Robust Subspace Segmentation by Simultaneously Learning Data Representations and Their Affinity Matrix

The goal of subspace segmentation is to partition a set of data drawn from a union of subspace into their underlying subspaces. The performance of spectral clustering based approaches heavily depends on learned data affinity matrices, which are usually constructed either directly from the raw data or from their computed representations. In this paper, we propose a novel method to simultaneously learn the representations of data and the affinity matrix of representation in a unified optimization framework. A novel Augmented Lagrangian Multiplier based algorithm is designed to effectively and efficiently seek the optimal solution of the problem. The experimental results on both synthetic and real data demonstrate the efficacy of the proposed method and its superior performance over the state-of-the-art alternatives.