论文|Jie Chen, Shengxiang Yang*, Zhu Wang, and Hua Mao： Efficient Sparse Representation for Learning with High-Dimensional Data

本文（Efficient Sparse Representation for Learning with High-Dimensional Data）原载IEEE Trans. Neural. Netw. Learn. Syst，由四川大学法学院王竹教授、四川大学计算机学院陈杰副教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract: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 (ALLR [Math Processing Error] ), 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.

Jie Chen, Shengxiang Yang*, Zhu Wang, and Hua Mao, Efficient Sparse Representation for Learning with High-Dimensional Data, IEEE Trans. Neural. Netw. Learn. Syst., pp. 1-15, Oct. 2021, DOI: 10.1109/TNNLS.2021.3119278.（论文下载）