Clustering vertical ground reaction force curves produced during countermovement jumps

Abstract

The aim of this study is to assess and compare the performance of commonly used hierarchical, partitional (k-means) and Gaussian model-based (Expectation–Maximization algorithm) clustering techniques to appropriately identify subgroup patterns within vertical ground reaction force data, using a continuous waveform analysis. In addition, we also compared the performance across each technique using normalized and non-normalization input scores. Both generated and real data (one hundred and twenty two vertical jumps) were analyzed. The performance of each cluster technique was measured by assessing the ability to explain variances in jump height using a stepwise regression analysis. Only k-means (normalized scores; 82%) and hierarchical clustering (normalized scores; 85%) were able to extend the ability to describe variances in jump height beyond that achieved using the group analysis (i.e. one cluster; 78%). Further, our findings strongly indicate the need to normalize the input data (similarity measure) when clustering. In contrast to the group analysis, the subgroup analysis was able to identify cluster specific phases of variance, which improved the ability to explain variances in jump height, due to the identification of cluster specific predictor variables. Our findings therefore highlight the benefit of performing a subgroup analysis and may explain, at least in part, the contrasting findings between previous studies that used a single group level of analysis.

Introduction

The countermovement jump (CMJ) is an important task in a number of sports (e.g. volleyball and basketball) and its biomechanics have been frequently studied (Klavora, 2000). However, identified features that relate to the performance outcome (jump height) are often inconsistent (Richter et al., 2014). For example, maximum vertical ground reaction force (vGRF) is reported in some studies as a performance related factor (Cormie et al., 2009, Dowling and Vamos, 1993, Sheppard et al., 2009), while it is not in others (Morrissey et al., 1998, Newton et al., 1999, Petushek et al., 2010). This makes it difficult to conclude which neuromuscular capacities or movement techniques should be altered to enhance jump height, the criterion performance outcome in CMJs. Recently, we have shown that some of the contrasting findings across studies may be due to the use of discrete point analysis (Richter et al., 2014). An alternative to discrete point analysis is a continuous waveform analysis (e.g. functional principal component analysis or analysis of characterizing phases) which has grown in popularity within many disciplines, including biomechanics, and has been reported to provide a better insight than discrete point analysis (Dona et al., 2009, Donoghue et al., 2008, Godwin et al., 2010, Harrison et al., 2007, Newell et al., 2006, Ramsay and Silverman, 2002, Richter et al., 2014, Ryan et al., 2006).

An additional reason for the inconsistencies across studies however, may be inter-subject variability. Vertical ground reaction curves generated during a CMJ can differ significantly in shape across subjects (e.g. non-modal, uni-modal or bi-modal), which could imply that different movement strategies are being employed, which may in turn have different performance related factors. This might explain some of the contrasting findings, since previous studies generally employed a single group analysis which can mask performance related factors if different shapes have different performance related factors (Bates, 1996, Stergiou, 2004, Stergiou and Scott, 2005). An alternative to a single group analysis is a subgroup analysis, which classifies similar patterns (curve shapes or movement strategies) into subgroups; so called clusters. An optimal clustering maximizes the ability to predict the dependent variable (e.g. jump height) of a data set (Han et al., 2006). To the authors׳ knowledge it appears that none of the previous CMJ studies have used a subgroup analysis, while subgroup analyses have been frequently performed in studies that examine human gait (Carriero et al., 2009, Kienast et al., 1999, OByrne et al., 1998, OMalley et al., 1997, Stout et al., 1995, Toro et al., 2007, von Tscharner et al., 2013).

A challenge in subgroup analysis is that a variety of clustering techniques exists that may result in different clusters (Hastie et al., 2001, Jain et al., 1999, Martinez et al., 2004, Witten and Frank, 2005). Additionally, while the number of studies that has used continuous waveform analysis in the area of biomechanics is increasing, little is known about the performance of different clustering techniques with continuous waveform analysis in biomechanics. The computed continuous features aim to represent the pattern of a curve over multiple phases of the movement cycle and can be highly collinear, which may influence results of some clustering techniques. Clustering approaches differ in their underlying assumptions and can be divided broadly into hierarchical, partitional and probabilistic clustering (Hastie et al., 2001, Martinez et al., 2004, Witten and Frank, 2005). The advantage of hierarchical clustering techniques is that they provide a highly interpretable description of the hierarchy within the data (i.e. dendrogram) and do not require the number of clusters to be chosen prior to the analysis. However, the assignment of samples into clusters requires the generation of inter-point distances of the input data (where different approaches can give very different results) and imposes a hierarchical structure within the examined data (Hastie et al., 2001, Martinez et al., 2004, Witten and Frank, 2005). In contrast, partitional clustering (e.g. k-means) can be performed without calculating inter-point distances, it is commonly used and is usually more suitable for large data sets (Martinez et al., 2004). However, k-means clustering also requires the user to choose the number of clusters (prior to analysis) and the construction of a dendrogram is computationally prohibitive (Hastie et al., 2001, Jain et al., 1999, Martinez et al., 2004, Witten and Frank, 2005). In addition, both hierarchical and partitional clustering techniques follow a deterministic process where the generated clusters and their members are somewhat dependent on the ordering of samples (Witten and Frank, 2005). Consequently, a third method, model-based clustering might be more appropriate for classifying biomechanical data. Model-based clustering techniques assign individuals into clusters based on their fit to a given mathematical model. An often used model is the Gaussian mixture model (Han et al., 2006), which assigns subjects into clusters based on the nature of the statistical inference, might be more appropriate for classifying movement strategies. Due to the variation in clustering approaches, and the relative novelty of classifying continuous biomechanical data/features, it is important to identify which clustering technique has the greatest ability to recognize and appropriately separate patterns within multiple curves.

The primary aim of this study is to assess and compare the performance of commonly used hierarchical, partitional and probabilistic clustering techniques to appropriately identify patterns within a sample of self-created curves (manipulated data set) and a sample of vGRF curves captured during countermovement jumps (real data set), using a continuous waveform analysis. A secondary aim is to examine if there are benefits to performing a subgroup analysis compared to the commonly used single group analysis when identifying vertical ground reaction vGRF factors related to jump height.