Clustering method based on deformation image similarity learning

Abstract

The invention relates to a clustering method based on deformation image similarity learning. The method comprises the following steps: S1, inputting an unaligned image data matrix # imgabs0 #; s2, initializing a spectrum characteristic matrix # imgabs 1 # and a rotation transformation vector # imgabs 2 #, and initializing an incidence matrix # imgabs 3 # by using an unaligned image data matrix; s3, setting the number of iterations t, sequentially iterating the initialized incidence matrix, spectrum characteristic matrix and rotation transformation vector by using the initialized incidence matrix, spectrum characteristic matrix and rotation transformation vector and adopting an alternating optimization strategy until the number of iterations is finished, and obtaining an optimized spectrum characteristic matrix; and S4, discretizing the optimized spectrum characteristic matrix to obtain a final clustering result. By designing the efficient deformation image clustering method, accurate clustering of unaligned images is achieved, and the method can be used for clustering research on deformation images.

Description

Technical Field

[0001] The present invention relates to the technical field of image clustering, and in particular to a clustering method based on deformation image similarity learning. Background Art

[0002] Image clustering has important application value in the fields of computer vision and image processing. It can help discover structured information from a large amount of image data and is used in many fields such as image retrieval, video analysis, and medical image analysis. Traditional image clustering methods usually rely on low-level features such as color, texture, and shape to calculate the similarity between images. However, the performance of these methods is seriously degraded when processing complex images or when there are large changes in viewing angles, and the obtained clustering results are not accurate. Therefore, studying how to accurately extract the main features of the original data and linearize the data space to obtain a higher quality association matrix, and then obtain a more accurate clustering result, has become a key direction in the study of image clustering methods. At present, most image clustering methods focus on solving simpler association matrices for the features of sparse data in order to solve the situation where the data is complex and nonlinear, but these methods often cannot make full use of the spatial structure characteristics of the data, resulting in limited clustering accuracy. Therefore, developing an image clustering method that effectively understands the spatial structure of data is not only innovative in theory, but also has important strategic value in practical applications. Summary of the invention

[0003] The present invention aims to provide a clustering method based on deformed image similarity learning, which linearizes the nonlinear space of data by performing adaptive optimization of rotation transformation, similarity learning and spectral clustering on severely deformed images at the same time, generates a higher quality correlation matrix, and obtains a better quality spectral feature matrix, so as to achieve the effect of improving clustering accuracy. The method of the present invention can not only improve the relevance of data samples, but also ignore interference factors such as noise to a certain extent, and realize accurate clustering of unaligned images.

[0004] In the first aspect, to achieve the above-mentioned object, the present invention provides the following solutions:

[0005] A clustering method based on deformation image similarity learning, comprising:

[0006] S1. Input unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers;

[0007] S2. Initialize the spectral feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector;

[0008] S3. Set the number of iterations t, use the initialized correlation matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the correlation matrix, spectral feature matrix and rotation transformation vector in turn, until the number of iterations ends, and obtain the optimized spectral feature matrix;

[0009] S4. Spectral feature matrix after discretization optimization , and obtain the final clustering result.

[0010] Optionally, initialize the spectral feature matrix , rotation transformation vector and the incidence matrix ,include:

[0011] Initialize the spectral feature matrix is a random matrix, all elements are not less than 0;

[0012] Initialize the rotation transformation vector is a vector of all 1s;

[0013] Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows:

[0014]

[0015] in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

[0016] Optionally, the alternating optimization strategy includes:

[0017] S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows:

[0018]

[0019] in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows:

[0020]

[0021] in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of

[0022] Among them, the spectral relationship matrix The calculation formula is as follows:

[0023]

[0024] in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ;

[0025] Among them, the composite rotation matrix The calculation formula is as follows:

[0026]

[0027] in, represents the spatial convolution operation, express The transpose of

[0028] S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows:

[0029]

[0030] S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows:

[0031]

[0032] in, represents the rotation transformation of the jth deformed image, express The increment is calculated as:

[0033]

[0034] in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as:

[0035]

[0036] in, is the symbol of partial derivative, yes The corresponding differential variable.

[0037] Optionally, discretize the spectral feature matrix The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is:

[0038]

[0039] in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

[0040] On the other hand, to achieve the above object, the present invention also provides the following solution:

[0041] A clustering system based on deformation image similarity learning, the system comprising: an input module, an initialization module, an iteration module and a discretization module;

[0042] The input module is used to input the unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers;

[0043] The initialization module is used to initialize the spectrum feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector;

[0044] The iterative module is used to set the number of iterations t, use the initialized association matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the association matrix, spectral feature matrix and rotation transformation vector in sequence, until the number of iterations is completed, and obtain the optimized spectral feature matrix;

[0045] The discretization module is used to discretize the optimized spectral feature matrix , and obtain the final clustering result.

[0046] Optionally, the spectral feature matrix is ​​initialized in the initialization module , rotation transformation vector and the incidence matrix ,include:

[0047] Initialize the spectral feature matrix is a random matrix, all elements are not less than 0;

[0048] Initialize the rotation transformation vector is a vector of all 1s;

[0049] Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows:

[0050]

[0051] in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

[0052] Optionally, the alternating optimization strategy in the iterative module includes:

[0053] S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows:

[0054]

[0055] in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows:

[0056]

[0057] in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of

[0058] Among them, the spectral relationship matrix The calculation formula is as follows:

[0059]

[0060] in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ;

[0061] Among them, the composite rotation matrix The calculation formula is as follows:

[0062]

[0063] in, represents the spatial convolution operation, express The transpose of

[0064] S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows:

[0065]

[0066] S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows:

[0067]

[0068] in, represents the rotation transformation of the jth deformed image, express The increment is calculated as:

[0069]

[0070] in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as:

[0071]

[0072] in, is the symbol of partial derivative, yes The corresponding differential variable.

[0073] Optionally, the discretization spectral feature matrix in the discretization module is The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is:

[0074]

[0075] in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

[0076] The beneficial effects of the present invention are:

[0077] The present invention introduces the rotation transformation vector The data matrix is ​​rotated to seek a linearly represented similarity structure. At this time, the data samples will become highly correlated, and the similarity learning effect will be better, thus obtaining a better correlation matrix.

[0078] The present invention imposes a restriction on the association matrix through similarity learning, so that the association matrix has a stronger block diagonalization feature and better quality.

[0079] Similarity learning and spectral clustering are unified into the same framework to further improve the performance of the overall model. The joint problem can be efficiently solved through the alternating optimization method. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0081] Figure 1 A schematic diagram of a clustering method based on deformation image similarity learning according to an embodiment of the present invention;

[0082] Figure 2 This is an example diagram of the image alignment effect of an embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0084] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] like Figure 1 As shown, this embodiment proposes a clustering method based on deformation image similarity learning, including:

[0086] S1. Input unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers;

[0087] S2. Initialize the spectral feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector;

[0088] S3. Set the number of iterations t, use the initialized correlation matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the correlation matrix, spectral feature matrix and rotation transformation vector in turn, until the number of iterations ends, and obtain the optimized spectral feature matrix;

[0089] S4. Spectral feature matrix after discretization optimization , and obtain the final clustering result.

[0090] The technical idea of ​​this embodiment is to build a joint model that optimizes similarity learning and spectral clustering methods at the same time, and use rotation transformation to linearize the nonlinear space of severely deformed images to achieve the effect of improving the accuracy of clustering unaligned images. First, input the original image data matrix , that is, the unaligned image data matrix; initialize the correlation matrix , spectral feature matrix and the rotation transformation vector ; Through the alternating optimization strategy, when optimizing a certain matrix variable, the other two matrix variables are fixed, and in this process a higher quality correlation matrix is ​​obtained ; Correlation matrix It is used to calculate the spectral feature matrix F, and the rotation transformation vector Z is adaptively optimized at the same time to obtain the continuous spectral feature matrix under this model. ; Finally, the discretized spectral feature matrix To ensure the clustering results.

[0091] Furthermore, initialize the spectral feature matrix , rotation transformation vector and the incidence matrix ,include:

[0092] Initialize the spectral feature matrix is a random matrix, all elements are not less than 0;

[0093] Initialize the rotation transformation vector is a vector of all 1s;

[0094] Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows:

[0095]

[0096] in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

[0097] Furthermore, the alternating optimization strategy includes:

[0098] S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows:

[0099]

[0100] in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows:

[0101]

[0102] in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of

[0103] Among them, the spectral relationship matrix The calculation formula is as follows:

[0104]

[0105] in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ;

[0106] Among them, the composite rotation matrix The calculation formula is as follows:

[0107]

[0108] in, represents the spatial convolution operation, express The transpose of

[0109] S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows:

[0110]

[0111] S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows:

[0112]

[0113] in, represents the rotation transformation of the jth deformed image, express The increment is calculated as:

[0114]

[0115] in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as:

[0116]

[0117] in, is the symbol of partial derivative, yes The corresponding differential variable.

[0118] Furthermore, the discretized spectral feature matrix The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is:

[0119]

[0120] in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

[0121] More specifically, this embodiment also performs data simulation, as follows:

[0122] Simulation conditions

[0123] This embodiment is tested in a data set, and the data set used is described in the following Table 1:

[0124] Table 1 Description of the datasets used in the experiment

[0125]

[0126] The experiment uses Python programming language for code simulation, and the computer configuration is (R) Core(TM) i7-13700KF 3.40 GHz 32.0 GB.

[0127] Simulation Method

[0128] The comparison method includes four traditional spectral clustering methods and three advanced spectral clustering methods. These seven clustering methods are compared with the results of the present invention to verify the superiority of the present invention. These methods are:

[0129] Method 1, Ncut: Normalized cutting.

[0130] Method 2, Rcut: Ratio cutting.

[0131] Method 3, KM: K-means.

[0132] Method 4, SR: spectral rotation.

[0133] Method 5, LSC: Large-Scale Spectral Clustering based on Landmark Representation.

[0134] Method 6, DnC-SC: Large-scale spectral clustering based on divide-and-conquer.

[0135] Method 7, CESC: Refining the k-nearest neighbor graph for computationally efficient spectral clustering.

[0136] Simulation content:

[0137] This embodiment uses three evaluation indicators, namely clustering accuracy (ACC), normalized mutual information (NMI) and purity (PUR), to evaluate clustering performance. Clustering accuracy refers to the proportion of samples that are correctly clustered among all samples. Normalized mutual information is used to measure the consistency between clustering labels and actual sample labels. Purity represents the sum of the proportions of correct samples and total samples in each group. The larger the value, the better the performance. The experimental results are shown in Tables 2-4. The results are all shown in percentages, and the best results are marked in bold.

[0138] Table 2 ACC (%) results of all methods

[0139]

[0140] Table 3 NMI (%) results of all methods

[0141]

[0142] Table 4 PUR (%) results of all methods

[0143]

[0144] It can be seen from the experimental results on all data sets that the method proposed in this embodiment is superior to other methods. In addition, this embodiment shows excellent performance in all three indicators. As can be seen from Table 2, compared with the second-ranked algorithm on the ORL image data set, this embodiment achieves significant improvements of 21.5%, 14.76% and 20% in clustering accuracy, normalized mutual information and purity, respectively. The image alignment effect of this embodiment is as follows: Figure 2 shown.

[0145] In summary, the present invention introduces the rotation transformation vector Align the data and seek a linearly expressed similarity structure. At this time, the data samples will become highly correlated, thus obtaining a better correlation matrix. Similarity learning makes the correlation matrix have stronger block diagonal characteristics and better quality. Unifying similarity learning and spectral clustering into the same framework can further improve the performance of the overall model. The algorithm can be solved efficiently through alternating optimization methods.

[0146] This embodiment also proposes a clustering system based on deformation image similarity learning, including: an input module, an initialization module, an iteration module and a discretization module;

[0147] Input module for inputting unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers;

[0148] Input module for inputting unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers;

[0149] Initialization module, used to initialize the spectral feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector;

[0150] An iteration module is used to set the number of iterations t, use the initialized association matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the association matrix, spectral feature matrix and rotation transformation vector in sequence, until the number of iterations is reached, and obtain the optimized spectral feature matrix;

[0151] Discretization module, used to discretize the optimized spectral feature matrix , and obtain the final clustering result.

[0152] Furthermore, the spectral feature matrix is ​​initialized in the initialization module , rotation transformation vector and the incidence matrix ,include:

[0153] Initialize the spectral feature matrix is a random matrix, all elements are not less than 0;

[0154] Initialize the rotation transformation vector is a vector of all 1s;

[0155] Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows:

[0156]

[0157] in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

[0158] Furthermore, the alternating optimization strategies in the iteration module include:

[0159] S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows:

[0160]

[0161] in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows:

[0162]

[0163] in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of

[0164] Among them, the spectral relationship matrix The calculation formula is as follows:

[0165]

[0166] in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ;

[0167] Among them, the composite rotation matrix The calculation formula is as follows:

[0168]

[0169] in, represents the spatial convolution operation, express The transpose of

[0170] S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows:

[0171]

[0172] S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows:

[0173]

[0174] in, represents the rotation transformation of the jth deformed image, express The increment is calculated as:

[0175]

[0176] in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as:

[0177]

[0178] in, is the symbol of partial derivative, yes The corresponding differential variable.

[0179] Furthermore, the discretization spectral feature matrix in the discretization module The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is:

[0180]

[0181] in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

[0182] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A clustering method based on deformation image similarity learning, characterized in that: include: S1. Input unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers; S2. Initialize the spectral feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector; S3. Set the number of iterations t, use the initialized correlation matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the correlation matrix, spectral feature matrix and rotation transformation vector in turn, until the number of iterations ends, and obtain the optimized spectral feature matrix; S4. Spectral feature matrix after discretization optimization , and obtain the final clustering result.

2. The clustering method based on deformation image similarity learning according to claim 1, characterized in that: Initialize the spectral feature matrix , rotation transformation vector and the incidence matrix ,include: Initialize the spectral feature matrix is a random matrix, all elements are not less than 0; Initialize the rotation transformation vector is a vector of all 1s; Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows: in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

3. The clustering method based on deformation image similarity learning according to claim 1, characterized in that: The alternating optimization strategy includes: S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows: in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows: in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of Among them, the spectral relationship matrix The calculation formula is as follows: in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ; Among them, the composite rotation matrix The calculation formula is as follows: in, represents the spatial convolution operation, express The transpose of S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows: S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows: in, represents the rotation transformation of the jth deformed image, express The increment is calculated as: in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as: in, is the symbol of partial derivative, yes The corresponding differential variable.

4. The clustering method based on deformation image similarity learning according to claim 1, characterized in that: Discretized spectral feature matrix The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is: in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

5. A clustering system based on deformation image similarity learning, characterized in that: Used to implement the clustering method according to any one of claims 1 to 4, the system comprises: an input module, an initialization module, an iteration module and a discretization module; The input module is used to input the unaligned image data matrix ,in, represents the dimension of the image sample, represents the number of image samples, represents the field of real numbers; The initialization module is used to initialize the spectrum feature matrix and the rotation transformation vector , using the unaligned image data matrix , initialize the incidence matrix ,in, represents the number of clusters, Represents the dimension of the rotation vector; The iterative module is used to set the number of iterations t, use the initialized association matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy, iteratively optimize the association matrix, spectral feature matrix and rotation transformation vector in sequence until the number of iterations is reached, and obtain the optimized spectral feature matrix; The discretization module is used to discretize the optimized spectral feature matrix , and obtain the final clustering result.

6. The clustering system based on deformation image similarity learning according to claim 5, characterized in that: The initialization module initializes the spectral feature matrix , rotation transformation vector and the incidence matrix ,include: Initialize the spectral feature matrix is a random matrix, all elements are not less than 0; Initialize the rotation transformation vector is a vector of all 1s; Utilizing unaligned image data matrices , initialize the incidence matrix , the calculation formula is as follows: in, is a matrix The i-th row and j-th column element of and Respectively represent matrices The i-th column vector and the j-th column vector of is the control parameter, represents the 2-norm of a vector, The k nearest neighbor represents the distance among N image samples Recent image samples, The k nearest neighbor represents the distance among N image samples Recent Image samples.

7. The clustering system based on deformation image similarity learning according to claim 5, characterized in that: The alternating optimization strategy in the iterative module includes: S31. Fixed spectral feature matrix and the rotation transformation vector , optimize the association matrix , the calculation formula is as follows: in, represents the coefficient matrix, yes The transposed matrix of The j-th column vector of The calculation formula is as follows: in, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, Represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, Represents a composite rotation matrix The j-th column vector of express The inverse matrix of Among them, the spectral relationship matrix The calculation formula is as follows: in, Represents the spectral relationship matrix The i-th row and j-th column element of and Represent the spectral feature transposed matrix The i-th and j-th column vectors of ; Among them, the composite rotation matrix The calculation formula is as follows: in, represents the spatial convolution operation, express The transpose of S32. Fixed correlation matrix and the rotation transformation vector , optimize the spectral feature matrix The method is to calculate the Laplacian matrix Before The smallest non-zero eigenvectors are composed of matrices, where the Laplace matrix The element in row i and column j The calculation formula is as follows: S33. Fixed correlation matrix Sum spectral feature matrix , optimize the rotation transformation vector The formula is as follows: in, represents the rotation transformation of the jth deformed image, express The increment is calculated as: in, Representation coefficient matrix The j-th column vector of Indicates the rotation transformation vector of the jth image The generalized inverse matrix of the Jacobi matrix at is calculated as: in, is the symbol of partial derivative, yes The corresponding differential variable.

8. The clustering system based on deformation image similarity learning according to claim 5, characterized in that: The discretization module discretizes the spectral feature matrix The method is: using The position of the maximum value in the i-th row is used as the cluster label of the i-th image, and the calculation formula is: in, represents the cluster label of the i-th image, Represents the optimized spectral feature matrix The element at row i and column j.

Images