A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering

Yubao Sun,Zhi Li,Min Wu

doi:10.1155/2015/572753

Abstract

This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data. Real-world data are frequently corrupted with both sparse error and noise. Our matrix decomposition model separates the low-rank, sparse error, and noise components from the data in order to enhance robustness to the corruption. In order to obtain the desired rank representation of the data within a dictionary, our model directly utilizes rank constraints by restricting the upper bound of the rank range. An alternative projection algorithm is proposed to estimate the low-rank representation and separate the sparse error from the data matrix. To further capture the complex relationship between data distributed in multiple subspaces, we use hypergraph to represent the data by encapsulating multiple related samples into one hyperedge. The final clustering result is obtained by spectral decomposition of the hypergraph Laplacian matrix. Validation experiments on the Extended Yale Face Database B, AR, and Hopkins 155 datasets show that the proposed method is a promising tool for subspace clustering.

Highlights

High-dimensional data spaces are frequently encountered in computer vision and machine learning tasks
Our model constrains the rank range of the coefficient matrix Z, which is valuable for subspace clustering problems, for example, face clustering and motion segmentation
rankconstrained matrix representation (RMR)-HyperGraph uses the hypergraph for clustering, according to Algorithm 2, while RMR-Graph uses a pairwise graph for clustering, just like the Subspace Clustering (SSC) and low-rank representation (LRR) methods

Summary

Introduction

High-dimensional data spaces are frequently encountered in computer vision and machine learning tasks. Different from sparse representation, LRR represents a data sample as a linear combination of the atoms in a dictionary and jointly constrains the low-rank property of all the coefficients of the sample set, so it captures the global structure of the data [15, 17]. Due to this advantage, LRR recently attracts much attention. (2) A hypergraph model is introduced to capture the complex and higher order relationships between data, in order to further improve the performance of subspace clustering

Rank-Constrained Matrix Representation

Solving the RMR Model

Hypergraph-Based Subspace Clustering

Experimental Results

Conclusion