Title: Clustering for multivariate functional data
Authors: Pai-Ling Li - Tamkang University (Taiwan) [presenting]
Ling-Cheng Kuo - Tamkang University (Taiwan)
Abstract: A novel multivariate $k$-centers functional clustering algorithm for the multivariate functional data is proposed. We assume that clusters can be defined via the functional principal components subspace projection for each variable. A newly observed subject with multivariate functions is classified into a best-predicted cluster by minimizing a weighted distance measure, which is a weighted sum of discrepancies in observed functions and their corresponding projections onto the subspaces for all variables, among all the clusters. The weight of each variable represents the importance of a variable to the cluster information and is determined by the within-variable variation or the between-variable correlations. The proposed method can take the means and modes of variation differentials among groups of each variable into account simultaneously. In addition, the weight of the proposed algorithm is flexible and can be chosen by the objective of clustering. Numerical performance of the proposed method is examined by simulation studies, with an application to a data example.