Abstract

Functional data analysis deals with data naturally represented as curves observed over a continuum. When the objective is to partition such curves into a limited number of clusters, fuzzy clustering provides an effective framework for handling the complexity of real-world data. By assigning membership degrees to clusters, it naturally manages all those complex situations in which curves share the features of more than one cluster. Several fuzzy clustering algorithms for functional data can be derived, including standard fuzzy k-means as well as variants based on entropic regularization and polynomial fuzzifiers. Furthermore, robust versions can also be considered to mitigate the influence of outlying curves in the dataset. A unified framework encompassing these algorithms is presented and their performance is illustrated through real-world applications.