Robust Subspace Discovery via Relaxed Rank Minimization

Abstract—In this paper, we study the problem of discovering a subspace from instances. We cast this problem as a robust subspace learning problem in the presence of overwhelming outliers and corruptions. The additional knowledge of having one positive instance per bag (the “bag ” concept inherits from traditional multiple instance learning) allows us to relax this highly combinatorial and prohibitive problem as a convex programming problem. Solving this program allows us to simultaneously identify which instances in the subspace and learn the subspace model. We give an efficient and effective algorithm based on the Augmented Lagrangian Multiplier method and provide extensive simulations and experiments to verify the effectiveness of our method. I