Exploratory Analysis of Functional Data via Clustering and Optimal Segmentation

TL;DR

This paper introduces an exploratory analysis method for functional data that clusters functions and creates simple prototypes with optimal segmentation, demonstrated on real datasets.

Contribution

The paper presents a novel clustering and segmentation algorithm for functional data using dynamic programming for optimal segment distribution.

Findings

Effective clustering of functional data demonstrated on real datasets

Prototypes with piecewise constant segments simplify data interpretation

Dynamic programming optimally distributes segments among clusters

Abstract

We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of segments in the prototypes, $P$, is chosen by the user and optimally distributed among the clusters via two dynamic programming algorithms. The practical relevance of the method is shown on two real world datasets.