Subspace Clustering By Block Diagonal Presentation

High-dimensional data is ubiquitous in many fields of machine learning.Looking for the compact representation of data by mining the structure of data is crucial to understanding the data with minimal storage.Recent studies had shown that many high-dimensional can be modeled as samples from the union of multiple low-dimensional linear subspaces.In this paper we study the subspace clustering,and propose two algorithms named New Subspace Clustering by Block Diagonal Representation(NBDR)and Robust Subspace Clustering by Block Diagonal Representation(RBDR)respectively.1.We review and analyze the recent research works of the subspace clustering.To address deficiencies in existing works,according to the spectral properties of matrix,we define a new block diagonal regularizer which can describe the subspace structure of the data more accurately.And then based on the new regularizer,the NBDR model is proposed.The model is solved by Alternating Direction Method,and it is proved theoretically that when the data set satisfies certain conditions,the Alternating Direction method is convergent when solving NBDR.The Spectral Project Gradient Method(SPG)is used to solve the sub-problem.The experimental results on the motion segmentation data set Hopkins 155 and the face recognition data set Extended Yale B show that the clustering accuracy of the NBDR algorithm is higher than that of the SSC,LRR,LSR and the new and high-performance algorithm BDR.At the same time,the experimental analysis also verifies the convergence of the algorithm.2.In order to solve the insufficient robustness and the unstable convergence of the NBDR algorithm,we add the F-norm as a regular term to its model,and propose the RBDR algorithm.To solve RBDR,we also adopt the Alternating Direction Method,and prove its convergence theoretically.The experimental results show that the RBDR algorithm outperforms all other algorithms including NBDR.Especially,the accuracy rate on the Extended Yale B dataset is significantly improved,which verifies the robustness of the RBDR.At the same time,the experimental analysis shows that both NBDR and RBDR algorithms are convergent,while the convergence of the RBDR algorithm is faster and more stable than that of the NBDR.NBDR and RBDR are both effective,but RBDR is more high-efficient.