Bound for the L2 Norm of Random Matrix and Succinct Matrix Approximation

Authors:
Rong Liu;Nian Yan;Yong Shi;Zhengxin Chen
Affiliations:
Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, China 100080;College of Information Science and Technology, University of Nebraska at Omaha, Omaha, USA NE 68182;School of Mathematical Science, Graduate University of Chinese Academy of Sciences, Beijing, China 100049;College of Information Science and Technology, University of Nebraska at Omaha, Omaha, USA NE 68182
Venue:
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Year:
2008

Citing 13
Cited 0

Using linear algebra for intelligent information retrieval

SIAM Review
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Clustering in large graphs and matrices

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fast computation of low rank matrix approximations

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Local and Global Methods in Data Mining: Basic Techniques and Open Problems

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Sampling lower bounds via information theory

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast Monte-Carlo Algorithms for finding low-rank approximations

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fast monte-carlo algorithms for finding low-rank approximations

Journal of the ACM (JACM)
Spectral techniques applied to sparse random graphs

Random Structures & Algorithms
Generalized Low Rank Approximations of Matrices

Machine Learning
All of Statistics: A Concise Course in Statistical Inference

All of Statistics: A Concise Course in Statistical Inference
A fast random sampling algorithm for sparsifying matrices

APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Adaptive sampling and fast low-rank matrix approximation

APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

This work furnished a sharper bound of exponential form for the L2norm of an arbitrary shaped random matrix. Based on the newly elaborated bound, a non-uniform sampling method was developed to succinctly approximate a matrix with a sparse binary one and hereby to relieve the computation loads in both time and storage. This method is not only pass-efficient but query-efficient also since the whole process can be completed in one pass over the input matrix and the sampling and quantizing are naturally combined in a single step.