From Local to Global Subspace Clustering for Image Data

Abstract

The subspace clustering problem arises in many applications that involve processing high-dimensional data, i.e. images and videos. In many of these applications, high dimensional data is often well approximated by union of low-dimensional subspaces. This motivated the development of various algorithms to cluster high dimensional data based on the underlying intrinsic low-dimensional subspaces. However, the existing approaches are based on global representation of data whereas this representation can be easily affected by errors, occlusions and severe illumination conditions. Here, we propose a multi-scale approach based on extracting local patches from different scales and then merging the shared information using a weighted scheme based on Grassmann manifolds. This approach not only benefits from the discriminative information from global representation of data but also makes the clustering task more robust using the information from local representations. Numerical results show that the proposed approach significantly outperforms existing subspace clustering algorithms.