Ensemble Subspace Segmentation Under Blockwise Constraints

The graph-based subspace segmentation technique has garnered a lot of attention in the visual data representation problem. In general, data (e.g., tracks of moving objects) are drawn from multiple linear subspaces. Thus, how to build a block-diagonal affinity matrix is the critical problem. In this paper, we propose a novel graph-based method, Ensemble Subspace Segmentation under Blockwise constraints (ESSB), which unifies least squares regression and a locality preserving graph regularizer into an ensemble learning framework. Specifically, compact encoding using least squares regression coefficients helps achieve a block-diagonal representation matrix among all samples. Meanwhile, the locality preserving regularizer tends to capture the intrinsic local structure, which further enhances the block-diagonal property. Both the blockwise efforts, i.e., least squares regression and the sparse regularizer, work jointly and are formulated in the ensemble learning framework, making ESSB more robust and efficient, especially when handling high-dimensional data. Finally, an efficient optimization solution based on inexact augmented Lagrange multiplier is derived with theoretical time complexity analysis. To demonstrate the effectiveness of the proposed method, we consider three different applications: face clustering, object clustering, and motion segmentation. Extensive results of both accuracy and normalized mutual information on four benchmarks, i.e., YaleB, ORL, COIL and Hopkins155, are reported. Also, the evaluations of computational cost are provided, based on which the superiority of our proposed method in both accuracy and efficiency is demonstrated compared with 12 baseline algorithms.