Neither global nor local: A hierarchical robust subspace clustering for image data

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.