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

• Published in: Information sciences Vol. 514; pp. 333 - 353
• Main Authors: Abdolali, Maryam, Rahmati, Mohammad
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2020
• Subjects: Graph fusion; Grassmann manifold; Group lasso; Sparse subspace clustering; Spectral clustering; Graph fusion; Spectral clustering; Sparse subspace clustering; Grassmann manifold; Group lasso
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2019.11.031

•We shed light on the importance of local representations for robust subspace clustering.•A hierarchical subspace clustering framework is proposed to bridge the gap between robust local representations and discriminant global alternative.•Efficiently summarize local representations using subspace analysis on Grassmann manifolds.•computing robust self-expressive representation using a novel weighted sparse group lasso optimization problem. 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.