# Matching Golfers' Movement Patterns during a Golf Swing
## 2 Methods
### Statistical Analysis  
Statistical analysis was completed using MATLAB and R (R Foundation for Statistical Computing, Vienna, Austria). The following stages of statistical analysis were performed: (i) principal component analysis of thorax axial rotation, pelvis axial rotation, COP\({}_{\text{ML}}\) and COG\({}_{\text{ML}}\) variables, (ii) fuzzy coding of retained principal components, clubhead velocity and ball velocity using a triangular fuzzy window coding system and, finally, (iii) multiple correspondence analysis of fuzzy-coded biomechanics variables with clubhead and ball velocity as supplementary points. In the first stage, a PCA was performed. For each golfer and variable, an \(n\times p\) data matrix was formed where \(n\) was the number of trials (\(n=5\)) and \(p\) each normalised time point throughout the swing (\(p=501\)) ready for PCA. Matrices for each golfer were vertically concatenated to form a single 110 \(\times\) 501 data matrix representing all the golfers' data for a given variable. The MATLAB function 'pca' was used to perform independent PCA on axial rotation variables, centre of pressure, and centre of gravity variables whereby data was normalised to have a mean of zero and then the singular value decomposition (SVD) algorithm used. Results of principal component analysis included the number of principal components (PCs), percentage of variance each PC explained, the PCs loading factors, and PC scores. Only principal components explaining at least 80% of the variance were considered due to the limited dataset of golfers and trials. A PC score, for each principal component, golfer, and trial was computed. A large negative (\(-\)ve) or positive (\(+\)ve) PC score represented golfers whose curves were further away from the mean curve in the portions of the swing that had higher loading factors. Loading factors were the same length as the original data and could help deduce the stage in the swing where the greatest variation in movement patterns occurred. Positive or negative loading factors had an additive or subtractive effect on the mean data curve at those stages in the swing. A loading factor close to zero contributed little to the PC and indicated that there was little difference between golfers' movement patterns at this stage in the swing and golfers tended towards the mean curve. Qualitative biomechanical interpretation of the PCs was achieved by examining the loading factors for each PC throughout the swing and by observing the mean data curves with plus and minus one standard deviation of the PC scores multiplied by the loading factor for each PC. The PCs which cumulatively explained at least 80% of the variance in the first stage of analysis were used in the second stage of the analysis. Thorax and pelvis axial rotation variable PC scores (five PCs), COPML PC scores (three PCs), COGML PC scores (two PCs), clubhead velocity, and ball velocity impact parameters were separately coded between zero and one using three triangular fuzzy membership functions related to three modalities; low, median, and high as used by [PERSON] et al. [13]. The membership values were determined based on the distribution of data for each variable whereby low and high boundaries corresponded to the 5 th and 95 th percentiles, respectively. Three membership values corresponding to the three modalities for each variable and golfer were deduced and vertically concatenated. The three membership values cumulatively equaled one. This process resulted in a fuzzy coded indicator matrix consisting of 110 rows \(\times\) 36 columns (i.e., rows = 22 golfers \(\times\) 5 trials and columns = 10 biomechanics PCs + 2 impact parameters \(\times\) 3 modalities). Thirdly, a correspondence analysis was carried out on the indicator matrix (i.e., MCA) using the R statistical analysis package 'FactoMineR'. Multiple correspondence analysis is a descriptive data analysis method useful for revealing associations between variables.