An Efficient Orthonormalization-Free Approach for Sparse Dictionary Learning and Dual Principal Component Pursuit

Sensors

Xiaoyin Hu¹  Xin Liu² 

[1] Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, Beijing 100049, China;

关键词: dual principal component pursuit;    orthogonality constraint;    sparse dictionary learning;    stiefel manifold;   

DOI  :  10.3390/s20113041

来源: DOAJ

【 摘 要 】

Sparse dictionary learning (SDL) is a classic representation learning method and has been widely used in data analysis. Recently, the ${\ell }_m$ -norm ( $m\ge 3,m\in \mathbb{N}$ ) maximization has been proposed to solve SDL, which reshapes the problem to an optimization problem with orthogonality constraints. In this paper, we first propose an ${\ell }_m$ -norm maximization model for solving dual principal component pursuit (DPCP) based on the similarities between DPCP and SDL. Then, we propose a smooth unconstrained exact penalty model and show its equivalence with the ${\ell }_m$ -norm maximization model. Based on our penalty model, we develop an efficient first-order algorithm for solving our penalty model (PenNMF) and show its global convergence. Extensive experiments illustrate the high efficiency of PenNMF when compared with the other state-of-the-art algorithms on solving the ${\ell }_m$ -norm maximization with orthogonality constraints.

【 授权许可】

Unknown