Direct-Optimization-Based DC Dictionary Learning With the MCP Regularizer

Direct-optimization-based dictionary learning has attracted increasing attention for improving computational efficiency. However, the existing direct optimization scheme can only be applied to limited dictionary learning problems, and it remains an open problem to prove that the whole sequence obtai...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 34; no. 7; pp. 3568 - 3579
Main Authors: Li, Zhenni, Yang, Zuyuan, Zhao, Haoli, Xie, Shengli
Format: Journal Article
Language:English
Published: United States IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Convergence
Convergence analysis
Convex functions
Critical point
Dictionaries
dictionary learning
direct optimization
Learning
Machine learning
minimax concave penalty (MCP) regularizer
Minimax technique
Objective function
Optimization
Robustness (mathematics)
Signal processing algorithms
Sparsity
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:Direct-optimization-based dictionary learning has attracted increasing attention for improving computational efficiency. However, the existing direct optimization scheme can only be applied to limited dictionary learning problems, and it remains an open problem to prove that the whole sequence obtained by the algorithm converges to a critical point of the objective function. In this article, we propose a novel direct-optimization-based dictionary learning algorithm using the minimax concave penalty (MCP) as a sparsity regularizer that can enforce strong sparsity and obtain accurate estimation. For solving the corresponding optimization problem, we first decompose the nonconvex MCP into two convex components. Then, we employ the difference of the convex functions algorithm and the nonconvex proximal-splitting algorithm to process the resulting subproblems. Thus, the direct optimization approach can be extended to a broader class of dictionary learning problems, even if the sparsity regularizer is nonconvex. In addition, the convergence guarantee for the proposed algorithm can be theoretically proven. Our numerical simulations demonstrate that the proposed algorithm has good convergence performances in different cases and robust dictionary-recovery capabilities. When applied to sparse approximations, the proposed approach can obtain sparser and less error estimation than the different sparsity regularizers in existing methods. In addition, the proposed algorithm has robustness in image denoising and key-frame extraction.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2021.3114400