Low-rank matrix decomposition in L1-norm by dynamic systems

Authors:
Yiguang Liu;Bingbing Liu;Yifei Pu;Xiaohui Chen;Hong Cheng
Affiliations:
Vision and Image Processing Lab, College of Computer, Sichuan University, Chengdu 610065, PR China and College of Computer and Information Technology China Three Gorges University Yichang, 443002, ...;Institute for Infocomm Research, A*STAR, 1 Fusionopolis Way, Singapore 138632;Vision and Image Processing Lab, College of Computer, Sichuan University, Chengdu 610065, PR China;College of Computer and Information Technology China Three Gorges University Yichang, 443002, PR China;Pattern Recognition and Machine Intelligence Lab., University of Electronic Science and Technology of China, Chengdu 611731, PR China
Venue:
Image and Vision Computing
Year:
2012

Citing 16
Cited 1

Shape and motion from image streams under orthography: a factorization method

International Journal of Computer Vision
A Sequential Factorization Method for Recovering Shape and Motion From Image Streams

IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust L" Norm Factorization in the Presence of Outliers and Missing Data by Alternative Convex Programming

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Damped Newton Algorithms for Matrix Factorization with Missing Data

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Generalized Low Rank Approximations of Matrices

Machine Learning
A functional neural network computing some eigenvalues and eigenvectors of a special real matrix

Neural Networks
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components

International Journal of Computer Vision
Fundamental study: A concise functional neural network computing the largest modulus eigenvalues and their corresponding eigenvectors of a real skew matrix

Theoretical Computer Science
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors

IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix

International Journal of Computer Vision
Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized low-rank approximations of matrices revisited

IEEE Transactions on Neural Networks
A Singular Value Thresholding Algorithm for Matrix Completion

SIAM Journal on Optimization
Stratification Approach for 3-D Euclidean Reconstruction of Nonrigid Objects From Uncalibrated Image Sequences

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
-NS: A Classifier by the Distance to the Nearest Subspace

IEEE Transactions on Neural Networks
Robust Video Restoration by Joint Sparse and Low Rank Matrix Approximation

SIAM Journal on Imaging Sciences

Sparse representation and learning in visual recognition: Theory and applications

Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Low-rank matrix approximation is used in many applications of computer vision, and is frequently implemented by singular value decomposition under L"2-norm sense. To resist outliers and handle matrix with missing entries, a few methods have been proposed for low-rank matrix approximation in L"1 norm. However, the methods suffer from computational efficiency or optimization capability. Thus, in this paper we propose a solution using dynamic system to perform low-rank approximation under L"1-norm sense. From the state vector of the system, two low-rank matrices are distilled, and the product of the two low-rank matrices approximates to the given measurement matrix with missing entries, in L"1 norm. With the evolution of the system, the approximation accuracy improves step by step. The system involves a parameter, whose influences on the computational time and the final optimized two low-rank matrices are theoretically studied and experimentally valuated. The efficiency and approximation accuracy of the proposed algorithm are demonstrated by a large number of numerical tests on synthetic data and by two real datasets. Compared with state-of-the-art algorithms, the newly proposed one is competitive.