Robust Subspace Segmentation with Block-Diagonal Prior

• Published in: 2014 IEEE Conference on Computer Vision and Pattern Recognition pp. 3818 - 3825
• Main Authors: Feng, Jiashi, Lin, Zhouchen, Xu, Huan, Yan, Shuicheng
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.06.2014
• Subjects: Affinity; Blocking; Clustering; Computer vision; Construction; Graphs; Image segmentation; Laplace equations; Linear programming; Motion segmentation; Noise; Optimization; Pattern recognition; Segmentation; Sparse matrices; Subspaces
• ISSN: 1063-6919; 1063-6919; 2575-7075
• DOI: 10.1109/CVPR.2014.482

The subspace segmentation problem is addressed in this paper by effectively constructing an exactly block-diagonal sample affinity matrix. The block-diagonal structure is heavily desired for accurate sample clustering but is rather difficult to obtain. Most current state-of-the-art subspace segmentation methods (such as SSC[4] and LRR[12]) resort to alternative structural priors (such as sparseness and low-rankness) to construct the affinity matrix. In this work, we directly pursue the block-diagonal structure by proposing a graph Laplacian constraint based formulation, and then develop an efficient stochastic subgradient algorithm for optimization. Moreover, two new subspace segmentation methods, the block-diagonal SSC and LRR, are devised in this work. To the best of our knowledge, this is the first research attempt to explicitly pursue such a block-diagonal structure. Extensive experiments on face clustering, motion segmentation and graph construction for semi-supervised learning clearly demonstrate the superiority of our novelly proposed subspace segmentation methods.