# Neither Global Nor Local: A Hierarchical Robust Subspace Clustering For Image Data

## TL;DR

This paper introduces a hierarchical robust subspace clustering method that combines local patch-based and global representations to improve robustness against noise, occlusion, and disguise in image data.

## Contribution

A novel hierarchical framework that integrates local and global data representations for enhanced robustness in subspace clustering.

## Key findings

- Effective in handling noise, occlusion, and disguise
- Outperforms existing methods on real datasets
- Provides robust clustering results in complex scenarios

## Abstract

In this paper, we consider the problem of subspace clustering in presence of contiguous noise, occlusion and disguise. We argue that self-expressive representation of data in current state-of-the-art approaches is severely sensitive to occlusions and complex real-world noises. To alleviate this problem, we propose a hierarchical framework that brings robustness of local patches-based representations and discriminant property of global representations together. This approach consists of 1) a top-down stage, in which the input data is subject to repeated division to smaller patches and 2) a bottom-up stage, in which the low rank embedding of local patches in field of view of a corresponding patch in upper level are merged on a Grassmann manifold. This summarized information provides two key information for the corresponding patch on the upper level: cannot-links and recommended-links. This information is employed for computing a self-expressive representation of each patch at upper levels using a weighted sparse group lasso optimization problem. Numerical results on several real data sets confirm the efficiency of our approach.