Subspace Clustering Based On Binuclear Norm Low-rank Representation

High-dimensional data usually lie in low-dimensional subspaces.With the increasingly high dimensions as well as large scale of data,it is essential to recover such low-dimensional subspaces to reveal latent low-dimensional structures of the data for deep understanding.Unfortunately,there is often a need to process such data with no label information due to the expensive cost of labeling.Thus,there is a crucial demand for effective unsupervised learning such as clustering before further data processing.Traditional clustering algorithms may suffer from several issues such as curse of dimensionality when facing such high-dimensional data.Among various clustering algorithms,subspace clustering methods are typical,which have been shown effective by exploiting the inherent low-rank or sparse structures of high-dimensional data.Despite the effectiveness and efficiency of existing subspace clustering methods,they still have some common drawbacks.For example,low-rank representation(LRR)and sparse subspace clustering(SSC)are typical subspace clustering methods with elegant theory and promising empirical.However,they all use the Frobenius norm to fit the error.In this way,for two-dimensional data,the structural information of the data itself is often ignored.This thesis proposes a subspace clustering algorithm based on double nuclear norm in the field of low rank-based subspace algorithms.The innovations are as follows:1.The data are usually stretched into the vector norm during processing data set in the previous subspace clustering algorithms.This method often leads to the loss of data structured information.Based on the above reasons,this thesis proposed to save the data set in the form of a two-dimensional matrix,thereby retaining the structural information of the data.2.This thesis propose a new subspace clustering method based on double-nuclear norm minimization,where the nuclear norm is used for both fitting error and representation terms for low-rank structure.The nuclear norm is the tightest convex approximation to the rank function,which is widely used for low-rank recovery problems.Compared with the Frobenius norm that adopts element-wise operation,the nuclear norm that adopts spectrum-wise operation is believed to better reveal structural information based on low-rank assumptions of the target matrix.By minimizing the nuclear norm of the residual for each example,it is expected that the proposed model minimizes structural information in the residual and thus maximumly retain such information in the reconstructed examples and learned representation matrix.With such information and the low-rank constraint on the representation matrix,the new model recovers the low-dimensional structures of data with stronger group information.3.This thesis introduces manifold term into the model for enhanced capability of capturing nonlinear relationships of the data.The manifold ensures the smooth of the low-dimensional representation in linear and nonlinear spaces,such that when the data samples have high similarity in the high-dimensional nonlinear space,the new expression form still has the characteristics of high similarity in the low-dimensional linear.In general,the subspace clustering algorithm based on the double nuclear norm proposed in this thesis is improved and innovated on the basis of the existing subspace clustering algorithm.Extensive experimental results confirm that the proposed method has significantly improved clustering performance compared with state-of-the-art subspace clustering methods.