Efficient Subspace Segmentation via Quadratic Programming

Abstract

We explore in this paper efficient algorithmic solutions to robustsubspace segmentation. We propose the SSQP, namely SubspaceSegmentation via Quadratic Programming, to partition data drawnfrom multiple subspaces into multiple clusters. The basic idea ofSSQP is to express each datum as the linear combination of otherdata regularized by an overall term targeting zero reconstructioncoefficients over vectors from different subspaces. The derivedcoefficient matrix by solving a quadratic programming problem istaken as an affinity matrix, upon which spectral clustering isapplied to obtain the ultimate segmentation result. Similar tosparse subspace clustering (SCC) and low-rank representation (LRR),SSQP is robust to data noises as validated by experiments on toydata. Experiments on Hopkins 155 database show that SSQP can achievecompetitive accuracy as SCC and LRR in segmenting affine subspaces,while experimental results on the Extended Yale Face Database Bdemonstrate SSQP's superiority over SCC and LRR. Beyond segmentationaccuracy, all experiments show that SSQP is much faster than bothSSC and LRR in the practice of subspace segmentation.