Manifold relation maintenance-based incomplete multi-view face image depth anchor image clustering method

Abstract

An incomplete multi-view face image depth anchor image clustering method based on manifold relationship maintenance belongs to the field of face image data processing in multimedia information processing, and comprises the following steps: firstly, constructing a subspace feature for each view through a graph neural network, and then maintaining an original feature and the subspace features by adopting a manifold relationship; meanwhile, anchor points specific to the view angle are randomly selected to be combined with the common subspace, the similarity between the result and original data is compared, gradient descent optimization is carried out on the network for many times, spectral clustering is carried out after a common subspace anchor map with discrimination is obtained, and finally the clustering result and accuracy are obtained. Compared with other methods, the method is higher in accuracy and more stable in performance.

Description

Technical Field

[0001] The present invention belongs to the field of face image data processing in multimedia information processing, and in particular relates to an incomplete multi-view face image data clustering method based on anchor point subspace and manifold relationship maintenance. Background Art

[0002] In the multimedia field, face images can be collected from a variety of different angles. Through information from depth images, RGB images and other angles, face images can be further analyzed. Among many technologies, the anchor subspace incomplete multi-view clustering method has been proven to be effective in recent practice. However, in the process of multi-view data collection, the data source is not comprehensive and cannot cover all perspectives, resulting in data missing and unbalanced collected samples, which leads to the problem of incomplete face image data processing. Because the existing methods can only solve the face image clustering problem under complete data sets, there is an urgent need for an efficient and novel clustering method to solve the incomplete problem in the field of face image data processing. Summary of the invention

[0003] A method for clustering incomplete multi-view face image depth anchor graphs based on manifold relationship maintenance, characterized in that the method comprises the steps of:

[0004] The existing sample features are extracted from an incomplete multi-view face image dataset, and each component of all feature vectors is normalized to the interval [0,1].

[0005] A k-nearest neighbor graph matrix is ​​constructed from the existing features and a multi-view common subspace learning network consisting of multiple view-specific graph convolutional encoding layers, a feature fusion layer, and a common subspace output layer is constructed, and the network weights are randomly initialized.

[0006] For each viewing angle, a high-dimensional manifold distribution matrix and n a learnable anchor points, whose initial value is samples uniformly randomly sampled from the view. The existing sample features of all viewpoints and the corresponding k nearest neighbor graph matrix are input into the subspace learning network, and the common subspace matrix output by the network is multiplied by the learnable anchor points of each viewpoint one by one to reconstruct the original features of each viewpoint. The corresponding loss function is the common subspace self-representation loss function. At the same time, a manifold regularization constraint is imposed on the representation learned by the network to obtain the manifold regularized common subspace self-representation overall loss function.

[0007] The common subspace learning network is trained to convergence using a mini-batch stochastic gradient descent algorithm to minimize the manifold-regularized common subspace self-representation overall loss function.

[0008] Perform spectral clustering on the common subspace learned by the converged network to obtain a final clustering result. According to the obtained clustering result, calculate the clustering accuracy on the incomplete multi-view face image dataset.

[0009] Furthermore, for the original face image dataset, extract each existing sample:

[0010]

[0011] in represents all the existing characteristics of the original data, represents the existence characteristics of the perspective v, d v represents the sample feature dimension under the viewing angle v, n v represents the total number of samples under the viewing angle v, and m represents the total number of all viewing angles;

[0012] Normalize the feature vector of sample i at each viewing angle v so that its value ranges between [0,1]:

[0013]

[0014] Where n is the number of samples, and Respectively represent the viewing angle v Maximum and minimum values ​​in a collection of vectors;

[0015] Furthermore, according to the standardized existing sample features, the corresponding adjacency matrix is ​​constructed for each view. Specifically, the matrix for view v is Construct the corresponding graph relation adjacency undirected graph matrix C v :

[0016]

[0017] in represents the connection relationship between samples i and j under the perspective v, and represents the 10 samples closest to sample i and sample j under view v. Each sample is equivalent to a node in the graph. If two nodes are in the set of 10 nearest neighboring samples on any side of each other, then the edge weight between the two nodes is set to 1, otherwise it is set to 0.

[0018] Through the above operations, the existence sample features of each perspective are obtained and the corresponding graph adjacency matrix C v, we need to further combine the two and perform iterative updates to better capture the geometric relationship between samples. The graph convolutional network is used as the feature extractor as input. The graph convolutional neural network feature extraction module used specifically includes two layers:

[0019]

[0020] Among them, ReLU represents the nonlinear activation function, BatchNorm represents the batch normalization operation, and They represent two independent graph convolutional neural network layers in the two layers under the perspective v, and They represent the output results of the two layers respectively. The input of the first layer is the sample features and their corresponding graph adjacency network, while the second layer receives the output results of the first layer. and C v Taken together as input, the output result is obtained Where d is the size of the common dimension of different perspectives after dimensionality reduction by the graph neural network;

[0021] Get the output results from different perspectives In the following, it is referred to as H v In order to fuse the results of multiple perspectives, let the indicator matrix of missing data be M∈{0,1} n×m , if sample j under the i-th perspective exists, then M ij =1, otherwise M ij = 0, due to the absence of H, each view generates v If the dimensions are not equal, they cannot be simply added. First, a new matrix of all zeros is created for each perspective. It is assigned to H by v Values:

[0022]

[0023] In the formula, H v The value of is assigned to the non-missing sample position through the missing indicator matrix, and the remaining positions are zero values. Then the subspace features of the graph under different perspectives are fused:

[0024]

[0025] Where H is the common subspace matrix.

[0026] The common subspace output layer is defined as follows:

[0027] Z = softmax(linear(H))

[0028] Among them, Linear is a fully connected layer with weights and biases, and softmax is an activation function layer that normalizes the sum of each row of the subspace matrix to 1; is the common subspace matrix of the network output, is the representation learned by the network; d is the feature dimension of the learned representation, n a is the number of anchor points,

[0029] Furthermore, a high-dimensional manifold distribution matrix is ​​constructed for each viewpoint where samples exist, and n a learnable anchor points, and initialized to n randomly sampled from the perspective a samples.

[0030] The high-dimensional manifold distribution matrix of the viewing angle v is defined as follows:

[0031]

[0032] in, are the feature vectors of samples i, j, l, and k respectively; is the Gaussian kernel width of sample i, determined by the perplexity parameter ppl. represents the probability that sample i is a neighbor of sample j in high-dimensional space; is the manifold distribution matrix P v The element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the high-dimensional space; ||·|| F Represents the F-norm of a matrix. It describes the manifold distribution of samples in high-dimensional space, so it is called a high-dimensional manifold distribution matrix.

[0033] For each perspective v, construct n a There are learnable anchor points, whose initial value is n randomly sampled from the view. a samples, defined as follows:

[0034]

[0035] v=1,2,…,m

[0036] Among them, the matrix v = 1, 2, ..., m represents the learnable anchor points of each view, which are initialized to n randomly sampled from the view. a samples, n a represents the number of anchor points; random-sample(X,c) means extracting c samples from the feature matrix X by uniform sampling.

[0037] The existing sample features of all perspectives and the corresponding k-nearest neighbor graph matrix are input into the subspace learning network, and the common subspace matrix output by the network is multiplied by the learnable anchor points of each perspective one by one to reconstruct the original features of each perspective. The corresponding loss function is the common subspace self-representation loss function. At the same time, a manifold regularization constraint is imposed on the representation learned by the network to obtain the manifold regularized common subspace self-representation overall loss function, which is defined as follows:

[0038]

[0039] Among them, L subspace is the common subspace self-representation loss function, M :,v represents the vth column of the missing indicator matrix, Z is the common subspace matrix of the network output, is the existence characteristic of the perspective v, C v is a learnable anchor point of perspective v; ||·|| F Represents the F-norm of the matrix.

[0040] The manifold regularization maintenance constraint of the network is defined as follows:

[0041]

[0042] Among them, Q v is the low-dimensional manifold distribution matrix of the viewing angle v, which is defined as follows:

[0043]

[0044] in, They are the representation vectors of samples i, j, l, and k corresponding to the view v represented by the network. is the matrix Q v The element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the low-dimensional space.

[0045] The common subspace self-representation loss function of the manifold regularization is given by the common subspace self-representation loss function L subspace and the manifold regularization constraint L reg Composition, which is defined as follows:

[0046] L=L subspace +λ·L reg

[0047] Where λ>0 is a trade-off parameter and L is the common subspace self-representation overall loss function of the manifold regularization.

[0048] Furthermore, the common subspace self-representation overall loss function L of the manifold regularization is minimized using a mini-batch stochastic gradient descent algorithm, and the common subspace learning network is trained to convergence. The update rules for the network weights and the learnable anchors for each view are defined as follows:

[0049]

[0050] v=1,2,…,m

[0051] Where Θ is the network weight, α is the learning rate, and L b _ is the overall loss function value estimated on the mini-batch data, yes Partial derivative with respect to the network weight Θ; C v It is a learnable anchor point. yes About Learnable Anchor Point C v The above update rule is applied repeatedly until The value of converges.

[0052] Furthermore, according to the clustering result, a clustering accuracy is calculated.

[0053] The present invention provides a manifold relationship-maintained incomplete multi-view face image deep anchor graph clustering method, which has the following advantages:

[0054] (1) The objective function of multi-view common subspace learning is utilized. The learned common subspace can simultaneously represent the original features of each view and fully exploit the multi-view common subspace structure.

[0055] (2) Use deep neural networks to learn the mapping relationship between multi-view high-dimensional manifold features and low-dimensional manifolds of graph structure subspace matrices, so as to better capture the nonlinear relationship between the two.

[0056] (3) The model can perform continuous predictions on small batches of streaming data, which can reduce system latency and memory usage, making it more suitable for real-time prediction scenarios.

[0057] (4) By utilizing learnable anchors, the locally optimal anchors are learned during network training, thus avoiding inflexible and non-optimal pre-specified anchors. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] 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 or the description of the prior art 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.

[0059] Figure 1 It is a flow chart of a manifold relationship-maintained incomplete multi-view face image deep anchor graph clustering method provided by the present invention;

[0060] Figure 2 It is a schematic diagram of a partial face image; DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0062] Exemplary Methods

[0063] like Figure 1 The present invention provides a manifold relationship-based incomplete multi-view face image deep anchor graph clustering method, the method steps are as follows:

[0064] Step S110: First, use the view missing matrix M∈{0,1} n×m Get the existence sample of the original input data where d v represents the sample feature dimension under the viewing angle v, n v represents the total number of samples under the viewing angle v, and m represents the total number of all viewing angles; then the feature vector of sample i under each viewing angle v is standardized so that its value range is between [0,1], and its expression formula is as follows:

[0065]

[0066] Where n is the number of samples, and Respectively represent the viewing angle v Maximum and minimum values ​​in a collection of vectors;

[0067] Step S120: For each view v Construct the corresponding undirected graph adjacency matrix The expression formula is as follows:

[0068]

[0069] in represents the connection relationship between samples i and j under the perspective v, and represents the 10 samples closest to sample i and sample j under the viewing angle v, and then C v and As input, a graph neural network is used to extract features, and its expression formula is as follows:

[0070]

[0071] Among them, ReLU represents the nonlinear activation function, BatchNorm represents the batch normalization operation, and Represent two independent graph convolutional neural network layers in the two layers under the perspective v, and then set a new matrix of all zeros for each perspective It is assigned to H by v Values:

[0072]

[0073] In the formula, H v The value of is assigned to the non-missing sample position through the missing indicator matrix, and the remaining positions are zero values. Then the subspace features of the graph under different perspectives are fused:

[0074]

[0075] Where H is the common subspace matrix, and the common subspace output layer is defined as follows:

[0076] Z = softmax(linear(H))

[0077] Among them, Linear is a fully connected layer with weights and biases, and softmax is an activation function layer that normalizes the sum of each row of the subspace matrix to 1; is the common subspace matrix of the network output,

[0078] Step S130: For each viewpoint, there are samples The following expression formula is used to construct the high-dimensional manifold distribution matrix:

[0079]

[0080] in, are the feature vectors of samples i, j, l, and k respectively; is the Gaussian kernel width of sample i, which is determined by the perplexity parameter ppl, and here we set its value to 0.3. represents the probability that sample i is a neighbor of sample j in high-dimensional space; is the manifold distribution matrix P vThe element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the high-dimensional space; ||·|| F Represents the F-norm of the matrix.

[0081] For each perspective v, construct n a There are learnable anchor points, whose initial value is n randomly sampled from the view. a samples, defined as follows:

[0082]

[0083] v=1,2,…,m

[0084] Among them, the matrix v = 1, 2, ..., m represents the learnable anchor points of each view, which are initialized to n randomly sampled from the view. a samples, n a represents the number of anchor points; random-sample(X,c) means extracting c samples from the feature matrix X by uniform sampling.

[0085] The common subspace matrix output by the network is multiplied by the learnable anchor points of each view to reconstruct the original features of each view. The corresponding loss function is the common subspace self-representation loss function. At the same time, a manifold regularization constraint is imposed on the representation learned by the network to obtain the manifold regularized common subspace self-representation overall loss function, which is defined as follows:

[0086]

[0087] Among them, L subspace is the common subspace self-representation loss function, M :,v represents the vth column of the missing indicator matrix, Z is the common subspace matrix of the network output, is the existence characteristic of the perspective v, C v is a learnable anchor point of perspective v; ||·|| F Represents the F norm of the matrix. By comparing the high-dimensional manifold distribution matrix with sample features in the original data and its corresponding subspace H v The low-dimensional manifold of the network is used to regularize the manifold and maintain the constraint term as follows:

[0088]

[0089] Among them, Q v is the low-dimensional manifold distribution matrix of the viewing angle v, which is defined as follows:

[0090]

[0091] in, They are the representation vectors of samples i, j, l, and k corresponding to the view v represented by the network. is the matrix Q v The element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the low-dimensional space. v It describes the manifold distribution of samples in low-dimensional space, so it is called a low-dimensional manifold distribution matrix.

[0092] The common subspace self-representation loss function of the manifold regularization is given by the common subspace self-representation loss function L subspace and the manifold regularization constraint L reg Composition, which is defined as follows:

[0093] L=L subspace +λ·L reg

[0094] Where λ>0 is a trade-off parameter and L is the common subspace self-representation overall loss function of the manifold regularization.

[0095] S140: Use a mini-batch stochastic gradient descent algorithm to minimize the common subspace self-representation overall loss function L of the manifold regularization, and train the common subspace learning network to convergence. The update rules of the network weights and the learnable anchor points of each perspective are defined as follows:

[0096]

[0097] v=1,2,…,m

[0098] Where Θ is the network weight, α is the learning rate, is the overall loss function value estimated on the mini-batch data, yes Partial derivative with respect to the network weight Θ; C v It is a learnable anchor point. yes About Learnable Anchor Point C v The above update rule is applied repeatedly until The value of converges.

[0099] S150: Perform spectral clustering on the finally generated common subspace output result Z to obtain a final result and calculate its clustering accuracy.

[0100] Through this implementation, first, the corresponding existing sample features are obtained according to the missing indicator matrix and normalized. Then, the k-neighboring method is used to generate the corresponding matrix adjacency graph for each perspective. The graph convolutional neural network module uses the existing samples and the corresponding adjacency graph as input to obtain the low-dimensional subspace corresponding to the perspective. After these low-dimensional subspaces are fused, the common subspace output layer is used to activate the common subspace matrix. Then, the common subspace matrix is ​​multiplied by the learnable anchor points of each perspective one by one to reconstruct the original features of each perspective. In this process, the relationship between the existing sample features and the corresponding subspace features is maintained in a manifold manner, and then the small batch stochastic gradient descent algorithm is used to minimize the overall loss function. Finally, the spectral clustering method is used to cluster the common subspace matrix to obtain the final clustering result, and its clustering accuracy is calculated.

[0101] To further illustrate, assuming that an incomplete multi-view face image dataset is clustered according to this embodiment, a clustering result with a higher clustering accuracy than most methods will be obtained.

[0102] Detailed description of the invention Results

[0103] This implementation uses the public face dataset ORL-40 and simulates the incomplete ORL-40 face dataset according to different sample missing ratios.

[0104] The face image dataset is a grayscale image dataset that contains 40 different categories. The dataset has the following three perspectives:

[0105] View 1 is the grayscale view, which reflects the lighting changes, shadows, and large-scale structural information of the face, such as the contour of the face, the basic positions of the eyes, nose, and mouth, etc.

[0106] Perspective 2 is the LBP feature perspective, which reflects the microscopic texture information of the face, such as the fineness of the skin, wrinkles, and local changes in the facial area.

[0107] View 3 is the Gabor feature view, which extracts local texture information at different scales and directions, and can effectively extract facial edge features, such as eye contours, lip edges, and nose bridge lines.

[0108] In order to verify the superiority of this implementation (OURS), this implementation is compared with several existing methods for clustering ORL-40 face data, including FIMVC-VIA, PIMVC, DAIMC, FMVCC and other methods. The clustering accuracy (ACC) of these methods for five incomplete sample ratios on the above public datasets will be compared. The specific data comparison is shown in Table 1.

[0109] Table 1 Clustering accuracy of ORL-40 dataset (%)

[0110]

[0111]

[0112] By comparing the data in the above table, we can clearly see that OURS has achieved the best performance and significantly improved the clustering accuracy of the incomplete multi-view face image dataset. The quantitative results fully demonstrate the superiority of OURS, because OURS can better capture the perspective consistency information and perspective difference information in the incomplete multi-view animal image dataset. OURS improves the accuracy of the experiment and enhances the robustness to the incomplete face image dataset through graph convolution feature extraction, manifold subspace structure preservation method and anchor-based data reconstruction method. A large number of experiments have shown that this method is superior to existing methods. Regarding the setting of the parameters of this embodiment, in all experiments, the number of anchor points n a Set to 10c, where c is the number of clusters.

[0113] This embodiment proposes a manifold relationship-maintained incomplete multi-view face image deep anchor graph clustering method for clustering analysis of incomplete face image datasets commonly seen in life. By using deep learning technology and graph convolutional neural network to extract sample features of face images and optimize anchor points for data reconstruction, manifold technology is used to maintain the relationship between the original data space and the common subspace to better preserve the local geometric structure of the data. Finally, spectral clustering is used to cluster the common subspace to obtain the final clustering result and calculate the accuracy. The experimental results on five incomplete sample ratios of the public dataset ORL-40 show that this embodiment has a higher clustering accuracy than other methods and has better superiority.

[0114] It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principles of the present invention, and do not constitute a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modifications that fall within the scope and boundaries of the appended claims, or the equivalent forms of such scope and boundaries.

Claims

1. A manifold relationship-based incomplete multi-view face image deep anchor graph clustering method, characterized in that: The method comprises the steps of: Extract existing sample features from an incomplete multi-view face image dataset and normalize each component of all feature vectors to the [0,1] interval; Construct a k-nearest neighbor graph matrix from existing features, and build a multi-view common subspace learning network consisting of multiple view-specific graph convolutional encoding layers, a feature fusion layer, and a common subspace output layer, and randomly initialize the network weights; For each viewing angle, a high-dimensional manifold distribution matrix is ​​constructed based on the existing sample characteristics. At the same time, for each viewing angle, n a There are n learnable anchor points, whose initial value is uniformly randomly sampled from the viewpoint. a samples, the k nearest neighbor graph matrix and the corresponding existing sample features are jointly input into the subspace learning network, and the common subspace matrix output by the network is multiplied by the learnable anchor points of each perspective one by one to reconstruct the original features of each perspective. The corresponding loss function is the common subspace self-representation loss function. At the same time, a manifold regularization maintenance constraint is imposed on the representation learned by the network to obtain the manifold regularized common subspace self-representation overall loss function; Minimizing the self-representation overall loss function of the common subspace regularized by the manifold using a mini-batch stochastic gradient descent algorithm, training the common subspace learning network until convergence, and then performing spectral clustering on the common subspace learned by the converged network to obtain a final clustering result; According to the obtained clustering results, the clustering accuracy on the incomplete multi-view face image dataset is calculated.

2. According to the incomplete multi-view face image deep anchor graph clustering method based on manifold relationship maintenance in claim 1, it is characterized by: For the original face image dataset, extract each existing sample: in represents all the existing characteristics of the original data, represents the existence characteristics of the perspective v, d v represents the sample feature dimension under the viewing angle v, n v represents the total number of samples under the viewing angle v, and m represents the total number of all viewing angles; Normalize the feature vector of sample i at each viewing angle v so that its value ranges between [0,1]: Where n is the number of samples, and Respectively represent the viewing angle v The maximum and minimum values ​​in a vector collection.

3. The method for clustering incomplete multi-view face images based on manifold relationship maintenance according to claim 1, characterized in that: First, according to the standardized existing sample features, the corresponding adjacency matrix is ​​constructed for each perspective. Specifically, the matrix for perspective v is Construct the corresponding graph relation adjacency undirected graph matrix C v : in represents the connection relationship between samples i and j under the perspective v, and represents the 10 samples closest to sample i and sample j under view v. Each sample is equivalent to a node in the graph. If two nodes are in the set of 10 nearest neighboring samples on any side of each other, then the edge weight between the two nodes is set to 1, otherwise it is set to 0. Through the above operations, the existence sample features of each perspective are obtained and the corresponding graph adjacency matrix C v , we need to further combine the two and perform iterative updates to better capture the geometric relationship between samples. The graph convolutional network is used as the feature extractor as input. The graph convolutional neural network feature extraction module used specifically includes two layers: Among them, ReLU represents the nonlinear activation function, BatchNorm represents the batch normalization operation, and They represent two independent graph convolutional neural network layers in the two layers under the perspective v, and They represent the output results of the two layers respectively. The input of the first layer is the sample features and their corresponding graph adjacency network, while the second layer receives the output results of the first layer. and C v Taken together as input, the output result is obtained Where d is the size of the common dimension of different perspectives after dimensionality reduction by the graph neural network; Get the output results from different perspectives In the following, it is referred to as H v In order to fuse the results of multiple perspectives, let the indicator matrix of missing data be M∈{0,1} n×m , if sample j under the i-th perspective exists, then M ij =1, otherwise M ij = 0, due to the absence of H, each view generates v If the dimensions are not equal, they cannot be simply added. First, a new matrix of all zeros is created for each perspective. It is assigned to H by v Values: In the formula, H v The value of is assigned to the non-missing sample position through the missing indicator matrix, and the remaining positions are zero values. Then the subspace features of the graph under different perspectives are fused: Where H is the common subspace matrix, The common subspace output layer is defined as follows: Z = softmax(linear(H)) Among them, Linear is a fully connected layer with weights and biases, and softmax is an activation function layer that normalizes the sum of each row of the subspace matrix to 1; is the common subspace matrix of the network output, is the representation learned by the network; d is the feature dimension of the learned representation, n a is the number of anchor points.

4. The method for clustering incomplete multi-view face images based on manifold relationship maintenance according to claim 1, characterized in that: For each viewpoint where samples exist, a k-nearest neighbor graph matrix and a high-dimensional manifold distribution matrix are constructed. For each viewpoint, n a learnable anchor points, and initialized to n randomly sampled from the perspective a samples; The k-nearest-neighbor graph matrix A of view v v is defined as follows: in, is the k-nearest-neighbor graph matrix The element in the i-th row and j-th column of , i and j represent two nodes on the k-nearest neighbor graph respectively; N v (i) is the k-neighborhood of node i, which consists of the k nodes closest to node i; if there is an edge between node i and node j, then otherwise The high-dimensional manifold distribution matrix of the viewing angle v is defined as follows: in, are the feature vectors of samples i, j, l, and k respectively; is the Gaussian kernel width of sample i, determined by the perplexity parameter ppl, represents the probability that sample i is a neighbor of sample j in high-dimensional space; is the manifold distribution matrix P v The element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the high-dimensional space; ||·|| F represents the F norm of the matrix, the matrix It describes the manifold distribution of samples in high-dimensional space, so it is called a high-dimensional manifold distribution matrix; For each perspective v, construct n a There are learnable anchor points, whose initial value is n randomly sampled from the view. a samples, defined as follows: v=1,2,…,m Among them, the matrix v = 1, 2, ..., m represents the learnable anchor points of each view, which are initialized to n randomly sampled from the view. a samples, n a represents the number of anchor points, random-sample(X,c) means extracting c samples from the feature matrix X by uniform sampling; The existing sample features of all perspectives and the corresponding k-nearest neighbor graph matrix are input into the subspace learning network, and the common subspace matrix output by the network is multiplied by the learnable anchor points of each perspective one by one to reconstruct the original features of each perspective. The corresponding loss function is the common subspace self-representation loss function. At the same time, a manifold regularization constraint is imposed on the representation learned by the network to obtain the manifold regularized common subspace self-representation overall loss function, which is defined as follows: Among them, L subspace is the common subspace self-representation loss function, M :,v represents the vth column of the missing indicator matrix, Z is the common subspace matrix of the network output, is the existence characteristic of the perspective v, C v is a learnable anchor point of perspective v; ||·|| F represents the F norm of the matrix; The manifold regularization maintenance constraint of the network is defined as follows: Among them, Q v is the low-dimensional manifold distribution matrix of the viewing angle v, which is defined as follows: in, They are the representation vectors of samples i, j, l, and k corresponding to the view v represented by the network. is the matrix Q v The element in the i-th row and j-th column represents the probability that sample i and sample j are neighbors of each other in the low-dimensional space, Q v It describes the manifold distribution of samples in low-dimensional space, so it is called low-dimensional manifold distribution matrix; The common subspace self-representation loss function of the manifold regularization is given by the common subspace self-representation loss function L subspace and the manifold regularization constraint L reg Composition, which is defined as follows: L=L subspace +λ·L reg Where λ>0 is a trade-off parameter and L is the common subspace self-representation overall loss function of the manifold regularization.

5. The method for clustering incomplete multi-view face images based on manifold relationship maintenance according to claim 1, characterized in that: The common subspace self-representation overall loss function L of the manifold regularization is minimized using a mini-batch stochastic gradient descent algorithm, and the common subspace learning network is trained to convergence. The update rules for the network weights and the learnable anchors of each perspective are defined as follows: v=1,2,…,m Where Θ is the network weight, α is the learning rate, is the overall loss function value estimated on the mini-batch data, yes Partial derivative with respect to the network weight Θ; C v It is a learnable anchor point. yes About Learnable Anchor Point C v The above update rule is repeatedly applied until The value of converges.

6. The method for clustering incomplete multi-view face images based on manifold relationship maintenance according to claim 1, characterized in that: The final result is calculated by spectral clustering based on the obtained common subspace output, and its clustering accuracy on an incomplete multi-view face image dataset is calculated.

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