Tensor Dictionary Learning for Positive Definite Matrices

Ravishankar Sivalingam, Daniel L Boley, Vassilios Morellas, Nikolaos P Papanikolopoulos

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.

Original languageEnglish (US)
Article number7117399
Pages (from-to)4592-4601
Number of pages10
JournalIEEE Transactions on Image Processing
Volume24
Issue number11
DOIs
StatePublished - Nov 1 2015

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Glossaries
Tensors
Learning
Computer vision
Cluster Analysis
Image processing
Software
Atoms

Keywords

  • dictionary learning
  • optimization
  • positive definite matrices
  • region covariance descriptors
  • Sparse coding

Cite this

Tensor Dictionary Learning for Positive Definite Matrices. / Sivalingam, Ravishankar; Boley, Daniel L; Morellas, Vassilios; Papanikolopoulos, Nikolaos P.

In: IEEE Transactions on Image Processing, Vol. 24, No. 11, 7117399, 01.11.2015, p. 4592-4601.

Research output: Contribution to journalArticle

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