Big data matrix singular value decomposition based on low-rank tensor train decomposition

Namgil Lee, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We propose singular value decomposition (SVD) algorithms for very large-scale matrices based on a low-rank tensor decomposition technique called the tensor train (TT) format. By using the proposed algorithms, we can compute several dominant singular values and corresponding singular vectors of large-scale structured matrices given in a low-rank TT format. We propose a large-scale trace optimization problem, and in the proposed methods, the large-scale optimization problem is reduced to sequential small-scale optimization problems.We show that the computational complexity of the proposed algorithms scales logarithmically with the matrix size if the TT-ranks are bounded. Numerical simulations based on very large-scale Hilbert matrix demonstrate the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)121-130
Number of pages10
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8866
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Big data processing
  • Curse-of-dimensionality
  • Eigenvalue decomposition
  • Matrix product states
  • Optimization
  • Singular value decomposition
  • Tensor network

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