On the Equivalence of the LC-KSVD and the D-KSVD Algorithms

Igor Kviatkovsky, Moshe Gabel, Ehud Rivlin, Ilan Shimshoni

Research output: Contribution to journalArticlepeer-review

Abstract

Sparse and redundant representations, where signals are modeled as a combination of a few atoms from an overcomplete dictionary, is increasingly used in many image processing applications, such as denoising, super resolution, and classification. One common problem is learning a 'good' dictionary for different tasks. In the classification task the aim is to learn a dictionary that also takes training labels into account, and indeed there exist several approaches to this problem. One well-known technique is D-KSVD, which jointly learns a dictionary and a linear classifier using the K-SVD algorithm. LC-KSVD is a recent variation intended to further improve on this idea by adding an explicit label consistency term to the optimization problem, so that different classes are represented by different dictionary atoms. In this work we prove that, under identical initialization conditions, LC-KSVD with uniform atom allocation is in fact a reformulation of D-KSVD: given the regularization parameters of LC-KSVD, we give a closed-form expression for the equivalent D-KSVD regularization parameter, assuming the LC-KSVD's initialization scheme is used. We confirm this by reproducing several of the original LC-KSVD experiments.

Original languageEnglish
Article number7439860
Pages (from-to)411-416
Number of pages6
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume39
Issue number2
DOIs
StatePublished - 1 Feb 2017

Bibliographical note

Publisher Copyright:
© 1979-2012 IEEE.

Keywords

  • Discriminative dictionary learning
  • discriminative K-SVD
  • equivalence proof
  • label consistent K-SVD

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Applied Mathematics
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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