Abstract: Clustering is an important tool for machine learning and data mining,and subspace clustering is a popular method in high-dimensional data analysis.Spectral clustering based subspace clustering method learns the self-representation coefficient matrix of data in subspace,and then the spectral clustering is carried out on the coefficient matrix.It is found that the subspace-based clustering cannot deal with nonlinear problem and neglect the local geometric structure of the data.To this end,this paper proposes a new subspace clustering method which first projects the data to a high-dimensional linear space by a nonlinear mapping function and applies a Laplacian-based manifold regularization constraint on the subspace clustering model to preserve the local structure of the data at the same time.Three kinds of Laplacian matrix are used to establish the different nonlinear subspace clustering models based on manifold regularization and block diagonal constraints.Experimental results on different data sets show the effectiveness of the proposed methods.

Key words: Block diagonal constraint, Manifold regularization, Nonlinear mapping, Subspace clustering