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

This work furnished a sharper bound of exponential form for the L 2 norm 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.

[1]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[2]  Heikki Mannila,et al.  Local and Global Methods in Data Mining: Basic Techniques and Open Problems , 2002, ICALP.

[3]  N. Alon,et al.  On the concentration of eigenvalues of random symmetric matrices , 2000, math-ph/0009032.

[4]  Dimitris Achlioptas,et al.  Fast computation of low rank matrix approximations , 2001, STOC '01.

[5]  T. Landauer,et al.  Indexing by Latent Semantic Analysis , 1990 .

[6]  Alan M. Frieze,et al.  Fast monte-carlo algorithms for finding low-rank approximations , 2004, JACM.

[7]  Gene H. Golub,et al.  Matrix computations , 1983 .

[8]  Jieping Ye,et al.  Generalized Low Rank Approximations of Matrices , 2005, Machine Learning.

[9]  Alan M. Frieze,et al.  Clustering in large graphs and matrices , 1999, SODA '99.

[10]  Susan T. Dumais,et al.  Using Linear Algebra for Intelligent Information Retrieval , 1995, SIAM Rev..

[11]  Larry Wasserman,et al.  All of Statistics: A Concise Course in Statistical Inference , 2004 .

[12]  Ziv Bar-Yossef,et al.  Sampling lower bounds via information theory , 2003, STOC '03.

[13]  Larry Wasserman,et al.  All of Statistics , 2004 .

[14]  Santosh S. Vempala,et al.  Adaptive Sampling and Fast Low-Rank Matrix Approximation , 2006, APPROX-RANDOM.

[15]  Sanjeev Arora,et al.  A Fast Random Sampling Algorithm for Sparsifying Matrices , 2006, APPROX-RANDOM.

[16]  U. Feige,et al.  Spectral techniques applied to sparse random graphs , 2005 .