Sparse subspace clustering using square-root penalty

Linghang Meng, Xinyue Shen, Yuantao Gu

Abstract: We study the sparse subspace clustering problem in presence of both sparse outliers and Gaussian additive noise based on data sparse self-representation. We propose a convex optimization problem which does not only induce sparsity on the representation coefficients and the outliers, but also adopts a square-root penalty to improve the robustness against Gaussian noise. An algorithm based on alternating direction method of multipliers (ADMM) is then devised as a solver for the proposed problem. As a real application, the proposed model and algorithm are applied in motion segmentation. The performances are demonstrated and analyzed by synthetic data, and more importantly, the effectiveness is verified by some real data. Compared with the reference method, numerical results show that the new method achieves higher cluster accuracy and that the choice of the parameter can be less sensitive to the noise level. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>