Functional data clustering via information maximization

A novel method for clustering functional data is introduced that utilizes information maximization. The method employs unsupervised learning to develop a probabilistic classifier that maximizes the mutual information or squared loss mutual information between data points and their corresponding cluster assignments. A significant advantage of this method is that it involves only continuous optimization of model parameters, which is simpler than discrete optimization of cluster assignments and avoids the drawbacks of generative models. Unlike existing methods, this method does not necessitate the estimation of probability densities of Karhunen-Loeve expansion scores under different clusters and does not require the common eigenfunction assumption. The efficacy of the proposed method is demonstrated through simulation studies and real data analysis. Additionally, the technique permits out-of-sample clustering, and its performance is comparable to that of supervised classifiers.