Aggregation of Tennis Multivariate Time-Series Using the Choquet Integral and Its Generalizations

The main aim of this paper is to increase the recognition accuracy of tennis movements obtained by various crisp classifiers on a basis Choquet integral and its generalizations serving as aggregation operators. The tennis forehand, backhand, and volley were taken into consideration with three-dimensional coordinates obtained from a motion capture system. The whole silhouette, together with the tennis racket, were involved in the study. The following classifiers with and without input fuzzification were applied: Naive Bayes, k-NN, Extreme Gradient Boosting, Light Gradient Boosting Machine, Random Forest, Extra Trees, CatBoost, Gradient Boosting, Ada Boost, Decision Tree, Ridge, and SVM. For the individual classifiers the highest accuracy of 75.10% was obtained without fuzzification and of 88.25% with fuzzification. Examinations with 25 families of t-norms were conducted and the best functions were chosen, including the Open Newton-Cotes 5 point quadrature. As a result of the aggregation the classification accuracy was improved and reached a lever of 90%.