A clustering method based on learning the similarity of deformed images

Abstract

The present invention relates to a clustering method based on the learning of deformed image similarity. S1. Input the unaligned image data matrix #imgabs0#; S2. Initialize the spectral feature matrix #imgabs1# and the rotation transformation vector #imgabs2#, and use the unaligned image data matrix to initialize the association matrix #imgabs3#; S3. Set the number of iterations t. Using the initialized association matrix, spectral feature matrix and rotation transformation vector, adopt an alternating optimization strategy to iteratively initialize the association matrix, spectral feature matrix and rotation transformation vector in turn until the number of iterations ends, and obtain the optimized spectral feature matrix; S4. Discretize the optimized spectral feature matrix to obtain the final clustering result. The present invention realizes the accurate clustering of unaligned images by designing an efficient deformed image clustering method, and can be used for the clustering research of deformed images.

Description

Technical Field

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

[0002] Image clustering has important application values in the fields of computer vision and image processing. It can help discover structured information from a large amount of image data and be used in multiple 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 severely degrades when dealing with complex images or images with large perspective changes, and the obtained clustering results have low accuracy. Therefore, researching 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 clustering result with higher accuracy, has become a key direction in the research of image clustering methods. Currently, most image clustering methods focus on solving a simpler association matrix for the features of sparse data in order to deal with the complex and non-linear situation of data, but these methods often cannot fully utilize the spatial structure characteristics of the data, resulting in limited clustering accuracy. Therefore, developing an image clustering method that can effectively understand the spatial structure of the data not only has innovation 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 similarity learning of deformed images. By simultaneously performing adaptive optimization of rotation transformation, similarity learning, and spectral clustering on severely deformed images, the non-linear space of the data is linearized, a higher-quality association matrix is generated, and a better spectral feature matrix is obtained, so as to achieve the effect of improving the clustering accuracy. The method of the present invention can not only improve the correlation of data samples but also, to a certain extent, ignore interference factors such as noise, and achieve precise clustering of unaligned images.

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

[0005] A clustering method based on similarity learning of deformed images, comprising:

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

[0007] S2. Initialize the spectral feature matrix and the rotation transformation vector , and use the unaligned image data matrix , initialize the association matrix , where represents the number of clusters, represents the dimension of the rotation vector;

[0008] S3. Set the number of iterations t. Using the initialized association matrix, spectral feature matrix, and rotation transformation vector, adopt the alternating optimization strategy to iteratively optimize the association 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. Discretize the optimized spectral feature matrix to obtain the final clustering result.

[0010] Optionally, initialize the spectral feature matrix , rotation transformation vector and association matrix , including:

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

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

[0013] Using the unaligned image data matrix , initialize the association matrix , and the calculation formula is as follows:

[0014]

[0015] where is the element in the i-th row and j-th column of the matrix , and respectively represent the i-th column vector and j-th column vector of the matrix , is the control parameter, represents the 2-norm of the vector, 's k nearest neighbors represent the nearest image samples among N image samples, 's k nearest neighbors represent the nearest image samples among N image samples.

[0016] Optionally, the alternating optimization strategy includes:

[0017] S31. Fix the spectral feature matrix and rotation transformation vector , Optimize the correlation matrix , The calculation formula is as follows:

[0018]

[0019] Among them, represents the coefficient matrix, is the transpose matrix of The j-th column vector of The calculation formula is as follows:

[0020]

[0021] Among them, is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relationship matrix, represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, represents the composite rotation matrix The j-th column vector of represents the inverse matrix of

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

[0023]

[0024] Among them, represents the element in the i-th row and j-th column of the spectral relationship matrix and respectively represent the i-th column and j-th column vectors of the spectral feature transpose matrix

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

[0026]

[0027] Among them, represents the spatial convolution operation, represents the spatial convolution operation, represents the transpose of

[0028] S32. Fix the correlation matrix and the rotation transformation vector , The method to optimize the spectral feature matrix is to calculate the first of the Laplacian matrix a matrix composed of the smallest non-zero eigenvectors, where the Laplacian matrix the element in the i-th row and j-th column has the following calculation formula:

[0029]

[0030] S33. Fix the incidence matrix and the spectral feature matrix and optimize the rotation transformation vector with the following formula:

[0031]

[0032] where represents the rotation transformation amount of the j-th deformed image, represents the increment of, and the calculation formula is:

[0033]

[0034] where represents the j-th column vector of the coefficient matrix , represents the generalized inverse matrix of the Jacobian matrix of the j-th image at the rotation transformation vector , and the calculation formula is:

[0035]

[0036] where is the partial derivative symbol, is the corresponding differential variable.

[0037] Optionally, the method for discretizing the spectral feature matrix is: using the position where the maximum value in the i-th row is located as the clustering label of the i-th image, and the calculation formula is:

[0038]

[0039] where represents the clustering label of the i-th image, represents the element in the i-th row and j-th column of the optimized spectral feature matrix .

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

[0041] A clustering system based on similarity learning of deformed images, the system includes: an input module, an initialization module, an iteration module, and a discretization module;

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

[0043] The initialization module is used to initialize the spectral feature matrix and the rotation transformation vector . Using the unaligned image data matrix , initialize the correlation matrix , where represents the number of clusters, represents the dimension of the rotation vector;

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

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

[0046] Optionally, in the initialization module, the spectral feature matrix , the rotation transformation vector , and the correlation matrix are initialized as follows:

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

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

[0049] Using the unaligned image data matrix , initialize the correlation matrix , and the calculation formula is as follows:

[0050]

[0051] where is the element in the i-th row and j-th column of the matrix , and respectively represent the i-th column vector and the j-th column vector of the matrix , is a control parameter, represents the 2-norm of the vector, The k-nearest neighbors of are the nearest image samples among N image samples, The k-nearest neighbors of are the nearest image samples among N image samples.

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

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

[0054]

[0055] where represents the coefficient matrix, is the transpose matrix of . The j-th column vector of

[0056]

[0057] is calculated as follows: is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relationship matrix, represents the spectral relationship matrix of the j-th column vector, represents the composite rotation matrix, represents the composite rotation matrix of the j-th column vector, represents the inverse matrix of

[0058] where the spectral relationship matrix is calculated as follows:

[0059]

[0060] where represents the element in the i-th row and j-th column of the spectral relationship matrix , and respectively represent the i-th column and j-th column vectors of the spectral feature transpose matrix ;

[0061] where the composite rotation matrix The calculation formula is as follows:

[0062]

[0063] Among them, represents the spatial convolution operation, represents the transpose of;

[0064] S32. Fix the association matrix and the rotation transformation vector The method for optimizing the spectral feature matrix is to calculate the matrix composed of the first non-zero eigenvectors of the Laplacian matrix . Among them, the element in the i-th row and j-th column of the Laplacian matrix has the following calculation formula:

[0065]

[0066] S33. Fix the association matrix and the spectral feature matrix The formula for optimizing the rotation transformation vector is as follows:

[0067]

[0068] Among them, represents the rotation transformation amount of the j-th deformed image, represents the increment of, and the calculation formula is:

[0069]

[0070] Among them, represents the j-th column vector of the coefficient matrix , represents the generalized inverse matrix of the Jacobian matrix at the rotation transformation vector for the j-th image, and the calculation formula is:

[0071]

[0072] Among them, is the partial derivative symbol, is the corresponding differential variable.

[0073] Optionally, the method for discretizing the spectral feature matrix in the discretization module is: using the position where the maximum value in the i-th row is located as the clustering label of the i-th image, and the calculation formula is:

[0074]

[0075] wherein, represents the clustering label of the i-th image, represents the element at the i-th row and j-th column of the optimized spectral feature matrix of the i-th row and j-th column.

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

[0077] The present invention introduces a rotation transformation vector to perform a rotation transformation on the data matrix, seeking a similarity structure of a linear representation. At this time, the data samples will become highly correlated, and the similarity learning effect is better, thereby obtaining a better correlation matrix.

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

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

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0081] Figure 1 is a schematic flowchart of a clustering method based on similarity learning of deformed images according to an embodiment of the present invention;

[0082] Figure 2 is an example diagram of the image alignment effect according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention.

[0084] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

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

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

[0087] S2. Initialize the spectral feature matrix and the rotation transformation vector , and use the unaligned image data matrix to initialize the association matrix , where represents the number of clusters, represents the dimension of the rotation vector;

[0088] S3. Set the number of iterations t, and use the initialized association matrix, spectral feature matrix, and rotation transformation vector. Adopt an alternating optimization strategy to iteratively optimize the association 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. Discretize the optimized spectral feature matrix to obtain the final clustering result.

[0090] The technical idea of this embodiment is: construct a joint model that simultaneously optimizes the similarity learning and spectral clustering methods, use rotation transformation to linearize the non-linear space of severely deformed images, and achieve the effect of improving the accuracy when clustering unaligned images. First, input the original image data matrix , that is, the unaligned image data matrix; initialize the association matrix , spectral feature matrix and rotation transformation vector ; through the alternating optimization strategy, fix the other two matrix variables when optimizing a certain matrix variable, and obtain a higher-quality association matrix in this process; the association matrix 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, discretize the spectral feature matrix to ensure that the clustering result is obtained.

[0091] Furthermore, initializing the spectral feature matrix , rotation transformation vector and association matrix includes:

[0092] Initialize the spectral feature matrix as a random matrix with all elements not less than 0;

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

[0094] Use the unaligned image data matrix to initialize the correlation matrix with the following calculation formula:

[0095]

[0096] where, is the element in the i-th row and j-th column of matrix , and respectively represent the i-th column vector and j-th column vector of matrix , is the control parameter, represents the 2-norm of the vector, 's k nearest neighbors represent the nearest image samples among N image samples, 's k nearest neighbors represent the nearest image samples among N image samples.

[0097] Furthermore, the alternating optimization strategy includes:

[0098] S31. Fix the spectral feature matrix and the rotation transformation vector , and optimize the correlation matrix with the following calculation formula:

[0099]

[0100] where, represents the coefficient matrix, is 's transpose matrix, 's j-th column vector has the following calculation formula:

[0101]

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

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

[0104]

[0105] Among them, represents the element in the i-th row and j-th column of the spectral relationship matrix of and respectively represent the i-th column and j-th column vectors of the spectral feature transpose matrix of

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

[0107]

[0108] Among them, represents the spatial convolution operation represents The transpose of

[0109] S32. Fix the association matrix and the rotation transformation vector , the method to optimize the spectral feature matrix is to calculate the matrix composed of the first non-zero eigenvectors of the Laplacian matrix of , among which, the element in the i-th row and j-th column of the Laplacian matrix The calculation formula is as follows:

[0110]

[0111] S33. Fix the association matrix and the spectral feature matrix , the formula to optimize the rotation transformation vector is as follows:

[0112]

[0113] Among them, represents the rotation transformation amount of the j-th deformed image represents The increment of , and the calculation formula is:

[0114]

[0115] Among them, represents the j-th column vector of the coefficient matrix , and represents the generalized inverse matrix of the Jacobian matrix of the j-th image at the rotation transformation vector . The calculation formula is:

[0116]

[0117] Among them, is the partial derivative symbol, is 's corresponding differential variable.

[0118] Furthermore, the method for discretizing the spectral feature matrix is: Using the position where the maximum value in the i-th row is located as the clustering label of the i-th image. The calculation formula is:

[0119]

[0120] Among them, represents the clustering label of the i-th image, represents the optimized spectral feature matrix 's element in the i-th row and j-th column.

[0121] More specifically, data simulation was also carried out in this embodiment, as follows:

[0122] Simulation conditions

[0123] This embodiment was tested in the dataset, and the dataset used is described in Table 1 below:

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

[0125]

[0126] The experiment was carried out using the Python programming language for code simulation, and the computer configuration was (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 respectively:

[0129] Method 1, Ncut: Normalized cut.

[0130] Method 2, Rcut: Ratio Cut.

[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: Refined k-Nearest Neighbor Graph for Efficient Spectral Clustering.

[0136] Simulation Content:

[0137] In this embodiment, three evaluation metrics, namely clustering accuracy (ACC), normalized mutual information (NMI), and purity (PUR), are used to evaluate the clustering performance. The clustering accuracy refers to the proportion of correctly clustered samples among all samples. The normalized mutual information is used to measure the consistency between the clustering labels and the actual sample labels. The purity represents the sum of the proportions of correct samples and total samples in each cluster. The larger the value, the better the performance. The experimental results are shown in Tables 2 - 4, and the results are all presented in percentage form, with the best results 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 datasets that the method proposed in this embodiment outperforms other methods. In addition, this embodiment shows excellent performance in all three metrics. As can be seen from Table 2, compared with the second-ranked algorithm on the ORL image dataset, this embodiment has achieved 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 Figure 2 shown.

[0145] In summary, the present invention introduces a rotation transformation vector Align the data and seek a similarity structure in a linear representation. 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 diagonalization characteristics and better quality. Unifying similarity learning and spectral clustering into the same framework can further improve the performance of the overall model, and the algorithm can be efficiently solved by the method of alternating optimization.

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

[0147] The input module is used to input an unaligned image data matrix , where, represents the dimension of the image sample, represents the number of image samples, represents the real number field;

[0148] The input module is used to input an unaligned image data matrix , where, represents the dimension of the image sample, represents the number of image samples, represents the real number field;

[0149] The initialization module is used to initialize the spectral feature matrix and the rotation transformation vector , and use the unaligned image data matrix to initialize the correlation matrix , where, represents the number of clusters, represents the dimension of the rotation vector;

[0150] The iteration module is used to set the number of iterations t, and use the initialized correlation matrix, spectral feature matrix, and rotation transformation vector, and adopt an alternating optimization strategy to 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;

[0151] The discretization module is used to discretize the optimized spectral feature matrix to obtain the final clustering result.

[0152] Furthermore, in the initialization module, initializing the spectral feature matrix , the rotation transformation vector and the correlation matrix includes:

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

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

[0155] Using the unaligned image data matrix , initialize the association matrix , and the calculation formula is as follows:

[0156]

[0157] where is the element in the i-th row and j-th column of the matrix , and respectively represent the i-th column vector and the j-th column vector of the matrix , is the control parameter, represents the 2-norm of the vector, The k-nearest neighbors of represent the image samples closest to among N image samples, The k-nearest neighbors of represent the

[0158] image samples closest to

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

[0160]

[0161] where represents the coefficient matrix, is the transpose matrix of The j-th column vector of is calculated as follows:

[0162]

[0163] where is the weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relationship matrix, represents the spectral relationship matrix The j-th column vector of represents the composite rotation matrix, represents the composite rotation matrix The j-th column vector of denotes the inverse matrix of

[0164] where the spectral relationship matrix is calculated as follows:

[0165]

[0166] where denotes the element in the i-th row and j-th column of the spectral relationship matrix ; and respectively denote the i-th column and j-th column vectors of the spectral feature transpose matrix ;

[0167] where the composite rotation matrix is calculated as follows:

[0168]

[0169] where represents the spatial convolution operation, denotes the transpose of

[0170] S32. Fix the correlation matrix and the rotation transformation vector , and the method to optimize the spectral feature matrix is to calculate the matrix composed of the first non-zero eigenvectors of the Laplacian matrix . Where the element in the i-th row and j-th column of the Laplacian matrix is calculated as follows:

[0171]

[0172] S33. Fix the correlation matrix and the spectral feature matrix , and the formula to optimize the rotation transformation vector is as follows:

[0173]

[0174] where denotes the rotation transformation amount of the j-th deformed image, denotes the increment of

[0175]

[0176] where Denote the coefficient matrix of the j-th column vector, Denote the generalized inverse matrix of the Jacobian matrix of the j-th image at the rotation transformation vector , and the calculation formula is:

[0177]

[0178] Wherein, is the partial derivative symbol, is the corresponding differential variable.

[0179] Furthermore, the method for discretizing the discretized spectral feature matrix in the discretization module is: Use the position where the maximum value of the i-th row is located as the clustering label of the i-th image, and the calculation formula is:

[0180]

[0181] Wherein, denotes the clustering label of the i-th image, denotes the element in the i-th row and j-th column of the optimized spectral feature matrix .

[0182] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A clustering method based on learning the similarity of deformed images, characterized in that, Including: S1. Input the misaligned image data matrix , where represents the dimension of the image sample, represents the number of image samples, represents the real number field; S2. Initialize the spectral feature matrix and the rotation transformation vector , and use the misaligned image data matrix to initialize the correlation matrix , where represents the number of clusters, represents the dimension of the rotation vector; S3. Set the number of iterations t. Using the initialized association matrix, spectral feature matrix, and rotation transformation vector, adopt an alternating optimization strategy to iteratively optimize the association matrix, spectral feature matrix, and rotation transformation vector in sequence until the number of iterations ends, and obtain the optimized spectral feature matrix; S4. The discretized and optimized spectral feature matrix , and obtain the final clustering result; Initialize the spectral feature matrix , rotation transformation vector and correlation matrix , including: Initialize the spectral feature matrix is a random matrix, and all elements are not less than 0; Initialize the rotation transformation vector to a vector of all ones; Using misaligned image data matrices , initialize the correlation matrix , and the calculation formula is as follows: Among them, is the element in the \(i\)-th row and \(j\)-th column of the matrix , and respectively represent the \(i\)-th column vector and \(j\)-th column vector of the matrix , is a control parameter represents the 2-norm of the vector The \(k\) nearest neighbors of refer to the image samples that are the closest to in the \(N\) image samples, and the \(k\) nearest neighbors of refer to the image samples that are the closest to The alternating optimization strategy includes: S31. Fixed spectral feature matrix and rotation transformation vector , optimize the correlation matrix , and the calculation formula is as follows: Among them, represents the coefficient matrix, is the transpose matrix of The j-th column vector of The calculation formula is as follows: Among them, is a weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relationship matrix, represents the spectral relationship matrix of the j-th column vector, represents the composite rotation matrix, represents the composite rotation matrix of the j-th column vector, represents the inverse matrix of; Among them, the spectral relationship matrix has the following calculation formula: Among them, represents the element in the i-th row and j-th column of the spectral relationship matrix , and respectively represent the i-th column and j-th column vectors of the spectral feature transposed matrix ; Among them, the composite rotation matrix has the following calculation formula: Among them, represents a spatial convolution operation, represents the transpose of; S32. Fixed association matrix and rotation transformation vector , the method for optimizing the spectral feature matrix is to calculate the matrix composed of the first non-zero eigenvectors of the Laplacian matrix . Among them, the element in the i-th row and j-th column of the Laplacian matrix is calculated as follows: S33. Fixed association matrix and spectral feature matrix , the formula for optimizing the rotation transformation vector is as follows: Among them, represents the rotation transformation amount of the j-th deformed image, represents the increment of, and the calculation formula is: Among them, represents the j-th column vector of the coefficient matrix , and represents the generalized inverse matrix of the Jacobian matrix of the j-th image at the rotation transformation vector . The calculation formula is as follows: Among them, is the partial derivative symbol, and is the corresponding differential variable.

2. The clustering method based on deformed image similarity learning according to claim 1, wherein Discretized spectral feature matrix The method is as follows: Using The position of the maximum value in the i-th row as the clustering label of the i-th image, and the calculation formula is: wherein, represents the clustering label of the i-th image, represents the optimized spectral feature matrix the element at the i-th row and j-th column.

3. A clustering system based on the learning of the similarity of deformed images, characterized in that, For implementing the clustering method as described in any one of claims 1 - 2, the system includes: an input module, an initialization module, an iteration module, and a discretization module; The input module is used to input an unaligned image data matrix , where represents the dimension of the image sample, represents the number of image samples, represents the real number field; The initialization module is used to initialize the spectral feature matrix and the rotation transformation vector , and initialize the correlation matrix by using the unaligned image data matrix , where represents the number of clusters, represents the dimension of the rotation vector; The 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, and iteratively optimize the association matrix, spectral feature matrix, and rotation transformation vector in sequence until the number of iterations ends, 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; Initialize the spectral feature matrix in the initialization module , rotation transformation vector and correlation matrix , including: Initialize the spectral feature matrix is a random matrix, and all elements are not less than 0; Initialize the rotation transformation vector as a vector of all ones; Using misaligned image data matrices , initialize the association matrix , and the calculation formula is as follows: Among them, is the element in the i-th row and j-th column of the matrix , and respectively represent the i-th column vector and the j-th column vector of the matrix , is the control parameter, represents the 2-norm of the vector, The k-nearest neighbors of refer to the image samples that are the closest to among the N image samples, and the k-nearest neighbors of refer to the image samples that are the closest to The alternating optimization strategy in the iteration module includes: S31. Fixed spectral feature matrix and rotation transformation vector , optimize the correlation matrix , and the calculation formula is as follows: Among them, represents the coefficient matrix, is the transposed matrix of, The j-th column vector of The calculation formula is as follows: Among them, is a weight parameter, represents the identity matrix, represents the transpose of the identity matrix, represents the spectral relation matrix, represents the spectral relation matrix of the j-th column vector, represents the composite rotation matrix, represents the composite rotation matrix of the j-th column vector, represents the inverse matrix of; Among them, the spectral relationship matrix has the following calculation formula: Among them, represents the element in the i-th row and j-th column of the spectral relationship matrix , and and respectively represent the i-th column and j-th column vectors of the spectral feature transposed matrix ; Among them, the composite rotation matrix has the following calculation formula: Among them, represents a spatial convolution operation, represents the transpose of; S32. Fixed association matrix and rotation transformation vector , the method for optimizing the spectral feature matrix is to calculate the matrix formed by the first non-zero eigenvectors of the Laplacian matrix where the element in the i-th row and j-th column of the Laplacian matrix is calculated as follows:​ S33. Fixed association matrix and spectral feature matrix , the formula for optimizing the rotation transformation vector is as follows: Among them, represents the rotation transformation amount of the j-th deformed image, represents the increment of, and the calculation formula is: Among them, represents the j-th column vector of the coefficient matrix , and represents the generalized inverse matrix of the Jacobian matrix of the j-th image at the rotation transformation vector . The calculation formula is as follows: Among them, is the partial derivative symbol, and is the corresponding differential variable.

4. The clustering system based on deformation image similarity learning according to claim 3, characterized in that The discretized spectral feature matrix in the discretization module The method is as follows: Using The position of the maximum value in the i-th row as the clustering label of the i-th image, and the calculation formula is: Among them, represents the clustering label of the i-th image, represents the optimized spectral feature matrix the element in the i-th row and j-th column.

Images