Analysis of juggling data: Alignment, extraction, and modeling of juggling cycles

Abstract

In this paper we present results from alignment, extraction, and statistical analysis of juggling trajectories using an elastic functional data analysis framework. This framework, specifically adapted for analyzing cyclostationary signals using an elastic Riemannian metric, was introduced recently by Kurtek et al. [2]. It relies on a special representation of curves called the square-root velocity function to pose the alignment problem as an optimization over the re-parametrization space. The cost function for alignment is a proper metric and is used to separate phase and amplitude components of juggling cycles. We present results of segmenting juggling trials into cycles, separating phase and amplitude components of cycles, and developing principal component analysis (PCA) based statistical models for these individual components.