Research On Block Diagonal Representation Based Spectral-type Subspace Clustering Algorithm

Subspace clustering research refers to the fact that the high-dimensional datasets are approximately drawn from a union of multiple different low-dimensional subspaces,and how to accurately divide these high-dimensional datasets into corresponding subspaces.In recent years,with the rapid development of the Internet of Things and edge comput-ing,a large amount of the high-dimensional nonlinear visual data is generated at the edge of the network,and these high-dimensional data contain a lot of rich and useful information.Finding the discriminative representation of data and effectively completing the data clustering is the key to achieve the efficient utilization of data,and is also one of the current research hotspots.The block diagonal representation subspace clustering algorithm has been an important direction in recent years,and has been successfully ap-plied in motion segmentation,face and object image clustering,image segmentation and other application fields.This thesis starts from the nonlinear characteristic of the visu-al data,the characteristic of the visual data residing on the Riemannian manifold,the multi-view characteristic of the visual data and the feature extraction ability of the deep neural network,studying the block diagonal representation based spectral-type subspace clustering algorithm to improve the clustering accuracy of the high-dimensional nonlinear visual data in complex backgrounds.The main work of this thesis is as follows.To solve the problem that the kernel subspace clustering algorithm uses a fixed kernel and the mapped feature space cannot ensure the low-rankness,an adaptive low-rank kernel block diagonal representation subspace clustering algorithm is proposed.The basic principle of the block diagonal representation subspace clustering algorithm is that the data is in the linear subspace model,but the actual visual data does not necessarily lie in a union of the linear subspaces,so the kernel method is introduced to deal with the nonlinear data.First,the original input space is mapped to the Reproducing kernel Hilbert space（RKHS）which is linearly separable,and then the clustering algorithm is applied in this feature space,and a kernel block diagonal representation subspace clustering algorithm is proposed.The adaptive low-rank kernel block diagonal representation subspace clustering algorithm is further designed,making the adaptive kernel matrix approach to the pre-defined kernel matrix,and enforcing the nuclear norm on the mapped feature space to make the RKHS space conform to the desired subspace structure.The experiments on the face and object dataset verify the effectiveness of the two algorithms,and the parameter analysis,time complexity and convergence analysis of the two algorithms are also given.To solve the problem that the adaptive low-rank kernel block diagonal representation subspace clustering algorithm only uses the feature in the Euclidean space,while the ac-tual visual data resides on the Riemannian manifold,and that the fusion of representation matrices in different spaces is considered,a multi-geometric block diagonal representation subspace clustering algorithm with the low rank kernel is proposed.The multi-geometric feature and the measuring method in the Riemannian manifold are introduced,and a multi-geometric block diagonal representation subspace clustering algorithm is proposed.In addition,the feature data in different spaces is mapped to the Reproducing kernel Hilbert space,and a multi-geometric kernel block diagonal representation subspace clus-tering algorithm is proposed.Meanwhile,for each mapped reproducing kernel Hilbert space,the multi-geometric block diagonal representation subspace clustering algorithm with the low-rank kernel makes the adaptive kernel matrix approach to the pre-defined kernel matrix,and enforces the nuclear norm on the mapped feature space.The experi-ments on the face and object dataset verify the effectiveness of these three algorithms,and the parameter analysis,ablation experiment,time complexity and convergence analysis of these three algorithms are also given.To address the problem of the deficiency of the l₁ or l₂ regularizer for not directly pursuing the block diagonal representation matrix in the deep subspace clustering net-work,and that the interdependence between the representation matrix and segmentation matrix is not considered,a self-supervised convolutional subspace clustering network with the block diagonal prior is proposed.A block diagonal regularizer is applied to the weight of the self-expressive module,replacing the original l₁ or l₂ regularizer.Meanwhile,a spectral clustering module is introduced to supervise the learning of the representation matrix and make it more discriminative.Compared with traditional clustering algorithm using raw image features,the self-supervised convolutional subspace clustering network with block diagonal prior can extract more discriminative image features.Simulation results show that the proposed self-supervised convolutional subspace clustering network achieves good clustering performance on face and object datasets.To address the problem that the deep subspace clustering network only uses the original single image feature,and there exists some redundancy among the multiple rep-resentation matrices generated by the multi-view subspace clustering algorithm,and a multi-view subspace clustering network with the block diagonal and diverse representa-tion is proposed.Based on the deep subspace clustering network,the network constructs multiple deep autoencoders for multi-view data to extract more discriminative image fea-tures for subsequent clustering.Meanwhile,the block diagonal regularizer is applied to the weight of the self-expression module to directly find the block diagonal representation matrix.Based on the Hilbert-schmidt independence criterion（HSIC）,a diverse repre-sentation module is introduced to reduce the redundancy among multiple representation matrices to make the representation matrices more discriminative and diverse.Exper-iments on several multi-view datasets verify the effectiveness of the algorithm,and the parameter analysis,ablation experiment,time complexity and convergence analysis are also given.