Deep non-convex low-rank subspace clustering

Subspace clustering is an important research topic in computer vision. The traditional low-rank model has potentiality in clustering for images with the linear subspace assumption. However, for images that do not meet the assumption, the manipulation of approximating rank function with nuclear norm in the above methods always results in the over-penalization for large singular values. Therefore, a non-convex low-rank subspace clustering method involved deep learning is proposed in this paper, which realizes the extraction of non-linear features of the image by introducing convolutional self-encoding and self-representation layer. Specially, for the low-rank attribute of the data, the non-convex Schatten-p (0 < p < 1) norm is used to characterize the matrix rank, which can bring more accurate solution than the traditional low-rank methods. Using the decomposition formula of non-convex Schatten-p norm, this paper also gives the corresponding optimization algorithm. Numerous numerical experiments show that the combination of auto-encoder with self-representation layer and non-convex Schatten-p norm can enhance the subspace clustering ability of nonlinear data.