CN109002854A - Based on hidden expression and adaptive multiple view Subspace clustering method - Google Patents

Abstract

The invention proposes a kind of based on hidden expression and adaptive multiple view Subspace clustering method, it mainly solves the problems, such as that cluster accuracy rate present in multiple view clustering method is low, realizes step are as follows: (1) obtain the multiple view data matrix of raw data set；(2) Laplacian Matrix of multiple view data matrix is calculated；(3) objective function based on hidden expression and adaptive multiple view subspace clustering is constructed；(4) objective function is optimized；(5) variable in the objective function after optimization is initialized；(6) alternating iteration is carried out to the variable in the objective function after optimization；(7) value of the multiple view in the objective function after calculation optimization from expression coefficient matrix；(8) raw data set is clustered.The present invention makes full use of the information of multiple views, effectively increases the accuracy rate of multiple view cluster, can be used for image segmentation, business analysis, the fields such as biological classification using hidden expression and adaptively.

Description

Multi-view Subspace Clustering Method Based on Hidden Representation and Adaptation

technical field

The invention belongs to the technical field of computer vision and pattern recognition, and relates to a multi-view subspace clustering method, in particular to a multi-view subspace clustering method based on implicit representation and self-adaptation, which can be used for image segmentation, business analysis and biological Classification etc.

Background technique

In recent years, due to the rapid development of computer information technology, while emerging technologies are changing human society, there is also an explosive growth of data, so data acquisition and analysis have become more and more important. Data mining is a process of discovering hidden information and extracting knowledge from a large amount of data. As an important data mining method, clustering is the process of dividing a collection of physical or abstract objects into multiple clusters composed of similar objects, so that objects in the same cluster have high similarity, and objects in different clusters have higher similarity. Objects have low similarity.

Traditional datasets are represented by a single feature, called single-view datasets. However, the information contained in the original data set in the single-view data set is not complete. To solve this problem, the existing technology enables the data set to be represented by multiple features, which is called a multi-view data set. For example, the same picture can be described by features such as SIFT and HOG; for the same news report, it can be expressed in different languages; for web page data, text and link information can be used as two different views. If the traditional clustering method is used to cluster this kind of data set, the clustering effect is often not ideal because the information of multiple views cannot be fully utilized. Therefore, multi-view clustering is proposed. Multi-view clustering can often get more accurate clustering results by utilizing the consistency and difference of multiple views.

Multi-view clustering algorithms can be divided into two categories: multi-view clustering algorithms based on K-means and multi-view clustering algorithms based on spectral clustering. Multi-view clustering algorithms based on K-means, because the selection of the initial point is random , and the clustering result has a relatively large correlation with the selection of the initial point, so the clustering result of this type of method is unstable.

The multi-view clustering algorithm based on spectral clustering can often obtain relatively stable clustering results because it can maintain the local geometric structure between the samples of the data set, so many multi-view clustering algorithms based on spectral clustering have emerged.

Since the samples in the data set are distributed in a specific low-dimensional subspace, based on this fact, many Subspace Clustering (SC) algorithms have emerged in recent years. Subspace clustering is one of the spectral clustering algorithms. part. This type of algorithm takes advantage of the property that any sample can be linearly combined with the samples in the subspace where the sample is located, and decomposes the data matrix into the product of the data matrix and the view self-expression coefficient matrix. Then the clustering result is obtained by using the self-expression coefficient matrix of the view. Due to the good interpretability and clear physical meaning of the view self-representation coefficient matrix, subspace clustering has become a basic tool for data clustering, and has a wide range of applications in single-view clustering and multi-view clustering.

For example, Hongchang Gao, Feiping Nie, Xuelong Li and Heng Huang published an article titled "Multi-View Subspace Clustering" in the IEEE conference on Computer Vision and Pattern Recognition in 2015, disclosing a multi-view subspace clustering Class method, this method decomposes each view matrix of the multi-view dataset to obtain the view self-expression coefficient matrix corresponding to each view matrix, in order to obtain consistent clustering results, this method uses each view self-representation coefficient matrix Construct the similarity matrix of the original data set, and use the method of spectral clustering to obtain the clustering results of the original data set. The difference between the product of the view data matrix and the self-expression coefficient matrix corresponding to the view is used as the noise data matrix, and then the noise data matrix is constrained, but this method can only remove specific types of noise data, and does not apply to general types of noise data It is robust, so Changqing Zhang, Qinghua Hu, Huazhu Fu and Pengfei Zhu et al. published an article called "Latent Multi-viewSubspace Clustering" in the 2017 IEEEconference onComputer Vision and Pattern Recognition, disclosing a hidden Multi-view subspace clustering method, in order to reduce the impact of noise data contained in the original data set on the accuracy of the clustering results of the original data set, this method assumes that all views of the original data set come from the same representation, called multi-view Implicit representation, each view matrix is obtained by multiplying the multi-view implicit representation and the base matrix corresponding to each view, the multi-view implicit representation is a consistent representation of an original data set obtained after the multi-view matrix is denoised, While obtaining the multi-view latent representation, the method enables the multi-view latent representation to be self-represented, thereby obtaining the self-representation coefficient matrix of the multi-view dataset, and then using spectral clustering to obtain consistent clustering results. However, this method regards the amount of information contained in each view as the same, but in fact, the amount of information contained in each view of the original dataset is different. This method ignores this fact and does not take into account the multi-view The implicit representation should preserve the local geometric structure within each view, which affects the accuracy of clustering results on the original dataset.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and propose a multi-view subspace clustering method based on implicit representation and self-adaptation, which is used to improve the accuracy of multi-view data set clustering.

The technical idea of the present invention is to learn the multi-view latent representation of the multi-view data set in an adaptive manner, while obtaining the multi-view latent representation, use graph regularization to make the multi-view latent representation maintain the local geometric structure, and perform matrix decomposition on multi-view implicit representation to obtain multi-view self-expression coefficient matrix, and use spectral clustering to obtain clustering results. The implementation steps are as follows:

(1) Obtain the multi-view data matrix of the original data set

Extract different types of feature data from multiple images contained in the original data set, the same feature data form a view matrix, and multiple view matrices form the multi-view data matrix of the original data set Wherein, X ^(v) represents the vth view matrix, v=1, 2,..., m, m represents the number of view matrices, m≥2;

(2) Calculate the multi-view data matrix The Laplacian matrix

(3) Construct the objective function J of multi-view subspace clustering based on implicit representation and self-adaptation:

(3a) will Decomposed into multi-view implicit representation matrix H and multi-view base matrix Set the constraint of the base matrix P ^(v) of X ^(v) to be O, O means P ^(v) P ^(v)T = I, will and and the product of H as the error reconstruction term Wherein, I represents the identity matrix, and ( ) ^T represents the transposition of the matrix;

(3b) calculation measure of Assume The adaptive weight of is Yes The weight parameter of , where, Indicates the square of the matrix F norm, γ indicates the adjustment parameter, γ≥0,

(3c) Decompose the multi-view implicit representation matrix H into a multi-view implicit representation matrix H and a multi-view self-representation coefficient matrix Z, and use the difference between H and the product of H and Z as the error reconstruction item E _r , E _r =H-HZ , and calculate the measure of E _r ||E _r || _2,1 , let the weight of ||E _{r || 2,1} be λ ₁ , where ||·|| number;

(3d) Construct the low-rank constraint item ||Z|| _* of the multi-view self-representation coefficient matrix Z, and set the weight of ||Z|| _* to λ ₂ , where ||·|| _* represents the kernel norm of the matrix;

(3e) Using the Laplacian matrix Construct multi-view data matrix Similarity constraints in set up The weight of is λ ₃ , where tr(·) represents the trace of the matrix;

(3f) will ||E _r || _2,1 , ||Z|| _* and Perform weighted addition to obtain the objective function J of multi-view subspace clustering based on implicit representation and self-adaptation:

(4) Optimize the objective function J:

The objective function J is optimized using the alternate direction multiplier method, and A is used as the auxiliary matrix variable of Z, and the constraint of A is set as A=Z, and the as The Lagrangian multiplier of , Q ₁ is used as the Lagrangian multiplier of E _r =H-HZ, Q ₂ is used as the Lagrangian multiplier of A=Z, and the optimized objective function J' is obtained:

in, <·,·> represents the inner product of the matrix, μ represents the regularization coefficient;

(5) Initialize the variables in the optimized objective function J':

will J' in Z, E _r , All elements contained in Q ₁ , Q ₂ and A are initialized to 0, all elements contained in H are initialized to random numbers between (0,1), and μ is initialized to 0.001;

(6) The variables in the optimized objective function J' are alternately iterated:

For the variables H, Z, and E _r , A. Q ₁ , Q ₂ and μ are alternately iterated to obtain the iterative update expressions H _S , Z _S , E _rS , A _S , Q _1S , Q _2S and μ _S ;

(7) Calculate the value of variable Z in the optimized objective function J':

(7a) setting the maximum number of iterations of the optimized objective function J';

(7b) Use the iterative update expression of each variable in J' to iteratively update the corresponding variables, and stop iterating until the number of iterations is equal to the set maximum number of iterations, and obtain the updated multi-view self-expression coefficient matrix

(8) Cluster the original data set:

(8a) Calculate the similarity matrix S of the original data set;

(8b) Calculate the clustering result of the original data set:

(8b1) Diagonalize the vector t obtained by summing each row of the similarity matrix S to obtain the degree matrix D of S, and calculate the Laplacian matrix L,

(8b2) performing eigenvalue decomposition on the Laplacian matrix L to obtain the matrix T formed by the eigenvectors corresponding to each eigenvalue in the eigenvalue set E and E;

(8b3) Arrange the eigenvalues in E in ascending order to obtain the eigenvalue set E', take the first _K eigenvalues of E' to form the set E _K , and select from T each The eigenvectors corresponding to the eigenvalues form the eigenvector matrix T', and then the normalized results of each row of T' are used as sample data points, where K represents the number of categories of sample data points in T', 2≤K<N, N represents the number of sample data points in the original dataset;

(8b4) Randomly select K sample data points in T', and use each sample data point as an initial cluster center of a class to obtain a cluster center set R composed of K cluster centers;

(8b5) Calculate the Euclidean distance from each sample data point in T' to each cluster center in R, and assign each sample data point to the category of the cluster center with the smallest Euclidean distance to itself, and calculate the The mean value of the sample data points of the kth category is used as the clustering center of the kth category, and the clustering centers of the K categories are obtained, and R is updated, where k=1,2,...,K;

(8b6) Step (8b5) is repeatedly executed until the cluster center set R no longer changes, and the clustering result of the original data set is obtained.

Compared with the prior art, the present invention has the following advantages:

When constructing the objective function, the present invention decomposes the multi-view data matrix to obtain the multi-view implicit representation, and uses an adaptive method to measure the importance of each view to obtain the multi-view implicit representation matrix. The view basis matrix and the multi-view implicit representation matrix represent the parameters of the error reconstruction item of the multi-view data matrix. At the same time, the similarity constraint item in the multi-view data matrix is constructed to make the multi-view implicit representation maintain the local geometric structure in each view, By making full use of the information of each view, a more accurate similarity matrix of the original data set can be obtained, and compared with the existing technology, the accuracy rate of multi-view clustering is effectively improved.

Description of drawings

Fig. 1 is the realization flowchart of the present invention;

Fig. 2-Fig. 4 is respectively the clustering accuracy rate simulation result comparison figure of the present invention and existing implicit multi-view subspace clustering method under BBCSport data set, MSRC-v1 data set and Caltech101-7 data set;

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Referring to Figure 1, a multi-view subspace clustering method based on implicit representation and self-adaptation includes the following steps:

Step 1) Obtain the multi-view data matrix of the original dataset

Since each image has multiple types of features, different types of features of each image can be extracted, and different types of feature data can be extracted from multiple images contained in the original data set, and the same feature data can form a view matrix. multi-view data matrix of the original dataset Wherein, X ^(v) represents the vth view matrix, v=1, 2, ..., m, m represents the number of view matrices, and m≥2.

Step 2) Calculate the multi-view data matrix The Laplacian matrix The implementation steps are:

(2a) Take each column of the vth view matrix X ^(v) as a sample point, and calculate any two sample points and Euclidean distance between i,j=1,2,...,N, N represents the number of sample points in the original data set;

(2b) Calculate the multi-view data matrix The incidence matrix where W ^(v) represents the incidence matrix of the vth view matrix, Represents the element of row i and column j of W ^(v) , and σ represents the bandwidth parameter of the Gaussian kernel;

(2c) for the incidence matrix The summation of each row of the vector r is obtained, and the diagonalization of r is obtained to obtain the diagonal multi-view matrix and calculate the multi-view data matrix The Laplacian matrix

Step 3) Construct the objective function J for multi-view subspace clustering based on hidden representation and self-adaptation:

(3a) Since the assumption adopted in the present invention is the multi-view data matrix is composed of the same multi-view implicit representation matrix H and multi-view basis matrix are multiplied together, so the Decomposed into multi-view implicit representation matrix H and multi-view base matrix Set the constraint of the base matrix P ^(v) of the vth view matrix X ^(v) to O, O means P ^(v) P ^(v)T = I, in order to measure and inconsistency, the and and the product of H as the error reconstruction term Wherein, I represents the identity matrix, and ( ) ^T represents the transposition of the matrix;

(3b) To measure and The magnitude of the inconsistency, computed by measure of Assume The adaptive weight of is Yes The weight parameter of , where, Indicates the square of the matrix F norm, γ indicates the adjustment parameter, γ≥0, Since the amount of information contained in the view matrix X ^(v) cannot be obtained, adaptive weights are used automatic learning The weight of , the role of γ is to adjust Distribution;

(3c) Since H is a multi-view implicit representation matrix, H is A comprehensive representation of , in order to obtain The matrix composed of the similarity between the samples in the multi-view hidden representation matrix H is decomposed into the multi-view latent representation matrix H and the multi-view self-expression coefficient matrix Z. In order to measure the inconsistency between H and HZ, H and H and The difference of the Z product is used as the error reconstruction item E _r , E _r =H-HZ, in order to measure the size of the inconsistency between H and HZ, calculate the measure of E _r ||E _r || _2,1 , let ||E _r | The weight of | _2,1 is λ ₁ , where ||·|| _2,1 represents the 2,1 norm of the matrix, and the calculation of the 2,1 norm of E _r is to enable the multi-view implicit representation to remove the general type Noise, enhance the robustness of the objective function of the present invention to general noise;

(3d) In order to obtain the unique Z and make Z have the low-rank structure of the similarity matrix of the original data set, the low-rank constraint item ||Z|| _* of Z is constructed, and the weight of ||Z|| _* is set to λ ₂ , where ||·|| _* represents the kernel norm of the matrix;

(3e) In order for H to hold The local geometry of the samples in , constructing the multi-view data matrix Similarity constraints in set up The weight of is λ ₃ , where tr(·) represents the trace of the matrix;

(3f) will ||E _r || _2,1 , ||Z|| _* and Perform weighted addition to obtain the objective function J of multi-view subspace clustering based on implicit representation and self-adaptation:

Step 4) optimize the objective function J:

Since the objective function J contains the constraints of the variables in J, it is impossible to directly obtain the expression of the solution of each variable in J, and optimize the objective function J:

The objective function J is optimized using the alternate direction multiplier method, and A is used as the auxiliary matrix variable of Z, and the constraint of A is set as A=Z, and the as The Lagrangian multiplier of , Q ₁ is used as the Lagrangian multiplier of E _r =H-HZ, Q ₂ is used as the Lagrangian multiplier of A=Z, and the optimized objective function J' is obtained:

in, <·,·> represents the inner product of the matrix, and μ represents the regularization coefficient.

Step 5) Initialize the variables in the optimized objective function J':

will J' in Z, E _r , All elements contained in Q ₁ , Q ₂ and A are initialized to 0, all elements contained in H are initialized to random numbers between (0,1), and μ is initialized to 0.001. When initializing the variables in J', in order to ensure J''s optimization algorithm can be run iteratively.

Step 6) Iterate alternately the variables in the optimized objective function J':

For the variables H, Z, and E _r , A. Q ₁ , Q ₂ and μ are alternately iterated to obtain the iterative update expressions H _S , Z _S , E _rS , A _S , Q _1S , Q _2S and μ _S , the realization steps are:

(I) Use lyap(P,Q,-T') to iteratively update the multi-view hidden representation matrix H, Among them, lyap( ) represents the solution of Sylvester equation;

(II) Use (H ^T H+I) ^-1 (A+H ^T HH ^T E _r +(Q ₂ +H ^T Q ₁ )/μ) to iteratively update the multi-view self-expression coefficient matrix Z;

(Ⅲ) Use Iteratively update the multi-view basis matrix in and representation matrix The set of matrices composed of left singular vectors and the set of matrices composed of right singular vectors;

(Ⅳ) Use Iterative update error reconstruction term

(Ⅴ) Utilization Iteratively update the jth column of the error reconstruction item E _r , where, B _:,j represents the jth column of matrix B;

(Ⅵ) Use Iteratively update the auxiliary matrix variable A, where U and V represent the matrix The left singular vector and right singular vector of , Σ represents the diagonal matrix composed of singular values, S _δ (X)=max(X-δ,0)+min(X+δ,0) represents the contraction operator, where max (·,·) represents the maximum value of two numbers, min(·,·) represents the minimum value of two numbers;

(VII) Utilization iterative update

(Ⅷ) Utilize Q ₁ +μ(H-HZ-E _r ) to iteratively update Q ₁ , iterative update Q ₂ =Q ₂ +μ(AZ) iteratively updates Q ₂ , and ρμ iteratively updates μ, where ρ represents an adjustment parameter of μ, and ρ≥1.

Step 7) Calculate the value of variable Z in the optimized objective function J':

(7a) setting the maximum number of iterations of the optimized objective function J';

(7b) Use the iterative update expression of each variable in J' to iteratively update the corresponding variables, and stop iterating until the number of iterations is equal to the maximum number of iterations set, because Z can reflect the relationship between the data in the original data set Similarity, get the updated multi-view self-representation coefficient matrix Since each variable in J' can be calculated with other variables in J' except itself, the variables in J' can be iteratively updated before reaching the set maximum number of iterations of J'. After reaching the set maximum number of iterations of J', get the updated variable of J'

Step 8) Cluster the original dataset:

(8a) due to Reflects the similarity relationship between samples in the original data set, so it can be used Calculate the similarity matrix S of the original data set, the calculation formula is:

Among them, |·| represents the matrix formed after taking the absolute value of each element of the matrix;

(8b) Calculate the clustering result of the original data set:

(8b1) Diagonalize the vector t obtained by summing each row of the similarity matrix S to obtain the degree matrix D of S, and calculate the Laplacian matrix L of S,

(8b2) Decompose the eigenvalues of the Laplacian matrix L to obtain the set E of the eigenvalues of L and the set T composed of the eigenvectors corresponding to each eigenvalue in E, and carry out the eigenvalues in E from small to large Sort to obtain the set E' of the sorted eigenvectors, take the first K eigenvalues E _K of E', take the eigenvectors in T corresponding to E _K to form the eigenvector matrix T', and normalize each row of T' , taking each row of T' as a sample data point;

(8b3) Randomly select K sample data points of the eigenvector matrix T' as the cluster centers R of the initial K classes;

(8b4) Randomly select K sample data points in T', and use each sample data point as an initial cluster center of a class to obtain a cluster center set R composed of K cluster centers;

(8b5) Calculate the Euclidean distance from each sample data point in T' to each cluster center in R, and assign each sample data point to the category of the cluster center with the smallest Euclidean distance to itself, and calculate the The mean value of the sample data points of the kth category is used as the clustering center of the kth category, and the clustering centers of the K categories are obtained, and R is updated, where k=1,2,...,K;

(8b6) Step (8b5) is repeatedly executed until the cluster center set R no longer changes, and the clustering result of the original data set is obtained.

The technical effects of the present invention will be further described below in combination with simulation experiments.

1. Simulation conditions and content:

Simulation conditions:

The computer configuration environment in the simulation experiment is Intel(R) Core(i7-7700) 3.60GHZ CPU, memory 32G, WINDOWS7 operating system, and the computer simulation software uses MATLAB R2016b software.

The simulation experiments use BBCSport data set, MSRC-v1 data set and Caltech101-7 data set respectively.

Simulation content:

Simulation 1

Using the present invention and the existing hidden multi-view subspace clustering method in the BBCSport data set, the accuracy of clustering is compared and simulated, and the results are shown in FIG. 2 .

Simulation 2

Using the present invention and the existing hidden multi-view subspace clustering method under the MSRC-v1 data set, the clustering accuracy rate is compared and simulated, and the results are shown in FIG. 3 .

Simulation 3

Using the present invention and the existing hidden multi-view subspace clustering method in the Caltech101-7 data set, the accuracy of clustering is compared and simulated, and the results are shown in FIG. 4 .

2. Simulation result analysis:

Referring to Figure 2, under the BBCSport data set, when the number of test samples is 60, 90, 120, 150, 180, 210 respectively, the accuracy rate of multi-view data set clustering by the present invention is significantly higher than that of the prior art The accuracy rate of multi-view data set clustering, and when the number of test samples is 180, the accuracy rate of the result of the multi-view data set clustering using the present invention is relative to the result of the multi-view data set clustering using the prior art The smallest, at 6.0%. Referring to Figure 3, under the MSRC-v1 data set, when the number of test samples is 28, 56, 84, 112, 140, 168, and 196 respectively, the accuracy of the multi-view data set clustering using the present invention is higher than The accuracy rate of multi-view data set clustering using the prior art, and when the number of test samples is 28, the result of the multi-view data set clustering using the present invention is relative to that of the multi-view data set clustering using the prior art The resulting improved accuracy is minimal at 2.0%. Referring to Fig. 4, under the Caltech101-7 data set, when the number of test samples is 35, 70, 105, 140, 175, 210 respectively, the accuracy rate of multi-view data set clustering by the present invention is obviously higher than that of the present invention. The accuracy rate of multi-view data set clustering by existing technologies, and when the number of test samples is 70, the result of clustering multi-view data sets using the present invention is improved compared to the result of clustering multi-view data sets using the prior art has the lowest accuracy rate of 2.3%.

From the simulation results of Fig. 2-Fig. 4, under different data sets, when different numbers of test data are used, the accuracy rate of the multi-view data set clustering using the present invention is obviously higher than that of the prior art for multi-view clustering This is because when performing multi-view clustering, compared with the prior art, the present invention obtains a common latent representation of multi-view data in an adaptive manner, and utilizes graph regularization to keep the multi-view latent representation original The local geometric structure of the samples in the data set makes the similarity matrix of the original data set have a more accurate structure. Compared with the existing technology, it effectively improves the accuracy of multi-view data set clustering.

Claims (4)

1. A multi-view subspace clustering method based on implicit representation and self-adaptation is characterized by comprising the following implementation steps:

(1) obtaining a multi-view data matrix of an original data set

Extracting different types of feature data from a plurality of images contained in an original data set respectively, wherein the same feature data form a view matrix, and a plurality of view matrices form multiple views of the original data setData matrixWherein, X^(v)The view matrix of the v-th is shown, v is 1,2, …, m represents the number of the view matrix, and m is more than or equal to 2;

(2) computing a multi-view data matrixLaplacian matrix of

(3) Constructing an objective function J of multi-view subspace clustering based on implicit representation and self-adaptation:

(3a) will be provided withDecomposed into a multi-view implicit representation matrix H and a multi-view basis matrixSet up X^(v)Base matrix P of^(v)With the constraint of O representing P^(v)P^(v)TIs as follows as IAndthe difference of the product of the sum and H is used as an error reconstruction term Wherein, I represents a unit matrix (.)^TRepresents a transpose of a matrix;

(3b) computingMeasure of (2)Is provided withIs adaptive weight ofIs thatThe weight parameter of (a), wherein,represents the square of the norm of the matrix F, gamma represents the adjusting parameter, gamma is more than or equal to 0,

(3c) decomposing the multi-view implicit expression matrix H into a multi-view implicit expression matrix H and a multi-view self-expression coefficient matrix Z, and taking the difference of the product of H and Z as an error reconstruction item E_r，E_rH-HZ and calculate E_rMeasure of (E)_r||_2,1Let | E_r||_2,1Has a weight of λ₁Wherein | · | purple light_2,1A 2,1 norm representing a matrix;

(3d) low-rank constraint term | Z | non-calculation method for constructing multi-view self-representation coefficient matrix Z_*Setting | Z | ceiling_*Has a weight of λ₂Wherein | · | purple light_*A kernel norm representing a matrix;

(3e) using Laplace matricesConstructing a multi-view data matrixSimilarity constraint term inIs provided withHas a weight of λ₃Where tr (-) represents a trace of the matrix;

(3f) will be provided with||E_r||_2,1- | Z | | andand (3) carrying out weighted addition to obtain an objective function J based on implicit representation and self-adaptive multi-view subspace clustering:

(4) optimizing an objective function J:

optimizing an objective function J by adopting an alternating direction multiplier method, taking A as an auxiliary matrix variable of Z, setting the constraint of A as that A is Z, and then optimizing the objective function J by adopting the alternating direction multiplier methodAsLagrangian multiplier of (1), Q₁As E_r(ii) Lagrangian multiplier of H-HZ, Q₂Obtaining an optimized objective function J' as a Lagrangian multiplier of A ═ Z:

wherein,< - > represents the inner product of the matrix, mu represents the regularization coefficient;

(5) initializing variables in the optimized objective function J':

to be in JZ、E_r、Q₁、Q₂And all elements contained in a are initialized to 0, all elements contained in H are initialized to random numbers between (0,1), and μ is initialized to 0.001;

(6) and performing alternate iteration on the variables in the optimized objective function J':

for the variable H, Z in JE_r、A、Q₁、Q₂And mu, performing alternate iteration to obtain an iteration update expression H with each variable_S、Z_S、 E_rS、A_S、Q_1S、Q_2SAnd mu_S；

(7) Calculating the value of the variable Z in the optimized objective function J':

(7a) setting the maximum iteration times of the optimized objective function J';

(7b) iteratively updating the corresponding variables by using the iterative updating expressions of the variables in the J', stopping iteration until the iteration times are equal to the set maximum iteration times, and obtaining an updated multi-view self-expression coefficient matrix

(8) Clustering the original data set:

(8a) calculating a similarity matrix S of the original data set;

(8b) calculating the clustering result of the original data set:

(8b1) diagonalizing a vector t obtained by summing each row of the similarity matrix S to obtain a degree matrix D of S, and calculating a Laplace matrix L,

(8b2) decomposing the eigenvalue of the Laplace matrix L to obtain a matrix T consisting of eigenvectors corresponding to each eigenvalue in the eigenvalue set E and E;

(8b3) arranging the characteristic values in the E according to the sequence from small to large to obtain a characteristic value set E ', and taking the first K characteristic values of the E' to form a set E_KAnd selecting and E from T_KThe eigenvector corresponding to each eigenvalue in the T 'forms an eigenvector matrix T', and then the normalization result of each row of the T 'is used as a sample data point, wherein K represents the number of types of the sample data point in the T', K is more than or equal to 2 and less than N, and N represents the number of sample data points in the original data set;

(8b4) randomly selecting K sample data points in the T', and taking each sample data point as an initial class of clustering centers to obtain a clustering center set R consisting of the K clustering centers;

(8b5) calculating the Euclidean distance from each sample data point in T' to each clustering center in R, distributing each sample data point to the category to which the clustering center with the minimum Euclidean distance with the sample data point belongs, calculating the mean value of the sample data points belonging to the kth category as the clustering center of the kth category, obtaining the clustering centers of K categories, and realizing the updating of R, wherein K is 1,2, … and K;

(8b6) and repeating the step (8b5) until the cluster center set R is not changed any more, and obtaining the clustering result of the original data set.

2. The hidden-representation-based and adaptive multi-view subspace clustering method according to claim 1, wherein said step (2) of computing a multi-view data matrixLaplacian matrix ofThe method comprises the following implementation steps:

(2a) will be the v view matrix X^(v)Each column of (1) is taken as a sample point, and any two sample points are calculatedAndeuropean distance betweeni, j is 1,2, …, N represents the number of sample data points in the original data set, v is 1,2, …, m, m represents the number of view matrixes, and m is more than or equal to 2;

(2b) computing a multi-view data matrixIs associated with the matrix Wherein, W^(v)A correlation matrix representing the v-th view matrix,represents W^(v)Row i and column j, σ represents the bandwidth parameter of the gaussian kernel;

(2c) for correlation matrixSumming the rows to obtain a vector r, and diagonalizing r to obtain a diagonal multiview matrixAnd computing a multi-view data matrixLaplacian matrix of

3. The hidden representation and adaptive-based multi-view subspace clustering method according to claim 1, wherein the step (6) of performing the alternate iteration on the variables in the optimized objective function J' comprises the following steps:

iteratively updating a multi-view hidden representation matrix H using lyap (P, Q, -T'), wherein lyap (. cndot.) represents the solution of Sylvester's equation,a matrix of multi-view data is represented,a multi-view basis matrix is represented,representing error reconstruction terms, E_rRepresenting an error reconstruction term, Z represents a multi-view self-representation coefficient matrix,denotes the Laplace matrix, λ₃Representing similarity constraint termsWeight of (2), Q₁、Q₂Represents the Lagrangian multiplier, I represents the identity matrix, μ represents the regularization coefficient, (. cndot.)^TRepresents a transpose of a matrix;

(II) utilization ofIteratively updating a multi-view self-representation coefficient matrix Z, wherein A represents an auxiliary matrix variable of Z;

(III) utilization ofIteratively updating a multi-view basis matrixWhereinAndrepresentation matrixOf left singular vectors and a set of matrices of right singular vectors, wherein,represents a Lagrangian multiplier;

(IV) utilization ofIteratively updating error reconstruction termsWherein,represents an adaptive weight parameter, and gamma represents an adjustment parameter;

(V) utilization ofIteratively updating the error reconstruction term E_rColumn j of (a), wherein,B_:,jdenotes the jth column, λ, of the matrix B₁Representing the error reconstruction term E_rMeasure of (E)_r||_2,1The weight of (| · |) non-calculation_2,1A 2,1 norm representing a matrix;

(VI) utilization ofIterative update assistA co-matrix variable A, where U and V represent a matrixLeft and right singular vectors of (d), sigma representing a diagonal matrix of singular values, S_δ(X) ═ max (X- δ,0) + min (X + δ,0) denotes the contraction operator, where max (·, ·) denotes the maximum of the two numbers, min (·,) denotes the minimum of the two numbers, λ₂Low-rank constraint term | Z | | non-woven phosphor represented by Z_*The weight of (| · |) non-calculation_*A kernel norm representing a matrix;

(VII) utilization ofIterative updating

(VIII) by Q₁+μ(H-HZ-E_r) Iteratively updating Q₁，Iterative updatingQ₂＝Q₂+ μ (A-Z) iteratively updating Q₂And repeatedly updating mu by rho mu, wherein rho represents the adjusting parameter of mu, and rho is larger than or equal to 1.

4. The hidden representation and adaptive-based multi-view subspace clustering method according to claim 1, wherein the similarity matrix S of the original data set is calculated in step (8a) according to the following formula:

wherein | represents a matrix composed of absolute values of each element of the matrix, (·)^TWhich represents the transpose of the matrix,and representing the updated multi-view self-representation coefficient matrix.