一种基于邻域的分段稀疏逼近算法及其在分散数据拟合中的应用

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

International Journal of Applied Mathematics and Computer Science Pub Date : 2022-12-01 DOI:10.34768/amcs-2022-0046

Yijun Zhong, Chongjun Li, Zhong-xue Li, Xiao-juan Duan

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引用次数: 0

摘要

摘要在某些应用中，需要恢复具有分段结构的信号。本文提出了一种分段稀疏逼近模型和一种分段近端梯度逼近方法(JPGA)。本文还对JPGA进行了基于微分方程的分析，从另一个角度分析了JPGA的收敛速度。此外，我们还证明了对给定分散数据的拟合曲面的稀疏表示问题可以看作是一个分段稀疏逼近。数值实验结果表明，该算法既能有效地拟合曲面，又能保护表示系数的分段稀疏性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting

Abstract In some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential equations, which provides another perspective on the convergence rate of the JPGA. In addition, we show that the problem of sparse representation of the fitting surface to the given scattered data can be considered as a piecewise sparse approximation. Numerical experimental results show that the JPGA can not only effectively fit the surface, but also protect the piecewise sparsity of the representation coefficient.

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来源期刊

International Journal of Applied Mathematics and Computer Science 工程技术-计算机：人工智能

CiteScore

4.10

自引率

21.10%

发文量

审稿时长

4.2 months

期刊介绍： The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas: -modern control theory and practice- artificial intelligence methods and their applications- applied mathematics and mathematical optimisation techniques- mathematical methods in engineering, computer science, and biology.