Linear convergence of the subspace constrained mean shift algorithm: from Euclidean to directional data.

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-09 eCollection Date: 2023-03-01 DOI:10.1093/imaiai/iaac005

Yikun Zhang, Yen-Chi Chen

引用次数: 0

Abstract

This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm.

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子空间约束均值移动算法的线性收敛：从欧几里得数据到方向数据。

本文研究了子空间约束均值移动（SCMS）算法的线性收敛性，这是一种著名的算法，用于识别由核密度估计器定义的密度脊。通过论证 SCMS 算法是具有自适应步长的子空间约束梯度上升（SCGA）算法的特殊变体，我们推导出了这种 SCGA 算法的线性收敛性。现有研究主要关注欧几里得空间中的密度脊，而我们将密度脊和 SCMS 算法推广到了方向性数据。特别是，我们建立了具有方向性数据的密度脊稳定性定理，并证明了我们提出的方向性 SCMS 算法的线性收敛性。

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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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.