Robust and efficient subspace segmentation via least squares regression

Authors:
Can-Yi Lu;Hai Min;Zhong-Qiu Zhao;Lin Zhu;De-Shuang Huang;Shuicheng Yan
Affiliations:
Department of Automation, University of Science and Technology of China, Hefei, China,Department of Electrical and Computer Engineering, National University of Singapore, Singapore;Department of Automation, University of Science and Technology of China, Hefei, China;School of Computer and Information, Hefei University of Technology, Hefei, China;Department of Automation, University of Science and Technology of China, Hefei, China;School of Electronics and Information Engineering, Tongji University, Shanghai, China;Department of Electrical and Computer Engineering, National University of Singapore, Singapore
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Year:
2012

Citing 14
Cited 1

A Multibody Factorization Method for Independently Moving Objects

International Journal of Computer Vision
Mixtures of probabilistic principal component analyzers

Neural Computation
Normalized Cuts and Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
k-Plane Clustering

Journal of Global Optimization
Acquiring Linear Subspaces for Face Recognition under Variable Lighting

IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Principal Component Analysis (GPCA)

IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Face Recognition via Sparse Representation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering appearances of objects under varying illumination conditions

CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Robust principal component analysis?

Journal of the ACM (JACM)
Multi-subspace representation and discovery

ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Optimization for Machine Learning

Optimization for Machine Learning
A general framework for motion segmentation: independent, articulated, rigid, non-rigid, degenerate and non-degenerate

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression

IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Hybrid Linear Models for Lossy Image Representation

IEEE Transactions on Image Processing

Online group feature selection

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.