A robust fuzzy clustering algorithm for functional data

Functional data frequently arise in many practical fields whenever observations are represented by curves. As is well-known, the fuzzy approach to clustering helps to manage all those situations where observations are characterized by intermediate behaviours between clusters. In the case of functional data, it refers to curves sharing the features of more than one cluster. Unfortunately, the obtained fuzzy partition may be affected by anomalous observations, i.e., curves far from the bulk of curves. To this purpose, a robust version of the fuzzy clustering algorithm for functional data is developed where outlying curves are automatically detected and assigned to an additional noise cluster.