An image clustering method fusing low-rank kernel learning and adaptive hypergraph

Abstract

The application relates to the field of image clustering, and discloses an image clustering method fusing low-rank kernel learning and adaptive hypergraph, which comprises the following steps: S1, acquiring image data; S2, iteratively constructing a hypergraph and updating a hypergraph Laplacian matrix, a coefficient matrix, a consensus kernel matrix and a candidate kernel weight through low-rank consensus kernel learning, image data self-expression in a kernel space and adaptive hypergraph regularization until a convergence condition is reached; S3, constructing a similarity matrix by applying the coefficient matrix obtained in the step S2; and S4, calling a spectral clustering algorithm by applying the similarity matrix obtained in the step S3 to obtain a clustering result. The method integrates adaptive hypergraph regularization, data self-expression in a kernel space and low-rank kernel learning into one framework, realizes the alternating guidance and dynamic promotion of the three, optimally utilizes the sample correlation under different candidate kernels, mines more stable high-order relationships, and thus more deeply mines the internal structure of data.

Description

TECHNICAL FIELD

[0001] The present application relates to an image clustering method fusing low-rank kernel learning and adaptive hypergraph, which can be used in the field of image clustering in pattern recognition. BACKGROUND

[0002] Cluster analysis of image data has broad research and application prospects. In the field of computer vision and pattern recognition, image is a most common visual information presentation. Image data is usually high-dimensional and nonlinearly separable, which is characterized by containing a large number of redundant features, more sparse distribution and containing at least one cluster with non-convex shape boundary. Data clustering as a basic data processing technology is increasingly mature, which provides a method basis for solving the clustering problem of image data. Spectral clustering method has the ability to detect complex data structure and process nonlinearly separable data, and is suitable for clustering of image data.

[0003] Measuring the similarity between data objects is crucial for spectral clustering. Spectral clustering converts the clustering problem into a graph partitioning problem by regarding the similarity between data objects and pairs of data objects as the vertices of a graph and the weights of the edges connecting two vertices, respectively. According to different ways of measuring similarity, spectral clustering methods are mainly divided into distance-based methods and representation-based methods. Distance-based methods are difficult to reveal the inherent similarity between data objects in nonlinear manifold and reflect the real distribution information, and are very sensitive to noise in data. Representation-based methods automatically and effectively measure the relationship between data objects through self-representation of data to improve clustering performance, which has attracted great attention.

[0004] However, when dealing with complex real-world image data, the self-representation property of related representation-based spectral clustering methods cannot effectively ensure that spatially close data objects also have similar representations in the latent coefficient space, so its ability to mine the intrinsic structure of data is limited. SUMMARY

[0005] In order to overcome the limitations of existing clustering methods in mining the similarity relationship between image data objects and the insufficient clustering performance, the present application provides an image clustering method fusing low-rank kernel learning and adaptive hypergraph, which can realize the alternating guidance and dynamic improvement of low-rank consensus kernel learning, data self-representation in kernel space and adaptive hypergraph regularization through alternating optimization and solution in the iteration process, more deeply mine the intrinsic similarity relationship between data objects, and be used for clustering of nonlinearly separable data. The adaptive hypergraph proposed in the present application dynamically constructs a probabilistic hypergraph by adaptively fusing the neighbor kernel of the candidate kernel, optimally utilizes the sample correlation under different candidate kernels, and mines more stable high-order relationships.

[0006] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0007] An image clustering method fusing low-rank kernel learning and adaptive hypergraph, comprising the following steps:

[0008] S1, obtaining image data;

[0009] S2, iteratively constructing a hypergraph and updating a hypergraph Laplacian matrix, a coefficient matrix, a consensus kernel matrix and a candidate kernel weight by low-rank consensus kernel learning, image data self-expression in kernel space and adaptive hypergraph regularization until a convergence condition is reached;

[0010] S3, constructing a similarity matrix by using the coefficient matrix obtained in the step S2;

[0011] S4, obtaining a clustering result by calling a spectral clustering algorithm by using the similarity matrix obtained in the step S3.

[0012] Preferably, in the step S1, it is assumed that the image data is n represents n data objects, d represents a feature dimension of the data objects, each data object in X is regarded as a vertex, and a vertex set is V={v1, v2, …, vn}. n}。

[0013] Preferably, the specific process of the step S2 is that the model shown in the formula (1) can directly learn the coefficient matrix, the consensus kernel matrix and the candidate kernel weight from the image data, and the model is as follows:

[0014]

[0015]

[0016] wherein the first term is a data self-expression constraint term in kernel space, the second term is a sparse or low-rank regularization term of the coefficient matrix, the third term is a consensus kernel learning constraint term, the fourth term is a low-rank regularization term of the consensus kernel, and the fifth term is an adaptive hypergraph regularization term;

[0017] Given m candidate kernel matrices, is the rth candidate kernel matrix, denotes an element in the ith row and the jth column of the rth candidate kernel matrix, is a coefficient matrix, is a consensus kernel matrix, is a candidate kernel weight vector, g r is the weight corresponding to the rth candidate kernel, φ(X) represents an unknown kernel mapping function, K=φ(X) T φ(X),‖·‖ F is a Frobenius norm, and the first term can be converted into p(Z) is ‖Z‖1 or ‖Z‖ * ‖·‖1 and ‖·‖ * are the l1 norm and the kernel norm, respectively, is the normalized hypergraph Laplacian matrix, and a, b, g and d are penalty parameters;

[0018] The alternating direction method of multipliers is used to solve Z, K, g in formula (1), and the steps are as follows: first, separate the variables in formula (1), introduce variables and and add the corresponding constraints; then rewrite the augmented Lagrangian function corresponding to formula (1):

[0019]

[0020] wherein, m is a penalty parameter, and are the Lagrange multipliers; finally, in order to obtain the optimal solution Z * , K * , g * that minimizes the augmented Lagrangian function (2), iteratively update Z, K, g, L symH also changes with g, and the Lagrange multipliers are updated using the feasibility error, and the iteration stops when the convergence condition is met.

[0021] Further, the specific process of the iteration is as follows: let the maximum number of iterations be T, and the optimization variables and Lagrange multipliers of the t(th) (0≤t≤T) iteration be {Z (t) , K (t) , g (t) , L symH (t) , J (t) , W (t)} and {Y1 (t) , Y2 (t)}, respectively, initialize g (0) =1, initialize Z (0) and J (0) to unit matrices, initialize K (0) , W (0) , Y1 (0) and Y1 (0) to zero matrices, and initialize m (0) from the range {1e-5, 1e-3, 0.1, 10, 1e3, 1e5}, and the specific iteration process of the parameters is as follows:

[0022] S21, fix g (t) , update L symH (t+1) as follows:

[0023] Weighted fusion of the neighbor kernel of the candidate kernel:

[0024]

[0025]

[0026] where H r (i,j) represents the element in the i-th row and j-th column of the neighbor kernel matrix H r of the r-th candidate kernel, N k (i) represents the k-neighborhood set of data object i, and G is the matrix after weighted fusion.

[0027] Constructing a hypergraph, the hypergraph contains a vertex set V = {v1, v2, …, v n} and a hyperedge set ε = {e1, e j , …, e n}, which is characterized by an incidence matrix H (t) and a hyperedge weight matrix W (t) .

[0028]

[0029]

[0030] where H(v i ,e j ) is the element in the i-th row and j-th column of the incidence matrix H, representing the similarity between vertex v i and hyperedge e j , the hyperedge weight matrix W is a diagonal matrix, w(e j ) is the element in the j-th row and j-th column of W, representing the weight of hyperedge e j , and G ij represents the element in the i-th row and j-th column of matrix G, is the element in the i-th row and j-th column of matrix ;

[0031] Update L symH (t+1) :

[0032]

[0033] where D e and D v are diagonal matrices containing the degrees of all hyperedges and the degrees of all vertices, respectively, the degree of hyperedge e j is the degree of vertex v i ​​​

[0034] S22, fix L symH (t+1) , K (t) , J (t) , Y1 (t) and μ (t) , update Z (t+1) :

[0035] Z (t+1) = (K (t) + μ (t) I + 2δL symH (t+1) ) -1 (K (t) + μ (t) J (t) + Y1 (t) ),#(8)

[0036] Set elements of Z (t+1) that are less than 0 to 0:

[0037] Z (t+1) = max(Z (t+1) , 0),#(9)

[0038] S23, fix Z (t+1) , g (t) , W (t) , μ (t) and Y2 (t) , update K (t+1) :

[0039]

[0040] Set elements of K (t+1) that are less than 0 to 0:

[0041] K (t+1) = max(K (t+1) , 0),#(11)

[0042] S24, fix Z (t+1) , μ (t) and Y1 (t) , update J (t+1) :

[0043] If ρ(J) = ‖J‖1, then:

[0044]

[0045] If ρ(J) = ‖J‖ * , then:

[0046]

[0047] in, C ij is the element in the i-th row and j-th column of the matrix C, U (t) 、V (t) and σ (t) They correspond to C (t) The left singular vector, right singular vector and singular value of the singular value decomposition of ;

[0048] Let J (t+1) Elements less than 0 are set to 0:

[0049] J (t+1) =max(J (t+1) ,0),#(14)

[0050] S25, fixed K (t+1) , μ (t) and Y2 (t) , update W (t+1) :

[0051]

[0052] in, and They correspond to D (t) The left singular vector, right singular vector and singular value of the singular value decomposition of ;

[0053] Let W (t+1) Elements less than 0 are set to 0:

[0054] W (t+1) =max(W (t+1) ,0),#(16)

[0055] S26, fixed K (t+1) , update g (t+1) :

[0056] Solve for g (t+1) The optimization problem becomes a quadratic programming problem with linear constraints, which can be solved using the existing MATLAB function quadprog.

[0057] S27, update the Lagrange multiplier Y1 (t+1) , Y2 (t+1) and μ (t+1) :

[0058] Y1 (t+1) =Y1 (t) +μ (t) (JZ),#(17)

[0059] Y2(t+1) = Y2 (t) + μ (t) (W - K), (18)

[0060] μ (t+1) = min(μ max , τμ (t) ), (19)

[0061] where τ is empirically adjusted, μ max is the maximum value of μ allowed;

[0062] S28, determine whether an iteration stopping condition is reached, the iteration stopping condition being:

[0063]

[0064] where ε is a threshold value, if the iteration stopping condition is reached, a final Z * is obtained, K * , g * , otherwise, continue to execute S21-S28.

[0065] Preferably, in the S3 step, the coefficient matrix obtained in the S2 step is applied to construct a similarity matrix as:

[0066] S = |Z| + |Z| T .(21)

[0067] Preferably, the S4 step specifically comprises: taking the similarity matrix as an input of a spectral clustering algorithm, calling the spectral clustering algorithm, and obtaining a clustering result.

[0068] Compared with the prior art, the present application has the following advantages:

[0069] The method of the present application is different from the existing spectral clustering method based on representation. The present application fuses low-rank kernel learning and adaptive hypergraph to obtain a similarity matrix for spectral clustering. The characteristics and innovations of the present application mainly lie in that: 1) the present application proposes to integrate adaptive hypergraph regularization, data self-expression and low-rank kernel learning into a unified objective function, and realizes the alternating guidance and dynamic improvement of the three by alternating optimization and solution, which can more deeply mine the internal similarity relationship of data and be used for clustering tasks of nonlinear separable data; 2) the present application proposes to adaptively fuse the neighbor kernel of the candidate kernel to dynamically construct a probabilistic hypergraph, which optimally utilizes the sample correlation under different candidate kernels and mines more stable high-order relationships; 3) compared with the traditional spectral clustering method based on representation and the spectral clustering method based on kernel, the present application can more effectively mine the internal similarity relationship between nonlinear separable data and improve the clustering performance. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1is a workflow diagram of clustering image data using the method of the present application. DETAILED DESCRIPTION

[0071] The purposes, advantages and features of the present application will be illustrated and explained by the following non-limiting description of preferred embodiments. These embodiments are only typical examples of application of the technical solutions of the present application, and any technical solutions formed by equivalent replacement or equivalent transformation fall within the scope of the present application.

[0072] The present application discloses an image clustering method fusing low-rank kernel learning and adaptive hypergraph, as shown in Figure 1 The method comprises the following steps:

[0073] S1, obtaining image data; assuming that the image data is X n represents n data objects, d represents the feature dimension of the data object, each data object in X is regarded as a vertex, and the vertex set is V={v1, v2, …, vn}; n};

[0074] S2, iteratively constructing a hypergraph and updating a hypergraph Laplacian matrix, a coefficient matrix, a consensus kernel matrix and a candidate kernel weight by low-rank consensus kernel learning, image data self-expression in kernel space and adaptive hypergraph regularization until a convergence condition is reached; the specific process is as follows:

[0075] The model shown in formula (1) can directly learn the coefficient matrix, the consensus kernel matrix and the candidate kernel weight from the image data, and the model is as follows:

[0076]

[0077]

[0078] wherein the first term is a data self-expression constraint term in kernel space, the second term is a sparse or low-rank regularization term of the coefficient matrix, the third term is a consensus kernel learning constraint term, the fourth term is a low-rank regularization term of the consensus kernel, and the fifth term is an adaptive hypergraph regularization term;

[0079] Given m candidate kernel matrices, is the rth candidate kernel matrix, denotes the element in the ith row and jth column of the rth candidate kernel matrix, is the coefficient matrix, is the consensus kernel matrix, is the candidate kernel weight vector, g r is the weight corresponding to the rth candidate kernel, and φ(X) represents an unknown kernel mapping function, K=φ(X) T φ(X),‖·‖ F is the Frobenius norm, and the first term Can be converted into ρ(Z) is ‖Z‖1 or ‖Z‖ * , ‖·‖1 and ‖·‖ * are the l1 norm and the nuclear norm, is the normalized hypergraph Laplacian matrix, α, β, γ, and δ are penalty parameters;

[0080] The alternating direction multiplier method is used to solve Z, K, and g in formula (1). The steps are as follows: First, separate the variables in formula (1) and introduce the variables and And add the corresponding constraints; then rewrite the augmented Lagrangian function corresponding to formula (1):

[0081]

[0082] Among them, μ is the penalty parameter, and is the Lagrange multiplier; Finally, in order to obtain the optimal solution Z that minimizes the augmented Lagrangian function (2) * , K * , g * , iteratively update Z, K, g, L symH It also changes adaptively with g, and uses the feasibility error to update the Lagrange multiplier. When the convergence condition is met, the iteration stops.

[0083] Furthermore, the specific process of the iteration is as follows: let the maximum number of iterations be T, the optimization variables and Lagrange multipliers of the tth iteration (0≤t≤T) are {Z (t) ,K (t) ,g (t) ,L symH (t) ,J (t) ,W (t)} and {Y1 (t) ,Y2 (t)}, initialize g (0) =1, initialize Z (0) and J (0) Initialize K as the identity matrix (0) , W (0) , Y1 (0) and Y1 (0) is a zero matrix, initialize μ from the range {1e-5, 1e-3, 0.1, 10, 1e3, 1e5} (0) , the specific iteration process of the parameters is as follows:

[0084] S21, fixed g (t) , update L symH (t+1)The process is as follows:

[0085] Weighted fusion of the neighbor kernel of the candidate kernel:

[0086]

[0087]

[0088] where H r (i,j) represents the element in the i-th row and the j-th column of the neighbor kernel matrix H r of the r-th candidate kernel, N k (i) represents the k-neighbor set of the data object i, and G is the matrix after weighted fusion.

[0089] Constructing a hypergraph, the hypergraph contains a vertex set V = {v1, v2, …, v n} and a hyperedge set ε = {e1, e j , …, e n}, which is characterized by the incidence matrix H (t) and the hyperedge weight matrix W (t) .

[0090]

[0091]

[0092] where H(v i ,e j ) is the element in the i-th row and the j-th column of the incidence matrix H, representing the similarity between the vertex v i and the hyperedge e j , the hyperedge weight matrix W is a diagonal matrix, w(e j ) is the element in the j-th row and the j-th column of W, representing the weight of the hyperedge e j , and G ij represents the element in the i-th row and the j-th column of the matrix G, is the element in the i-th row and the j-th column of the matrix ;

[0093] Update L symH (t+1) :

[0094]

[0095] where D e and D v are diagonal matrices containing the degrees of all hyperedges and all vertices, respectively, the degree of the hyperedge e j is d(e ), and the degree of the vertex v is d(v ).i of degrees

[0096] S22, fix L symH (t+1) , K (t) , J (t) , Y1 (t) and μ (t) , update Z (t+1) :

[0097] Z (t+1) = (K (t) + μ (t) I + 2δL symH (t+1) ) -1 (K (t) + μ (t) J (t) + Y1 (t) ),#(8)

[0098] Let the elements of Z (t+1) that are less than 0 be 0:

[0099] Z (t+1) = max(Z (t+1) , 0),#(9)

[0100] S23, fix Z (t+1) , g (t) , W (t) , μ (t) and Y2 (t) , update K (t+1) :

[0101]

[0102] Let the elements of K (t+1) that are less than 0 be 0:

[0103] K (t+1) = max(K (t+1) , 0),#(11)

[0104] S24, fix Z (t+1) , μ (t) and Y1 (t) , update J (t+1) :

[0105] If ρ(J) = ||J||1, then:

[0106]

[0107] If ρ(J) = ||J|| * , then:

[0108]

[0109] where, C ij is the element in the i-th row and j-th column of matrix C, U (t) , V (t) and σ (t) are the left singular vector, right singular vector and singular value corresponding to the singular value decomposition of C (t) , respectively;

[0110] Let the elements in J (t+1) that are less than 0 be 0:

[0111] J (t+1) = max(J (t+1) , 0),#(14)

[0112] S25, fix K (t+1) , μ (t) and Y2 (t) , update W (t+1) :

[0113]

[0114] where, and are the left singular vector, right singular vector and singular value corresponding to the singular value decomposition of D (t) , respectively;

[0115] Let the elements in W (t+1) that are less than 0 be 0:

[0116] W (t+1) = max(W (t+1) , 0),#(16)

[0117] S26, fix K (t+1) , update g (t+1) :

[0118] Solving the optimization problem for g (t+1) becomes solving a quadratic programming problem with linear constraints, which can be solved by the existing MATLAB function quadprog;

[0119] S27, update the Lagrange multipliers Y1 (t+1) , Y2 (t+1) and μ (t+1) :

[0120] Y1 (t+1) = Y1 (t) + μ (t) (J-Z),#(17)

[0121] Y2 (t+1) = Y2 (t) + μ (t) (W-K),#(18)

[0122] μ (t+1) = min(μ max ,τμ (t) ),#(19)

[0123] where τ is empirically adjusted, μ max is the maximum value of μ allowed;

[0124] S28, determine whether an iteration stopping condition is reached, the iteration stopping condition being:

[0125]

[0126] where ε is a threshold value, if the iteration stopping condition is reached, a final Z * is obtained, K * , g * , otherwise, continue to execute S21-S28.

[0127] S3, construct a similarity matrix using the coefficient matrix obtained in the S2 step:

[0128] S = |Z| + |Z| T .(21)

[0129] S4, use the similarity matrix obtained in the S3 step as an input of a spectral clustering algorithm, call the spectral clustering algorithm, and obtain a clustering result.

[0130] Performance comparison:

[0131] The image clustering method of the present application is used in the JAFFE face image dataset and the COIL20 target image dataset, and the clustering performance of the method of the present application and the comparative clustering method is evaluated using a clustering evaluation index, and comparative analysis is performed.

[0132] Specifically, the JAFFE dataset contains 213 photos, and 10 Japanese women make seven expressions (including sadness, happiness, anger, disgust, surprise, fear and neutrality) according to instructions in an experimental environment, and the face expressions are photographed by a camera, and there are about 3 or 4 samples for each expression. The COIL20 dataset contains 1440 images, and 20 objects are photographed from different angles (one image is taken every 5 degrees), and each object has 72 images. The feature dimensions of the JAFFE dataset and the COIL20 dataset used in the experiment are 676 and 1024 respectively.

[0133] In the same experimental setup, eight relevant representative clustering methods were selected as comparison methods (K-means, Normalized cut (Ncut), Sparse Subspace Clustering (SSC), Least Squares Regression (LSR), Low-Rank Representation (LRR), Single Kernel-based Learning Method (SKLM), Multiple Kernel-based Learning Method (MKLM) and Low-rank Kernel Learning for Graph Matrix (LKG)), and the method Joint Low-rank Consensus Kernel Learning and Adaptive Probabilistic Hypergraph Regularization for Spectral Clustering (LKHR) was used for comparison experiments, LKGs and LKGr represent ρ(Z) = ‖Z‖1 and ρ(Z) = ‖Z‖ * LKG methods in the case of LKHRs and LKHRr represent ρ(Z) = ‖Z‖1 and ρ(Z) = ‖Z‖ * LKG methods in the case of LKHRs and LKHRr represent ρ(Z) = ‖Z‖1 and ρ(Z) = ‖Z‖

[0134] Two widely used clustering evaluation indicators, Accuracy (ACC) and Normalized Mutual Information (NMI), were used to measure the performance of the algorithm, and the clustering evaluation indicator values of each method in the table were the average values of 100 clustering, and the clustering evaluation indicator values of the SKLM method in the table were the average values (maximum value, minimum value) under multiple single kernels (linear kernel, polynomial kernel and Gaussian kernel).

[0135] The experimental results are as follows:

[0136] Table 1: Experimental results of various methods on the JAFFE dataset

[0137]

[0138]

[0139] Table 2: Experimental results of various methods on the COIL20 dataset

[0140] Method ACC NMI K-means 0.65 0.76 Ncut 0.85 0.91 SSC 0.72 0.86 LSR 0.68 0.77 LRR 0.66 0.78 SKLM 0.75(0.9,0.66) 0.84(0.94,0.76) MKLM 0.74 0.82 LKGs 0.78 0.91 LKGr 0.79 0.85 LKHRs 0.92 0.96 LKHRr 0.92 0.96

[0141] The application proposes to integrate adaptive hypergraph regularization, data self-expression and low-rank kernel learning into a unified objective function, and to realize the alternating guidance and dynamic promotion of the three by alternating optimization and solution, to mine the internal similarity relationship of data at a deeper level, and to be used for the clustering task of nonlinear separable data. Moreover, the application proposes to adaptively fuse the neighbor kernel of the candidate kernel to dynamically construct a probability hypergraph, to optimally utilize the sample correlation under different candidate kernels, and to mine more stable high-order relationships. In the experiment, the clustering indexes of Accuracy (ACC) and Normalized Mutual Information (NMI) are used to measure the clustering performance of the algorithm. The results in Table 1 and Table 2 show that the clustering performance of the method proposed by the application is better than that of other comparative clustering methods, indicating that the method of the application can significantly improve the clustering performance of image data.

[0142] The application has various embodiments, and all the technical solutions formed by using equivalent transformation or equivalent transformation fall within the protection scope of the application.

Claims

1. An image clustering method integrating low-rank kernel learning and adaptive hypergraph, characterized by: The method comprises the following steps: S1, acquire image data; S2, through low-rank consensus kernel learning, image data self-expression in kernel space and adaptive hypergraph regularization, it iteratively constructs a hypergraph and updates the hypergraph Laplacian matrix, coefficient matrix, consensus kernel matrix and candidate kernel weights until the convergence condition is reached; The specific process of step S2 is: The model shown in formula (1) can directly learn the coefficient matrix, consensus kernel matrix, and candidate kernel weights from image data. The model is as follows: ； ； Among them, the first term is the data self-expression constraint term in the kernel space, the second term is the sparse or low-rank regularization term of the coefficient matrix, the third term is the consensus kernel learning constraint term, the fourth term is the low-rank regularization term of the consensus kernel, and the fifth term is the adaptive hypergraph regularization term; Given candidate kernel matrices, It is candidate kernel matrices, Indicates the The candidate kernel matrix Rank Elements of the column, is the coefficient matrix, is the consensus kernel matrix, is the candidate kernel weight vector, It is The weight corresponding to the candidate core, represents the unknown kernel mapping function, , is the Frobenius norm, the first term Can be converted into , for or , and They are norm and nuclear norm, is the normalized hypergraph Laplacian matrix, 、 、 and is the penalty parameter; Use the alternating direction multiplier method to solve the equation (1) , , , the steps are as follows: First, separate the variables in formula (1) and introduce the variables and , and add the corresponding constraints; then, rewrite the augmented Lagrangian function corresponding to formula (1): ； in, is the penalty parameter, and is the Lagrange multiplier; finally, in order to obtain the optimal solution that minimizes the augmented Lagrangian function (2) , , , iterative update , , , Also follow Adaptive changes are made, and the feasibility error is used to update the Lagrange multiplier. When the convergence condition is met, the iteration stops; S3, applying the coefficient matrix obtained in step S2 to construct a similarity matrix; S4, applying the similarity matrix obtained in step S3, calling the spectral clustering algorithm, and obtaining a clustering result.

2. The image clustering method integrating low-rank kernel learning and adaptive hypergraph according to claim 1, characterized in that: In the step S1, it is assumed that the image data is , Indicates that there is data objects, Represents the characteristic dimension of the data object, Each data object in is considered as a vertex, and the vertex set is .

3. The image clustering method integrating low-rank kernel learning and adaptive hypergraph according to claim 1, characterized in that: In step S3, the coefficient matrix obtained in step S2 is applied to construct a similarity matrix:

4. The image clustering method integrating low-rank kernel learning and adaptive hypergraph according to claim 1, characterized in that: The specific process of the iteration is: let the maximum number of iterations be , No. The optimization variables and Lagrange multipliers of the iteration are and ,initialization ,initialization and Initialize the identity matrix , , , and is a zero matrix, from Initialization in scope , the specific iteration process of the parameters is as follows: S21, fixed ,renew The process is as follows: Weighted fusion of neighbor kernels of candidate kernels: ； ； in, Indicates the The neighbor kernel matrix of candidate kernels Middle Rank Elements of the column, Represents a data object of A set of nearest neighbors, is the matrix after weighted fusion; Building a hypergraph, a hypergraph Contains vertex sets and hyperedge sets , through the incidence matrix and the hyperedge weight matrix Characterization: ； ； in, is the incidence matrix Middle Rank Elements of the column, representing vertices With super edge Similarity between, hyperedge weight matrix is a diagonal matrix, yes Middle Rank The elements of the column represent hyperedges The weight of Representation matrix Middle Rank Elements of the column, , is a matrix Middle Rank Elements of the column; renew : ； in, and are diagonal matrices containing the degrees of all hyperedges and the degrees of all vertices, respectively. degree ,vertex degree ; S22, fixed , , , and ,renew : ； make Elements less than 0 are set to 0: ； S23, fixed , , , and ,renew : ； ； make Elements less than 0 are set to 0: ； S24, fixed , and ,renew : like ,but: ； like ,but: ； in, , is a matrix Middle Rank Elements of the column, 、 and They correspond to The left singular vector, right singular vector and singular value of the singular value decomposition of ; make Elements less than 0 are set to 0: ； S25, fixed , and ,renew : ； in, , 、 and They correspond to The left singular vector, right singular vector and singular value of the singular value decomposition of ; make Elements less than 0 are set to 0: ； S26, fixed ,renew : Solution The optimization problem becomes a quadratic programming problem with linear constraints, which can be solved using the existing MATLAB function quadprog. S27, Update Lagrange multipliers , and : ； ； ； in, Adjust based on experience, yes The maximum value allowed; S28, judging whether the iteration stopping condition is met, the iteration stopping condition is: ； in, is the threshold value. If the iteration stop condition is reached, the final , , , otherwise continue to execute S21-S28.

5. The image clustering method integrating low-rank kernel learning and adaptive hypergraph according to claim 1, characterized in that: The step S4 specifically includes: taking the similarity matrix as the input of the spectral clustering algorithm, calling the spectral clustering algorithm, and obtaining the clustering result.

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