Clustering of functional data in a low-dimensional subspace

Authors:
Michio Yamamoto
Affiliations:
Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-8531
Venue:
Advances in Data Analysis and Classification
Year:
2012

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Abstract

To find optimal clusters of functional objects in a lower-dimensional subspace of data, a sequential method called tandem analysis, is often used, though such a method is problematic. A new procedure is developed to find optimal clusters of functional objects and also find an optimal subspace for clustering, simultaneously. The method is based on the k-means criterion for functional data and seeks the subspace that is maximally informative about the clustering structure in the data. An efficient alternating least-squares algorithm is described, and the proposed method is extended to a regularized method. Analyses of artificial and real data examples demonstrate that the proposed method gives correct and interpretable results.