A scalable approach to column-based low-rank matrix approximation

Authors:
Yifan Pi;Haoruo Peng;Shuchang Zhou;Zhihua Zhang
Affiliations:
Institute for Theoretical Computer Science, IIIS, Tsinghua University, Beijing, China;Department of Computer Science & Technology, Tsinghua University, Beijing, China;State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China and Google Inc., Beijing, China;College of Computer Science & Technology, Zhejiang University, Hangzhou, China
Venue:
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Year:
2013

Citing 21
Cited 0

Efficient algorithms for computing a strong rank-revealing QR factorization

SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Incomplete cross approximation in the mosaic-skeleton method

Computing
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose

IEEE Transactions on Pattern Analysis and Machine Intelligence
Eigentaste: A Constant Time Collaborative Filtering Algorithm

Information Retrieval
Pass efficient algorithms for approximating large matrices

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Acquiring Linear Subspaces for Face Recognition under Variable Lighting

IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Compression of Low Rank Matrices

SIAM Journal on Scientific Computing
Fast Monte Carlo Algorithms for Matrices III: Computing a Compressed Approximate Matrix Decomposition

SIAM Journal on Computing
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning

The Journal of Machine Learning Research
Robust Object Recognition with Cortex-Like Mechanisms

IEEE Transactions on Pattern Analysis and Machine Intelligence
Relative-Error $CUR$ Matrix Decompositions

SIAM Journal on Matrix Analysis and Applications
An improved approximation algorithm for the column subset selection problem

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Spectral Algorithms

Foundations and Trends® in Theoretical Computer Science
FlumeJava: easy, efficient data-parallel pipelines

PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

SIAM Review
Near Optimal Column-Based Matrix Reconstruction

FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Optimal column-based low-rank matrix reconstruction

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Column subset selection via sparse approximation of SVD

Theoretical Computer Science
Randomized Algorithms for Matrices and Data

Foundations and Trends® in Machine Learning
RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images

IEEE Transactions on Pattern Analysis and Machine Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we address the column-based low-rank matrix approximation problem using a novel parallel approach. Our approach is based on the divide-and-combine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns into the final output. Our approach enjoys a theoretical relative-error upper bound. In addition, our column-based low-rank approximation partitions data in a deterministic way and makes no assumptions about matrix coherence. Compared with other traditional methods, our approach is scalable on large-scale matrices. Finally, experiments on both simulated and real world data show that our approach is both efficient and effective.