Paper Info
Title
A Structured Sparse Plus Structured Low-Rank Framework for Subspace Clustering and Completion.
Abstract
Recent advances in a low-rank matrix completion have enabled the exact recovery of incomplete data drawn from a low-dimensional subspace of a high-dimensional observation space. However, in many applications, the data are drawn from multiple low-dimensional subspaces without knowing which point belongs to which subspace. In such cases, using a single low-dimensional subspace to complete the data may lead to erroneous results, because the complete data matrix need not be low rank. In this paper, we propose a structured sparse plus structured low-rank ($\\text{S}^3$LR) optimization framework for clustering and completing data drawn from a union of low-dimensional subspaces. The proposed $\\text{S}^3$LR framework exploits the fact that each point in a union of subspaces can be expressed as a sparse linear combination of all other points and that the matrix of the points within each subspace is low rank. This framework leads to a nonconvex optimization problem, which we solve efficiently by using a combination of a linearized alternating direction method of multipliers and spectral clustering. In addition, we discuss the conditions that guarantee the exact matrix completion in a union of subspaces. Experiments on synthetic data, motion segmentation data, and cancer gene data validate the effectiveness of the proposed approach.
Year
DOI
Venue
2016
10.1109/TSP.2016.2613070
IEEE Trans. Signal Processing
Keywords
Field
DocType
Sparse matrices,Optimization,Trajectory,Motion segmentation,Computer vision,Convex functions,Clustering algorithms
Spectral clustering,Mathematical optimization,Subspace topology,Matrix completion,Matrix (mathematics),Linear subspace,Synthetic data,Cluster analysis,Sparse matrix,Mathematics
Journal
Volume
Issue
ISSN
64
24
1053-587X
Citations 
PageRank 
References 
15
0.51
28
Authors
2
Name
Order
Citations
PageRank
Chun-Guang Li131017.35
rene victor valqui vidal25331260.14