Laplacian regularized deep low-rank subspace clustering network

Self-expression-based deep subspace clustering, integrating traditional subspace clustering methods into deep learning paradigm to enhance the representative capacity, has become an important branch in unsupervised learning methods. However, most existing methods investigate to impose only sparse constraint on the coefficient matrix to sparsely and independently represent all data, yet omitting another essential global low-rank prior. Meanwhile, some non-linear geometric structures within data has not been well utilized for deep subspace clustering. To conquer these challenges, this paper proposes a novel deep subspace clustering method, named Laplacian Regularized Deep Low-Rank Subspace Clustering Network (LDLRSC), in which the low-rank prior and non-linear geometric information in data are captured simultaneously. Specifically, LDLRSC utilizes the nonconvex surrogate instead of sparsity to describe the global low-rankness of the self-representation matrix. Moreover, two types of Laplacian constraints are exploited to mine the geometric structure of the data samples. Extensive experiments on the several widely-used datasets have demonstrated the effectiveness of the proposed LDLRSC over existing state-of-the-arts.