Functional Clustering through Independent Component Analysis

H. Ortiz, C. Acal, F. Fortuna, A. Naccarato, A. M. Aguilera del Pino

In this work, we tackle the problem of clustering functional data using an approach based on Functional Independent Component Analysis (FICA). The main goal is to uncover group structures often missed by more traditional methods. To do this, the method makes use of higher-order statistical properties, which helps identify non-Gaussian patterns useful for distinguishing between groups. We evaluate the performance of the approach through a series of simulation studies, considering different sample sizes, noise levels, and types of underlying structures. The results suggest that this method performs better than clustering techniques based on spline representations or functional principal components, especially with larger samples or more complex settings. Another interesting finding is that most of the relevant information for separating groups can be captured with just a few components, making it possible to work with a lower-dimensional and more efficient representation for clustering.

Keywords: Functional Data Analysis, Functional Independent Component Analysis, Functional Clustering

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