Dimension-Reduced Clustering of Functional Data via Subspace Separation

We propose a new method for finding an optimal cluster structure of functions as well as an optimal subspace for clustering simultaneously. The proposed method aims to minimize a distance between functional objects and their projections with the imposition of clustering penalties. It includes existing approaches to functional cluster analysis and dimension reduction, such as functional principal component k-means (Yamamoto, 2012) and functional factorial k-means (Yamamoto and Terada, 2014), as special cases. We show that these existing methods can perform poorly when a disturbing structure exists and that the proposed method can overcome this drawback by using subspace separation. A novel model selection procedure has been proposed, which can also be applied to other joint analyses of dimension reduction and clustering. We apply the proposed method to artificial and real data to demonstrate its performance as compared to the extant approaches.