consistent embedding matrix ,in, , Is Before The eigenvector corresponding to the smallest eigenvalue is composed; is the preset number of clusters; Intermediate Matrix Calculated by the following formula: ； Result output module: used to solve the objective function , the objective function is: ； in, Represents a public matrix containing information about the optimal clustering results; Indicates The weight of each view; express The i-th dimension column vector of ; The clustering of the i-th sample is given by The maximum value of the i-th row is specified.

4. The multi-view clustering system of adaptive fusion similarity graph according to claim 3, characterized in that: The method for solving the objective function is to repeat the following steps in sequence until convergence or the preset maximum number of iterations is reached: S3.1: Update using the following formula : ； S3.2: Update using the following formula : ； in, , Depend on The SVD decomposition of is obtained, namely: ; S3.3: Solve the following problem to obtain The update formula of : ； S3.4: Updated by the following formula : 。

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