Abstract
In this study, we consider the problem of subspace clustering in the presence of spatially contiguous noise, occlusion, and disguise. We argue that self-expressive representation of data, which is a key characteristic of current state-of-the-art approaches, is severely sensitive to occlusions and complex real-world noises. To alleviate this problem, we highlight the importance of previously neglected local representations in improving robustness and propose a hierarchical framework that combines the robustness of local-patch-based representations and the discriminative property of global representations. This approach consists of two main steps: 1) A top-down stage, in which the input data are subject to repeated division to smaller patches and 2) a bottom-up stage, in which the low rank embedding of representation matrices of local patches in the field of view of a corresponding patch in the upper level are merged on a Grassmann manifold. This unified approach provides two key pieces of information for neighborhood graph of the corresponding patch on the upper level: cannot-links and recommended-links. This supplies a robust summary of local representations which is further employed for computing self-expressive representations using a novel weighted sparse group lasso optimization problem. Numerical results for several data sets confirm the efficiency of our approach.
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