Analysis of juggling data: Object oriented data analysis of clustering in acceleration functions

Xiaosun Lu,J S Marron

doi:10.1214/14-ejs937d

Abstract

This paper describes an analysis of acceleration variability among the juggling cycles. The Fisher Rao curve registration is used for curve alignment. Five different choices of data objects are considered in this paper. We show that one of these choices of data objects leads to a much better clustering into two distinct types of juggling cycles than the other choices.

Highlights

This paper studies acceleration variability among the juggling cycles from Ramsay et al (2014)
Object Oriented Data Analysis turns out to be very useful terminology throughout the discussion, where data objects are understood as the atoms of the statistical analysis
Two manifold approaches were used separately, Principal Geodesic Analysis (PGA, Fletcher et al (2004)) and Principal Nested Spheres (PNS, Lu and Marron (2013)), which are two different extensions of Functional Principal Component Analysis (FPCA) for data lying on curved manifolds

Summary

Introduction

This paper studies acceleration variability among the juggling cycles from Ramsay et al (2014). An intuitive choice of data objects is the acceleration curves of each juggling cycle.

Results

Conclusion