Tangent Space Based Alternating Projections for Nonnegative Low Rank Matrix Approximation

Guangjing Song, Michael K. Ng, Tai Xiang Jiang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


In this article, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed rank matrices can be expensive as the singular value decomposition is required. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by the alternating projections onto the tangent spaces of the fixed rank matrices manifold and the nonnegative matrix manifold, converge linearly to a point in the intersection of the two manifolds where the convergent point is sufficiently close to optimal solutions. This convergence result based inexact projection onto the manifold is new and is not studied in the literature. Numerical examples in data clustering, pattern recognition and hyperspectral data analysis are given to demonstrate that the performance of the proposed method is better than that of nonnegative matrix factorization methods in terms of computational time and accuracy.

Original languageEnglish
Pages (from-to)11917-11934
Number of pages18
JournalIEEE Transactions on Knowledge and Data Engineering
Issue number11
Early online date30 Nov 2022
Publication statusPublished - 1 Nov 2023

Scopus Subject Areas

  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

User-Defined Keywords

  • Alternating projection method
  • low rank
  • manifolds
  • nonnegative matrices
  • nonnegativity
  • tangent spaces


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