An Application of Nonparametric Functional Data Analysis in the Sport Biomechanics Big Data Processing

Big data has ۵Vs (Volume, Variety, Velocity, Veracity, and Value) that are present in many fields like sports biomechanics with devices such as wearables, markers, etc. Among different statistical methods for big data analysis, functional data analysis (FDA) provides a methodology to analyze the dataset by considering underlying functions and curves. The open dataset includes ۵۷ healthy subjects with ۵۴ markers among the full-body and three-dimensional ground reaction force (GRF) that is a functional predictor. The GRF curves have registered with three methods: Group-wise function alignment and PCA Extractions, Bayesian methods in Ambient and Quotient space. The result with two indices: The synchronization (Sync) coefficient and the inverse of pairwise correlation (IPC) are compared. And four functional prediction methods considering weight, height, and body mass index (BMI) as continuous responses are used including regression, median, mode, and multimethod (nonlinear) operator. Two kernel functions (Triangle and Quadratic), and three semi-metrics (first and second derivative, PCA) with a local selection of the optimal numbers of the neighbors for kernel estimation are compared to each other. The result showed that the Mean Square Error (MSE) in group-wise function alignment for BMI with second derivative semi-metric and with the quadratic kernel is the lowest: regression (۱.۰۳,۴.۳۲ - ۱.۳۶,۵.۶۹), conditional mode (۱.۷۲,۷.۰۲ - ۰.۹۷,۴.۰۷), conditional median (۱.۴۷,۶.۱۵-۱.۸۳,۷.۶۵), multimethod (۴.۴۳,۵.۶۴- ۴.۹۸,۴.۵۳) for train, test and left-right GRF dataset, respectively. We conclude that the nonparametric FDA methods provide comprehensive methods for studying complex relationships in big data and they are popular in the sports biomechanics literature.

Keywords:

Big data , Functional data analysis , Curve registration , Sport biomechanics , Open dataset