Efficient Subspace Segmentation via Quadratic Programming

Shusen Wang, Xiaotong Yuan, Tiansheng Yao, Shuicheng YAN, Jialie Shen

Abstract: We explore in this paper efficient algorithmic solutions to robust subspace segmentation. We propose the SSQP, namely Subspace Segmentation via Quadratic Programming, to partition data drawn from multiple subspaces into multiple clusters. The basic idea of SSQP is to express each datum as the linear combination of other data regularized by an overall term targeting zero reconstruction coefficients over vectors from different subspaces. The derived coefficient matrix by solving a quadratic programming problem is taken as an affinity matrix, upon which spectral clustering is applied to obtain the ultimate segmentation result. Similar to sparse subspace clustering (SCC) and low-rank representation (LRR), SSQP is robust to data noises as validated by experiments on toy data. Experiments on Hopkins 155 database show that SSQP can achieve competitive accuracy as SCC and LRR in segmenting affine subspaces, while experimental results on the Extended Yale Face Database B demonstrate SSQP's superiority over SCC and LRR. Beyond segmentation accuracy, all experiments show that SSQP is much faster than both SSC and LRR in the practice of subspace segmentation.