Fuzzy C-means: Differences on Clustering Behavior between High Dimensional and Functional Data (Student Abstract)

Abstract Fuzzy c-means (FCM) is a generalization of the classical k-means clustering algorithm to the case where an observation can belong to several clusters at the same time. The algorithm was previously observed to have initialization problems when the number of desired clusters or the number of dimensions of the data are high. We have tested FCM against clustering problems with functional data, generated from stationary Gaussian processes, and thus in principle infinite-dimensional. We observed that when the data is more functional in nature, which can be obtained by tuning the length-scale parameter of the Gaussian process, the aforementioned problems do not appear. This not only indicates that FCM is suitable as a clustering method for functional data, but also illustrates how functional data differs from traditional multivariate data. In addition this seems to suggest a qualitative way to measure the latent dimensionality of the functional distribution itself.