Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data

2016/07/18 by Patrick S. Medina, Medina, Patrick S., R. W. Doerge +1
Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Other Statistics (stat.OT) #stat.AP #stat.OT

paper · pdf · doi:10.48550/arxiv.1607.05150

15 pages, 7 Figures, 27th Annual Conference on Applied Statistics in Agriculture

arxiv created 2016/07/18 · arxiv updated 2016/07/19

Abstract

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject.

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