A double-layer structure sparse subspace clustering method and system based on hypergraph regularization

Abstract

The present invention relates to the field of image clustering technology, and discloses a double-layer structure sparse subspace clustering method and system based on hypergraph regularization, the method comprising: obtaining image data to be clustered; calculating node degree matrix; calculating hyperedge degree matrix; calculating hypergraph matrix; defining and initializing each factor matrix of hypergraph regular double-layer structure sparse subspace clustering; setting the number of iterations; obtaining the hypergraph regular double-layer structure sparse subspace clustering update formula to obtain clustering results. The present application effectively solves the clustering problem of complex data by introducing hypergraph regularization technology and double-layer structure sparse representation, and improves the accuracy and robustness of clustering results.

Description

Technical Field

[0001] The present invention relates to the technical field of image clustering, and in particular to a double-layer structure sparse subspace clustering method and system based on hypergraph regularization. Background Art

[0002] Image clustering is a technique that groups pixels or regions in an image according to their feature similarities. Common clustering algorithms include k-means clustering, which iteratively optimizes clustering results by assigning data points to the nearest cluster center until convergence is reached.

[0003] K-means clustering is an unsupervised clustering algorithm. Its basic idea is to divide the data set into k clusters so that the data points in each cluster are as similar as possible, while the data points in different clusters are as different as possible. The algorithm steps are as follows:

[0004] Step 1, ‌Initialization‌: Randomly select k points as initial cluster centers.

[0005] Step 2, ‌Assign Samples‌: Assign each data point to the nearest cluster center.

[0006] Step 3, ‌Update cluster centers‌: recalculate the center point of each cluster.

[0007] Step 4, ‌Iteration‌: Repeat steps 2 and 3 until the cluster center no longer changes significantly or the preset number of iterations is reached.

[0008] Image clustering is widely used in image segmentation, feature extraction, and image retrieval. Its advantages include simple implementation, parallel computing, and direct use without parameter adjustment for many problems. However, the main disadvantage of the k-means algorithm is that the number of clusters k needs to be set in advance. If k is not chosen properly, it will lead to poor clustering results.

[0009] Moreover, with the rapid growth of data scale and the increase of data complexity, traditional clustering algorithms have shown limitations in processing high-dimensional and complex data. For example, the classic k-means clustering and hierarchical clustering algorithms cannot effectively capture the local geometric structure of data, while clustering methods based on matrix decomposition, such as non-negative matrix factorization (NMF), have improved this problem to a certain extent, but still have the following defects:

[0010] 1. The local geometric structure of the data is not fully mined, making it difficult to capture high-order relationships.

[0011] 2. The lack of constraints on the global structure of the data and the sparsity of the subspace leads to low accuracy of the clustering results.

[0012] 3. The data noise has a great impact and the clustering results are not robust enough. Summary of the invention

[0013] The purpose of the present invention is to provide a double-layer structure sparse subspace clustering method and system based on hypergraph regularization. By introducing hypergraph regularization technology and double-layer structure sparse representation, the clustering problem of complex data is effectively solved and the accuracy and robustness of the clustering results are improved.

[0014] In order to achieve the above purpose, the technical solutions adopted are as follows:

[0015] In a first aspect, the present invention provides a double-layer structure sparse subspace clustering method based on hypergraph regularization, the method comprising:

[0016] Obtain image data to be clustered;

[0017] Calculate the node degree matrix;

[0018] Calculate the hyperedge degree matrix;

[0019] Compute the hypergraph matrix;

[0020] Define and initialize the factor matrices of the hypergraph regularized two-layer structure sparse subspace clustering;

[0021] Set the number of iterations;

[0022] Obtain the hypergraph regularized two-layer structure sparse subspace clustering update formula to obtain the clustering result;

[0023] Obtain the hypergraph regularized two-layer structure sparse subspace clustering update formula to obtain the clustering results, including:

[0024] Define the objective equation, the expression is:

[0025] ;

[0026] in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F is the Frobenius norm, , , and is the regularization parameter, tr is the trace of the matrix;

[0027] Find the Lagrangian function based on the objective function , the expression is:

[0028] ;

[0029] in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable;

[0030] According to the alternating direction multiplier method, update and ;

[0031] Calculate the similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

[0032] Further, according to the alternating direction multiplier method, update and ,include:

[0033] Update the noisy coefficient matrix by the following method :

[0034] Remove and Unrelated items, update The sub-problems are:

[0035] ;

[0036] Will update The sub-problem of Derivation, then The final solution is expressed as:

[0037] ;

[0038] in:

[0039] ;

[0040] The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm; T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter,I is the identity matrix;

[0041] Update the clean coefficient matrix by :

[0042] Remove and Unrelated items, update The sub-problems are:

[0043] ;

[0044] Will update The sub-problem of Derivation, determination The update formula is:

[0045] ;

[0046] Update the matrix by :

[0047] Remove and Unrelated items, update The sub-problems are:

[0048] ;

[0049] in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve:

[0050] Update the approximation consistent matrix by the following method :

[0051] Remove and Unrelated items, update The sub-problems are:

[0052] ;

[0053] Update the Solve the sub-problems of

[0054] Update the Lagrange multiplier matrix by the following formula :

[0055] ;

[0056] in, Y 2 represents the updated Lagrange multiplier matrix, Y 1 represents the Lagrange multiplier matrix before updating.

[0057] Furthermore, the simplex projection algorithm is used to solve the classic quadratic problem P Solve, including:

[0058] Input Vector and scalar ;

[0059] right Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest, and minimum values ​​in ;

[0060] turn up ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension,

[0061] definition ;in, is the intermediate parameter;

[0062] Output ;in, is an element of n+1 dimensional space, is the real number real.

[0063] Furthermore, the node degree matrix is ​​calculated by the following formula:

[0064] ;

[0065] Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

[0066] Furthermore, the hyperedge degree matrix is ​​calculated by the following formula;

[0067] ;

[0068] in, represents the hyperedge degree matrix.

[0069] Furthermore, the hypergraph matrix is ​​calculated by the following formula: :

[0070] ;

[0071] in, are all diagonal matrices, and the element values ​​are respectively and Decide, is the relationship matrix between nodes and hyperedges, is the hyperedge weight matrix, which represents the weight of each hyperedge.

[0072] In a second aspect, the present invention provides a double-layer structure sparse subspace clustering system based on hypergraph regularization, the system comprising:

[0073] A data acquisition module, configured to acquire image data to be clustered;

[0074] A first computing module is configured to compute a node degree matrix;

[0075] A second computing module is configured to calculate a hyperedge degree matrix;

[0076] A third computing module, configured to compute a hypergraph matrix;

[0077] A matrix definition module is configured to define and initialize each factor matrix of the hypergraph regularized two-layer structure sparse subspace clustering;

[0078] An iteration setting module, configured to set the number of iterations;

[0079] The clustering module is configured to obtain the hypergraph regular double-layer structure sparse subspace clustering update formula to obtain the clustering result:

[0080] Define the objective equation, the expression is:

[0081] ;

[0082] in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F is the Frobenius norm, , , and is the regularization parameter, tr is the trace of the matrix;

[0083] Find the Lagrangian function based on the objective function , the expression is:

[0084] ;

[0085] in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable;

[0086] According to the alternating direction multiplier method, update and ;

[0087] Calculate the similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

[0088] Furthermore, the clustering module is further configured to:

[0089] Update the noisy coefficient matrix by the following method :

[0090] Remove and Unrelated items, update The sub-problems are:

[0091] ;

[0092] Will update The sub-problem of Derivation, then The final solution is expressed as:

[0093] ;

[0094] in:

[0095] ;

[0096] The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm;T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter, I is the identity matrix;

[0097] Update the clean coefficient matrix by :

[0098] Remove and Unrelated items, update The sub-problems are:

[0099] ;

[0100] Will update The sub-problem of Derivation, determination The update formula is:

[0101] ;

[0102] Update the matrix by :

[0103] Remove and Unrelated items, update The sub-problems are:

[0104] ;

[0105] in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve:

[0106] Update the approximation consistent matrix by the following method :

[0107] Remove and Unrelated items, update The sub-problems are:

[0108] ;

[0109] Update the Solve the sub-problems of

[0110] Update the Lagrange multiplier matrix by the following formula :

[0111] ;

[0112] in, Y 2 represents the updated Lagrange multiplier matrix, Y 1 represents the Lagrange multiplier matrix before updating.

[0113] Furthermore, the clustering module is further configured to perform a simplex projection algorithm on the quadratic form problem. P To solve:

[0114] Input Vector and scalar ;

[0115] right Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest and minimum values ​​in ;

[0116] turn up ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension,

[0117] definition ;in, is the intermediate parameter;

[0118] Output ;in, is an element of n+1 dimensional space, is the real number real.

[0119] Furthermore, the first calculation module is further configured to calculate the node degree matrix by the following formula:

[0120] ;

[0121] Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

[0122] The beneficial effects of the present invention are:

[0123] 1. Hypergraph regularization: Hypergraph regularization can capture high-order relationships of data and enhance the global structure expression ability of subspace clustering.

[0124] 2. Two-layer structure: The denoised sparse representation matrix C helps to improve the robustness and accuracy of clustering.

[0125] 3. Sparsity constraint: Sparse regularization enhances the robustness of the model and reduces the impact of noise on clustering results. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 A flowchart of a double-layer structure sparse subspace clustering method based on hypergraph regularization according to an embodiment of the present invention is shown.

[0127] Figure 2 A comparison curve of the image clustering accuracy between the present invention and the existing method is shown.

[0128] Figure 3 A structural diagram of a double-layer structure sparse subspace clustering system based on hypergraph regularization according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0129] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0130] The specific implementation of the present invention is further described in detail below in conjunction with the drawings and examples.

[0131] The embodiment of the present invention provides a double-layer structure sparse subspace clustering method based on hypergraph regularization, which is used to process high-dimensional and complex data and significantly improve the accuracy and efficiency of data clustering. Figure 1 FIG. 4 shows a flowchart of a double-layer structure sparse subspace clustering method based on hypergraph regularization according to an embodiment of the present invention. Figure 1 As shown, the method includes steps S100 to S700, which are described in detail as follows.

[0132] S100: Obtain image data to be clustered.

[0133] S200: Calculate the node degree matrix.

[0134] In some embodiments, the node degree matrix is ​​calculated by the following formula:

[0135] ;

[0136] Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

[0137] S300: Calculate the hyper-edge degree matrix.

[0138] In some embodiments, the hyperedge degree matrix is ​​calculated by the following formula:

[0139] ;

[0140] in, represents the hyperedge degree matrix.

[0141] S400: Calculate the hypergraph matrix.

[0142] In some embodiments, the hypergraph matrix is ​​calculated by the following formula: :

[0143] ;

[0144] in, are diagonal matrices, and the element values ​​are respectively and Decide, is the relationship matrix between nodes and hyperedges, is the hyperedge weight matrix, which represents the weight of each hyperedge.

[0145] S500: Define and initialize the factor matrices of the hypergraph regularized two-layer structure sparse subspace clustering.

[0146] S600: Set the number of iterations.

[0147] S700: Obtain a hypergraph regularized double-layer structure sparse subspace clustering update formula to obtain a clustering result.

[0148] In this embodiment, step S700 specifically includes the following steps:

[0149] S710: Define the target equation, the expression is:

[0150] ;

[0151] in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F is the Frobenius norm, , , and is the regularization parameter, tr is the trace of the matrix.

[0152] S720: Find the Lagrangian function based on the objective function , the expression is:

[0153] ;

[0154] in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable.

[0155] S730: Update the values ​​of the alternating direction multipliers respectively. and .

[0156] In some embodiments, step S730 includes:

[0157] Update the noisy coefficient matrix by the following method :

[0158] Remove and Unrelated items, update The sub-problems are:

[0159] ;

[0160] Will update The sub-problem of Derivation, then The final solution is expressed as:

[0161] ;

[0162] in:

[0163] ;

[0164] The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm; T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter, I is the identity matrix;

[0165] Update the clean coefficient matrix by :

[0166] Remove and Unrelated items, update The sub-problems are:

[0167] ;

[0168] Will update The sub-problem of Derivation, determination The update formula is:

[0169] ;

[0170] Update the matrix by :

[0171] Remove and Unrelated items, update The sub-problems are:

[0172] ;

[0173] in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve.

[0174] In some embodiments, the quadratic problem is solved by a simplex projection algorithm.P Solve, including:

[0175] S7310: Input vector and scalar ;

[0176] S7320: Yes Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest and minimum values ​​in ;

[0177] S7330: Found ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension,

[0178] S7340: Definition ;in, is the intermediate parameter;

[0179] S7350: Output ;in, is an element of n+1 dimensional space, is the real number real.

[0180] Update the approximation consistent matrix by the following method :

[0181] Remove and Unrelated items, update The sub-problems are:

[0182] ;

[0183] Update the Solve the sub-problem of .

[0184] Update the Lagrange multiplier matrix by the following formula :

[0185] ;

[0186] in, Y 2 represents the updated Lagrange multiplier matrix, Y1 represents the Lagrange multiplier matrix before updating.

[0187] S740: Calculate similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

[0188] In this embodiment, based on the update formula of each matrix obtained above, each factor matrix is ​​optimized and updated at the tth iteration. When t does not reach the set number of iterations, t=t+1, and each factor matrix is ​​optimized and updated again until the set number of iterations is reached. Here, the consistency matrix is ​​obtained. , and calculate the similarity matrix , for the similarity matrix Perform spectral clustering and obtain clustering results.

[0189] The feasibility and advancement of the present invention are further described in detail below in conjunction with simulation experiments.

[0190] The hardware test platform used in the simulation experiment of the embodiment of the present invention is: the processor is InterCorei7, the main frequency is 2.20GHz, and the memory is 32GB; the software platform is: Windows 10 Home Edition 64-bit operating system, MatlabR2022a for simulation.

[0191] Taking image data as the data to be clustered, a specific implementation step of the double-layer structure sparse subspace clustering method based on hypergraph regularization is as follows:

[0192] Step 1, input data: original data matrix X, hypergraph Laplacian matrix , as well as the hypergraph regularization parameter and the sparsity constraint parameter.

[0193] Step 2: Two-layer sparse representation:

[0194] Construct the noisy sparse coefficient matrix Z and the denoised sparse coefficient matrix C;

[0195] Define the data reconstruction error to ensure that Z and C can effectively represent the local and global relationships of the data.

[0196] Step 3, hypergraph regularization:

[0197] Adding a hypergraph regularization term to the objective function , high-order data relations are represented by hypergraphs, preserving local geometric structures.

[0198] Step 4, objective function definition:

[0199] The objective function consists of the following parts:

[0200] Data reconstruction error: ;

[0201] Hypergraph regularization term: ;

[0202] Double-layer structure constraints: ;

[0203] Sparsity regularization term: ;

[0204] Graph connectivity constraints: .

[0205] Step 5: Set constraints:

[0206] The non-negativity and normalization of matrices C and S are ensured by the following constraints:

[0207] ;

[0208] : Data reconstruction error, ensure that the value of the C matrix is ​​physically reasonable. Ensure that the value of the C matrix is ​​physically reasonable.

[0209] : Normalize the columns of matrix C.

[0210] : Normalize the columns of the matrix S.

[0211] :s is The constant of the interval.

[0212] Step 6, Optimization: Use the alternating optimization method to iteratively update variables such as Z, C, and S until convergence.

[0213] Specifically, Lagrangian functions are constructed for Z, C, and S respectively, and the update formula is derived. The alternating optimization method is used to update Z, C, and S successively until the objective function converges.

[0214] Step 7, clustering output: Get the consistent matrix S and calculate ; Perform spectral clustering on W and obtain the clustering results.

[0215] In the embodiment of the present invention, a simulation experiment of the image clustering method is carried out on the image data, and the clustering accuracy of the image clustering method is compared with that of the existing method under different number of categories. Figure 2 In the experiment, 10% of the pixels were randomly selected as training samples, and the rest were used as test samples. After 10 independent runs, the average value was taken as the final clustering accuracy.

[0216] Figure 2 It is a comparison curve of the image clustering accuracy of the present invention and the existing methods, showing the comparison of clustering accuracy obtained after image clustering on the selected image data set PIE by three existing methods (NMF, SSC, GNMF) and the present invention (HDSSC). Figure 2 The horizontal axis represents the number of selected categories k, and the vertical axis represents the clustering accuracy (%). Figure 2 The curve marked with a triangle represents the result of the NMF method simulation experiment, the curve marked with a plus sign represents the result of the SSC method simulation experiment, the curve marked with a circle represents the result of the GNMF method simulation experiment, and the curve marked with a square represents the result of the simulation experiment of the present invention. Figure 2 It can be seen that for the image dataset PIE, under different selected category numbers, the accuracy of the present invention is higher than that of other algorithms. From the graphical analysis, the accuracy curve of the present invention is always above the curves of other algorithms, and the clustering accuracy is the highest.

[0217] The embodiment of the present invention also provides a double-layer structure sparse subspace clustering system based on hypergraph regularization, please refer to Figure 3 , the system comprises:

[0218] A data acquisition module 301 is configured to acquire image data to be clustered;

[0219] A first calculation module 302 is configured to calculate a node degree matrix;

[0220] A second calculation module 303 is configured to calculate a hyper-edge degree matrix;

[0221] A third calculation module 304 is configured to calculate a hypergraph matrix;

[0222] The matrix definition module 305 is configured to define and initialize the matrix of each factor of the hypergraph regular double-layer structure sparse subspace clustering;

[0223] An iteration setting module 306 is configured to set the number of iterations;

[0224] The clustering module 307 is configured to obtain a hypergraph regular double-layer structure sparse subspace clustering update formula to obtain a clustering result:

[0225] Define the objective equation, the expression is:

[0226] ;

[0227] in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F is the Frobenius norm, , , and is the regularization parameter, tr is the trace of the matrix;

[0228] Find the Lagrangian function based on the objective function , the expression is:

[0229] ;

[0230] in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable;

[0231] According to the alternating direction multiplier method, update and ;

[0232] Calculate the similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

[0233] In some embodiments, the clustering module is further configured to:

[0234] Update the noisy coefficient matrix by the following method :

[0235] Remove and Unrelated items, update The sub-problems are:

[0236] ;

[0237] Will update The sub-problem of Derivation, then The final solution is expressed as:

[0238] ;

[0239] in:

[0240] ;

[0241] The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm; T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter, I is the identity matrix;

[0242] Update the clean coefficient matrix by :

[0243] Remove and Unrelated items, update The sub-problems are:

[0244] ;

[0245] Will update The sub-problem of Derivation, determination The update formula is:

[0246] ;

[0247] Update auxiliary variables by :

[0248] Remove and Unrelated items, update The sub-problems are:

[0249] ;

[0250] in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve:

[0251] Update the approximation consistent matrix by the following method :

[0252] Remove and Unrelated items, update The sub-problems are:

[0253] ;

[0254] Update the Solve the sub-problems of

[0255] Update the Lagrange multiplier matrix by the following formula :

[0256] ;

[0257] in, Y 2 represents the updated Lagrange multiplier matrix, Y 1 represents the Lagrange multiplier matrix before updating.

[0258] In some embodiments, the clustering module is further configured to perform a simplex projection algorithm on the quadratic form problem. P To solve:

[0259] Input Vector and scalar ;

[0260] right Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest and minimum values ​​in ;

[0261] turn up ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension,

[0262] definition ;in, is the intermediate parameter;

[0263] Output ;in, for, for.

[0264] In some embodiments, the first calculation module is further configured to calculate the node degree matrix by the following formula:

[0265] ;

[0266] Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

[0267] It should be noted that the double-layer structure sparse subspace clustering system based on hypergraph regularization belongs to the same technical concept as the previously described method, and has the same technical principles and beneficial effects, so it will not be repeated here.

[0268] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention should be defined by the claims.

Claims

1. A double-layer structure sparse subspace clustering method based on hypergraph regularization, characterized in that: The method comprises: Obtain image data to be clustered; Calculate the node degree matrix; Calculate the hyperedge degree matrix; Compute the hypergraph matrix; Define and initialize the factor matrices of the hypergraph regularized two-layer structure sparse subspace clustering; Set the number of iterations; Obtain the hypergraph regularized two-layer structure sparse subspace clustering update formula to obtain the clustering result; Obtain the hypergraph regularized two-layer structure sparse subspace clustering update formula to obtain the clustering results, including: Define the objective equation, the expression is: ； in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F is the Frobenius norm, , , and is the regularization parameter, tr is the trace of the matrix; Find the Lagrangian function based on the objective function , the expression is: ； in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable; According to the alternating direction multiplier method, update and ; Calculate the similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

2. The method according to claim 1, characterized in that According to the alternating direction multiplier method, update and ,include: Update the noisy coefficient matrix by the following method : Remove and Unrelated items, update The sub-problems are: ； Will update The sub-problem of Derivation, then The final solution is expressed as: ； in: ； The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm; T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter, I is the identity matrix; Update the clean coefficient matrix by : Remove and Unrelated items, update The sub-problems are: ； Will update The sub-problem of Derivation, determination The update formula is: ； Update auxiliary variables by : Remove and Unrelated items, update The sub-problems are: ； in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve: Update the approximation consistent matrix by the following method : Remove and Unrelated items, update The sub-problems are: ； Update the Solve the sub-problems of Update the Lagrange multiplier matrix by the following formula : ； in, Y 2 represents the updated Lagrange multiplier matrix, Y 1 represents the Lagrange multiplier matrix before updating.

3. The method according to claim 2, characterized in that The classic quadratic problem is solved by the simplex projection algorithm P Solve, including: Input Vector and scalar ; right Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest and minimum values ​​in ; turn up ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension, definition ;in, is the intermediate parameter; Output ;in, is an element of n+1 dimensional space, is the real number real.

4. The method according to claim 1, characterized in that The node degree matrix is ​​calculated using the following formula: ； Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

5. The method according to claim 4, characterized in that The hyperedge degree matrix is ​​calculated by the following formula; ； in, represents the hyperedge degree matrix.

6. The method according to claim 5, characterized in that The hypergraph matrix is ​​calculated by the following formula : ； in, are diagonal matrices, and the element values ​​are respectively and Decide, is the relationship matrix between nodes and hyperedges, is the hyperedge weight matrix, which represents the weight of each hyperedge.

7. A double-layer sparse subspace clustering system based on hypergraph regularization, characterized in that: The system comprises: A data acquisition module, configured to acquire image data to be clustered; A first computing module is configured to compute a node degree matrix; A second computing module is configured to calculate a hyperedge degree matrix; A third computing module is configured to compute a hypergraph matrix; A matrix definition module is configured to define and initialize each factor matrix of the hypergraph regularized two-layer structure sparse subspace clustering; An iteration setting module, configured to set the number of iterations; The clustering module is configured to obtain the hypergraph regular double-layer structure sparse subspace clustering update formula to obtain the clustering result: Define the objective equation, the expression is: ； in, is the objective equation for the hypergraph regularized two-layer sparse subspace clustering, represents the data matrix, is the coefficient matrix with noise, is the clean coefficient matrix, is the consistent matrix of the approximation, is the hypergraph Laplacian matrix, represents the matrix transpose, s for The constant of the interval, F for, , , and for, tr for; Find the Lagrangian function based on the objective function , the expression is: ； in, for, is the Lagrange multiplier matrix, is the adaptive balance parameter, is an auxiliary variable; According to the alternating direction multiplier method, update and ; Calculate the similarity matrix , , for the similarity matrix Perform spectral clustering and obtain clustering results.

8. The system according to claim 7, characterized in that The clustering module is further configured to: Update the noisy coefficient matrix by the following method : Remove and Unrelated items, update The sub-problems are: ； Will update The sub-problem of Derivation, then The final solution is expressed as: ； in: ； The final solution of is a standard Sylvester equation, solved by the Bartels-Stewart algorithm; T A is the first construction matrix, T B is the second construction matrix, T C is the third construction matrix, is the regularization parameter, I is the identity matrix; Update the clean coefficient matrix by : Remove and Unrelated items, update The sub-problems are: ； Will update The sub-problem of Derivation, determination The update formula is: ； Update auxiliary variables by : Remove and Unrelated items, update The sub-problems are: ； in, P represents a quadratic problem, , the quadratic problem is solved by the simplex projection algorithm P To solve: Update the approximation consistent matrix by the following method : Remove and Unrelated items, update The sub-problems are: ； Update the Solve the sub-problems of Update the Lagrange multiplier matrix by the following formula : ； in, Y 2 represents the updated Lagrange multiplier matrix, Y 1 represents the Lagrange multiplier matrix before updating.

9. The system according to claim 8, characterized in that The clustering module is further configured to perform a simplex projection algorithm on the quadratic form problem. P To solve: Input Vector and scalar ; right Sort and get ;in, is the vector to be found, , , are the sorted vectors The maximum, second largest and minimum values ​​in ; turn up ;in, is the optimal parameter, For vector Middle Quantity, is the index value, is the index value, is the feature space dimension, definition ;in, is the intermediate parameter; Output ;in, is an element of n+1 dimensional space, is the real number real.

10. The system according to claim 7, characterized in that The first calculation module is further configured to calculate the node degree matrix by the following formula: ； Among them, the hypergraph middle Represents a collection of nodes. represents the set of hyperedges, represents the weight set of hyperedges, Representation Node Is it a super edge? ,like ,but ,otherwise , Representation Node The degree matrix of .

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