Clustering Curves on a Reduced Subspace

The aim of this article is to propose a procedure to cluster functional observations in a subspace of reduced dimension. The dimensional reduction is obtained by constraining the cluster centroids to lie into a subspace which preserves the maximum amount of discriminative information contained in the original data. The model is estimated by using penalized least squares to take into account the functional nature of the data. The smoothing is carried out within the clustering and its amount is adaptively calibrated. A simulation study shows how the combination of these two elements, feature-extraction and automatic data-driven smoothing, improves the performance of clustering by reducing irrelevant and redundant information in the data. The effectiveness of the proposal is demonstrated by an application to a real dataset regarding a speech recognition problem. Implementation details of the algorithm together with a computer code are available in the online supplements.