Spherical random projection

Author:

Kang Seungwoo1ORCID,Oh Hee-Seok1ORCID

Affiliation:

1. Department of Statistics, Seoul National University , Seoul , Republic of Korea

Abstract

Abstract We propose a new method for dimension reduction of high-dimensional spherical data based on the nonlinear projection of sphere-valued data to a randomly chosen subsphere. The proposed method, spherical random projection, leads to a probabilistic lower-dimensional mapping of spherical data into a subsphere of the original. In this paper, we investigate some properties of spherical random projection, including expectation preservation and distance concentration, from which we derive an analogue of the Johnson–Lindenstrauss Lemma for spherical random projection. Clustering model selection is discussed as an application of spherical random projection, and numerical experiments are conducted using real and simulated data.

Funder

National Research Foundation of Korea

Publisher

Oxford University Press (OUP)

Reference58 articles.

1. Database-friendly random projections: Johnson–Lindenstrauss with binary coins;Achlioptas;Journal of Computer and System Sciences,2003

2. An algorithmic theory of learning: Robust concepts and random projection;Arriaga;Machine Learning,2006

3. Clustering on the unit hypersphere using von Mises–Fisher distributions;Banerjee;Journal of Machine Learning Research,2005

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3