Bilinear Dictionary Update via Linear Least Squares

Qi Yu, Wei Dai, Zoran Cvetkovic, Jubo Zhu

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

3 Citations (Scopus)

Abstract

Algorithms for dictionary learning aim to learn a dictionary under which training data have sparse representations. This paper addresses the dictionary update sub-problem, the goal of which is to update the dictionary and the corresponding sparse coefficients given a fixed sparsity pattern. It is a non-convex bilinear inverse problem, and hence challenging to solve. Inspired by a recent work by Ling and Strohmer, we re-formulate the dictionary update problem as a linear least squares problem, which is convex and easy to solve. Necessary bounds on the number of training samples required for a unique solution are derived when exact sparsity pattern is known. Further, for dictionary update with unknown sparsity patterns, an efficient iterative algorithm based on total least squares is developed. Embedding the new dictionary update procedure into an overall dictionary learning algorithm achieves better numerical performance compared to state of the art algorithms.

Original languageEnglish
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7923-7927
Number of pages5
Volume2019-May
ISBN (Electronic)9781479981311
DOIs
Publication statusPublished - 1 May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: 12 May 201917 May 2019

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/TerritoryUnited Kingdom
CityBrighton
Period12/05/201917/05/2019

Keywords

  • Bilinear inverse problem
  • dictionary learning
  • dictionary update
  • linear least squares
  • total least squares

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