Supervised classification for human movement data : A comparative study of functional and traditional methods

Sammanfattning: Functional data analysis (FDA) has a growing importance in statistics, especially in disciplines like biomechanics, where it is common to observe data over time. The objective of this thesis is to employ FDA techniques and compare the classification performance of supervised classification models utilizing functional data with the same models using a discrete summary measurement (max-values) as input. The classification revolves around predicting whether individuals, who underwent anterior cruciate ligament (ACL) reconstruction surgery, have a limb symmetry index higher or lower than 90% based on their observed movements during squat and step-down exercises executed, on average, nine months prior. Expanding the knowledge of the rehabilitation process after ACL injuries is not only interesting for affected individuals but can also improve the utilization of medical resources and reduce societal costs.  The data comes from two occasions where 15 individuals who underwent ACL surgery performed the specified exercises. A total of 72 functional variables related to joint angles and moments, along with five additional univariate variables (e.g., the time elapsed between surgery and the first test occasion), were considered as potential predictors. Following an initial variable selection process using permutation tests, 14 variables were used separately in three different classification models: support vector machine (SVM), k-nearest neighbors (KNN), and naïve Bayes (NB). The classification performance was evaluated by the correct classification rate by leave-one-out cross-validation.  The results showed that, when considering the variable that yielded the highest accuracy for each specific method, models utilizing functional data generally outperformed their counterparts using max-values. With functional data, SVM achieved an accuracy of 100%, KNN 93%, and NB 80%. The accuracy using max-values as input was 87%, 87%, and 80% for the SVM, KNN, and NB, respectively.