Klasifikace realizací náhodných množin

Abstract

Random sets have gained significant importance in recent years as a valuable tool for modelling a wide range of phenomena in fields such as biology, geology, medicine, or material sciences. However, to the best of our knowledge, classification of their realisations has not yet been studied. In the presented work, a link between methods for random sets and functional data analysis is built that focusses on evaluating functional characteristics from individual components in the realisations based on their shape. Such obtained functional data is then used for nonparametric classification using both supervised and unsupervised approach based on k-nearest neighbours and k-means algorithms, respectively. The proposed procedures have been justified through a simulation study. Finally, the procedure is applied to medical data to show its applicability in practice.

Random sets have gained significant importance in recent years as a valuable tool for modelling a wide range of phenomena in fields such as biology, geology, medicine, or material sciences. However, to the best of our knowledge, classification of their realisations has not yet been studied. In the presented work, a link between methods for random sets and functional data analysis is built that focusses on evaluating functional characteristics from individual components in the realisations based on their shape. Such obtained functional data is then used for nonparametric classification using both supervised and unsupervised approach based on k-nearest neighbours and k-means algorithms, respectively. The proposed procedures have been justified through a simulation study. Finally, the procedure is applied to medical data to show its applicability in practice.