Efficient Sparse Representation for Learning With High-Dimensional Data

Due to the capability of effectively learning intrinsic structures from high-dimensional data, techniques based on sparse representation have begun to display an impressive impact on several fields, such as image processing, computer vision, and pattern recognition. Learning sparse representations i...

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Published in:IEEE transaction on neural networks and learning systems Vol. 34; no. 8; pp. 4208 - 4222
Main Authors: Chen, Jie, Yang, Shengxiang, Wang, Zhu, Mao, Hua
Format: Journal Article
Language:English
Published: United States IEEE 01.08.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Computational geometry
Computer vision
Constraints
Convergence
Convex functions
Convexity
Dictionaries
Image processing
Iterative algorithms
Iterative methods
Learning
Linear representation
low-dimensional structures
Machine learning
Optimization
Pattern recognition
probabilistic simplex
Representations
Sparse matrices
sparse representation
Sparsity
Theoretical analysis
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:Due to the capability of effectively learning intrinsic structures from high-dimensional data, techniques based on sparse representation have begun to display an impressive impact on several fields, such as image processing, computer vision, and pattern recognition. Learning sparse representations isoften computationally expensive due to the iterative computations needed to solve convex optimization problems in which the number of iterations is unknown before convergence. Moreover, most sparse representation algorithms focus only on determining the final sparse representation results and ignore the changes in the sparsity ratio (SR) during iterative computations. In this article, two algorithms are proposed to learn sparse representations based on locality-constrained linear representation learning with probabilistic simplex constraints. Specifically, the first algorithm, called approximated local linear representation (ALLR), obtains a closed-form solution from individual locality-constrained sparse representations. The second algorithm, called ALLR with symmetric constraints (ALLRSC), further obtains a symmetric sparse representation result with a limited number of computations; notably, the sparsity and convergence of sparse representations can be guaranteed based on theoretical analysis. The steady decline in the SR during iterative computations is a critical factor in practical applications. Experimental results based on public datasets demonstrate that the proposed algorithms perform better than several state-of-the-art algorithms for learning with high-dimensional data.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2021.3119278