2018年8月1日
Dictionary learning with the ℓ<inf>1 / 2</inf> -regularizer and the coherence penalty and its convergence analysis
International Journal of Machine Learning and Cybernetics
- ,
- ,
- ,
- 巻
- 9
- 号
- 8
- 開始ページ
- 1351
- 終了ページ
- 1364
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s13042-017-0649-9
© 2017, Springer-Verlag Berlin Heidelberg. The ℓ1 / 2-regularizer has been studied widely in compressed sensing, but there have been few studies about dictionary learning problems. The dictionary learning method with the ℓ1 / 2-regularizer aims to learn a dictionary, which requires solving a very challenging nonconvex and nonsmooth optimization problem. In addition, the low mutual coherence of a dictionary is an important property that ensures the optimality of the sparse representation in the dictionary. In this paper, we address a dictionary learning problem involving the ℓ1 / 2-regularizer and the coherence penalty, which is difficult to solve quickly and efficiently. We employ a decomposition scheme and an alternating optimization, which transforms the overall problem into a set of minimizations of single-vector-variable subproblems. Although the subproblems are nonsmooth and even nonconvex, we propose the use of proximal operator technology to conquer them, which leads to a rapid and efficient dictionary learning algorithm. In a theoretical analysis, we establish the algorithm’s global convergence. Experiments were performed for dictionary learning using both synthetic data and real-world data. For the synthetic data, we demonstrated that our algorithm performed better than state-of-the-art algorithms. Using real-world data, the learned dictionaries were shown to be more efficient than algorithms using ℓ1-norm for sparsity.
- リンク情報
- ID情報
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- DOI : 10.1007/s13042-017-0649-9
- ISSN : 1868-8071
- eISSN : 1868-808X
- ORCIDのPut Code : 52745438
- SCOPUS ID : 85046588438