Functional data clustering via information maximization

TL;DR

This paper introduces a novel unsupervised clustering method for functional data using information maximization, which simplifies the process by avoiding density estimation and eigenfunction assumptions, and performs well in simulations and real data.

Contribution

It proposes a new information maximization-based clustering approach that simplifies functional data clustering without density estimation or eigenfunction assumptions.

Findings

Effective in simulation studies

Comparable to supervised classifiers in out-of-sample clustering

Avoids complex density and eigenfunction estimation

Abstract

A new method for clustering functional data is proposed via information maximization. The proposed method learns a probabilistic classifier in an unsupervised manner so that mutual information (or squared loss mutual information) between data points and cluster assignments is maximized. A notable advantage of this proposed method is that it only involves continuous optimization of model parameters, which is simpler than discrete optimization of cluster assignments and avoids the disadvantages of generative models. Unlike some existing methods, the proposed method does not require estimating the probability densities of Karhunen-Lo`eve expansion scores under different clusters and also does not require the common eigenfunction assumption. The empirical performance and the applications of the proposed methods are demonstrated by simulation studies and real data analyses. In addition, the proposed method allows for out-of-sample clustering, and its effect is comparable with that of some supervised classifiers.