Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold

Hiroyuki Kasai; Bamdev Mishra

Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold

Computer Vision and Pattern Recognition 2019-02-13 v1 Artificial Intelligence Machine Learning Applications Machine Learning

Authors: Hiroyuki Kasai , Bamdev Mishra

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Abstract

Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals. This paper presents a proposal of a novel Riemannian joint dimensionality reduction and dictionary learning (R-JDRDL) on symmetric positive definite (SPD) manifolds for classification tasks. The joint learning considers the interaction between dimensionality reduction and dictionary learning procedures by connecting them into a unified framework. We exploit a Riemannian optimization framework for solving DL and DR problems jointly. Finally, we demonstrate that the proposed R-JDRDL outperforms existing state-of-the-arts algorithms when used for image classification tasks.

Keywords

dimensionality reduction dictionary learning symmetric positive definite manifold riemannian optimization image classification joint learning

Cite

@article{arxiv.1902.04186,
  title  = {Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold},
  author = {Hiroyuki Kasai and Bamdev Mishra},
  journal= {arXiv preprint arXiv:1902.04186},
  year   = {2019}
}

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European Signal Processing Conference (EUSIPCO 2018)

Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold

Abstract

Keywords

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