Solving sparse non-negative tensor equations: algorithms and applications

Xutao Li, Kwok Po NG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)

Abstract

We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)649-680
Number of pages32
JournalFrontiers of Mathematics in China
Volume10
Issue number3
DOIs
Publication statusPublished - Jun 2015

Scopus Subject Areas

  • Mathematics (miscellaneous)

User-Defined Keywords

  • community
  • information retrieval
  • iterative method
  • multi-dimensional network
  • multivariate polynomial equation
  • Nonnegative tensor

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