Improved Block Diagonal Representation Via Manifold Learning And Its Application Research

Many sparse subspace clustering methods are devoted to finding a representation model that can learn a proper representation coefficient matrix and representing sample points as a linear combination of other as simple points.The block diagonal representation model(BDR)constraints coefficient representation matrix in a block-diagonal form directly,which effectively promotes subspace segmentation and improves subspace clustering performance.The BDR cannot well capture and utilize the inherent nonlinear manifold structure information of high-dimensional data because of the limitation that sparse subspace clustering uses the global linear combinations to represent the data.As a result,the BDR cannot guarantee that the final result is the global optimal solution.In this paper,we focus on the BDR model and study the manifold information generated by BDR.And then,we propose the improved method to cope with the problem that the manifold information in BDR can not be used effectively.The main work of this paper is summarized as follows:(1)Improved Block Diagonal Representation via Local Invariance(BDRL)is proposed to solve the problem that subspace clustering cannot well capture and use the underlying manifold information of high-dimensional data.BDRL approximates the local manifold structure by using the local linear combination of the data and generates the global representation of data.The local manifold structure and block diagonal representation are considered jointly to uncover the intrinsic structure of high-dimensional data.The synthetic experiment shows that the BDRL can generate the coefficient matrix more stably by the supplement of the non-linear manifold information of the data.The experiment on the standard datasets shows that the representation matrix generated by BDRL can well uncover the natural structure of the data and contribute to the final subspace segmentation.(2)Improved Block Diagonal Representation via Manifold Information(BDRM)is proposed,which solves the problem of insufficient connection within the intra-subspace caused by the dispersion of local manifold information.Although BDRL generates a manifold-preserving coefficient representation matrix,which can more closely approximate the real data structure,the manifold information is scattered in each subspace.BDRL still cannot guarantee the optimal solution.The BDRM proposed in this paper uses the diffusion process to spread the affinity matrix pair information along the data manifold structure.By re-evaluating the similarity between data points,BDRM improves the connectivity of the intra-subspaces,and is more conducive to the final division of the subspace.Experiments on the synthetic dataset show that the coefficients enhanced by diffusion indicate that the edges of the matrix are clearer,the connectivity of the same intra-sub space,and the accuracy of subspace segmentation is improved.Secondly,in the experiments on a face dataset with a strong manifold structure,it can be seen that BDRM can make good use of the manifold structure information of the data.It can significantly improve the clustering accuracy on the face dataset.