Dictionary filtering: a probabilistic approach to online matrix factorisation Articles uri icon

publication date

  • June 2019

start page

  • 737

end page

  • 744


  • 4


  • 13

International Standard Serial Number (ISSN)

  • 1863-1703

Electronic International Standard Serial Number (EISSN)

  • 1863-1711


  • This paper investigates a link between matrix factorisation algorithms and recursive linear filters. In particular, we describe a probabilistic model in which sequential inference naturally leads to a matrix factorisation procedure. Using this probabilistic model, we derive a matrix-variate recursive linear filter that can be run efficiently in high-dimensional settings and leads to the factorisation of the data matrix into a dictionary matrix and a coefficient matrix. The resulting algorithm, referred to as the dictionary filter, is inherently online and has easy-to-tune parameters. We provide an extension of the proposed method for the cases where the dataset of interest is time-varying and nonstationary, thereby showing the adaptability of the proposed framework to non-standard problem settings. Numerical results, which are provided for image restoration and video modelling problems, demonstrate that the proposed method is a viable alternative to existing methods.


  • online matrix factorisation; kalman filtering; stochastic optimisation