Kernelized Low Rank Representation on Grassmann Manifolds

Abstract

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized framework. The new methods have many applications in computer vision tasks. Several clustering experiments are conducted on handwritten digit images, dynamic textures, human face clips and traffic scene sequences. The experimental results show that the proposed methods outperform a number of state-of-the-art subspace clustering methods.

13 pages

References in corpus (4)

• Robust Recovery of Subspace Structures by Low-Rank Representation
• Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation
• Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment
• Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach

Cited by in corpus (2)

• Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds
• Image segmentation with superpixel-based covariance descriptors in low-rank representation