In this paper we propose a novel clustering method for functional data based on the principal curve clustering approach. By this method functional data are approximated using functional principal component analysis (FPCA) and the principal curve clustering is then performed on the principal scores. The proposed method makes use of the nonparametric principal curves to summarize the features of the principal scores extracted from the original functional data, and a probabilistic model combined with Bayesian Information Criterion is employed to automatically and simultaneously find the appropriate number of features, the optimal degree of smoothing and the corresponding cluster members. The simulation studies show that the proposed method outperforms the existing functional clustering approaches considered. The capability of this method is also demonstrated by the applications in the human mortality and fertility data.
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(http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits noncommercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Funding Information: This work was jointly funded by the Institute and Faculty of Actuaries (IFoA) and the College of Science and Engineering of the University of Leicester (UoL) through a PhD studentship.
- functional data analysis
- functional principal component analysis
- principal curves
ASJC Scopus subject areas
- Statistics and Probability