函数数据非线性降维及其在聚类中的应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-01 DOI:10.5705/ss.202021.0393

Ruoxu Tan, Yiming Zang, G. Yin

引用次数: 0

摘要

功能数据通常具有非线性结构，例如相位变化，因此线性降维技术可能无效。基于假设数据位于一个未知的带有噪声的流形上，研究了函数数据的非线性降维问题。我们将最近开发的用于高维数据的流形学习方法推广到我们的环境中，并在考虑噪声的情况下推导出渐近收敛结果。基于综合算例的结果往往比传统的功能等高线方法产生更精确的测地线距离估计。我们进一步开发了一种基于流形学习结果的聚类策略，并证明如果数据位于弯曲流形上，我们的方法优于其他方法。给出了两个实际数据示例来说明。1.中国统计:预印本doi:10.5705/ss.202021.0393

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Nonlinear dimension reduction for functional data with application to clustering

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.