Subspace clustering via adaptive-loss regularized representation learning with latent affinities

High-dimensional data that lies on several subspaces tend to be highly correlated and contaminated by various noises, and its affinities across different subspaces are not always reliable, which impedes the effectiveness of subspace clustering. To alleviate the deficiencies, we propose a novel subspace learning model via adaptive-loss regularized representation learning with latent affinities (ALRLA). Specifically, the robust least square regression with nonnegative constraint is firstly proposed to generate more interpretable reconstruction coefficients in low-dimensional subspace and specify the weighted self-representation capability with adaptive loss norm for better robustness and discrimination. Moreover, an adaptive latent graph learning regularizer with an initialized affinity approximation is considered to provide more accurate and robust neighborhood assignment for low-dimensional representations. Finally, the objective model is solved by an alternating optimization algorithm, with theoretical analyses on its convergence and computational complexity. Extensive experiments on benchmark databases demonstrate that the ALRLA model can produce clearer structured representation under redundant and noisy data environment. It achieves competing clustering performance compared with the state-of-the-art clustering models.