Fast Monte-carlo low rank approximations for matrices

Shmuel Friedland, Amir Niknejad, Mostafa Kaveh, Hossein Zare

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

In many applications, it is of interest to approximate data, given by m × n matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carlo algorithm for iteratively computing a k-rank approximation to the data consisting of m × n matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our algorithm is O(kmn). Our algorithm, distinguished from other known algorithms, guarantees that each iteration is a better k-rank approximation than the previous iteration. We believe that this algorithm will have many applications in data mining, data storage and data analysis.

Original languageEnglish (US)
Title of host publicationProceedings 2006 IEEE/SMC International Conference on System of Systems Engineering
Pages218-223
Number of pages6
StatePublished - Dec 1 2006
Event2006 IEEE/SMC International Conference on System of Systems Engineering - Los Angeles, CA, United States
Duration: Apr 24 2006Apr 26 2006

Publication series

NameProceedings 2006 IEEE/SMC International Conference on System of Systems Engineering
Volume2006

Other

Other2006 IEEE/SMC International Conference on System of Systems Engineering
Country/TerritoryUnited States
CityLos Angeles, CA
Period4/24/064/26/06

Keywords

  • Fast k-rank approximation
  • Monte-Carlo algorithm
  • SVD decomposition

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