Title: Automatic multivariate functional clustering for spatial longitudinal data
Authors: Noritoshi Arai - Chuo University (Japan) [presenting]
Toshihiro Misumi - Yokohama City University (Japan)
Hidetoshi Matsui - Shiga University (Japan)
Yoshihiko Maesono - Chuo University (Japan)
Sadanori Konishi - Kyushu University (Japan)
Abstract: Huge amount of multivariate longitudinal data with spatial information have been collected in recent years. So far, a problem of clustering for such data is little discussed. Functional clustering approach is one of the promising approaches for the multivariate longitudinal data. However, existing functional clustering does not consider the spatial dependence on the clustering algorithm even if the data contains spatial information. We introduce a novel multivariate functional clustering for spatial longitudinal data. A functional kriging approach with regularized basis expansions is applied to incorporate the spatial correlation for predicting functional data on unobserved point in the modeling process. After obtaining the predicted spatial functional data, a $x$-means clustering is implemented to the estimated coefficient vector of basis functions. The $x$-means is an extended method of $k$-means that automatically provides the optimal number of clustering. Numerical examples are presented to examine the effectiveness of our proposed clustering procedure.