On effectiveness of k-means clustering of functional data with marginal covariance matrix

Abstract

Recent developments in many scientific fields, including biology, economics, and signal processing, have produced large number of huge collections of functional data. Examples are gene expression levels measured over time from microarray?experiments, functional magnetic resonance imaging, mass spectrometry data from proteinomics, lipidomics, and auction. Those measurements are often intricate?mixtures of the initial signal sources of interest. Clustering analysis coupled with PCA is often employed to search for homogeneous subgroups of individuals and identify mixed sources. In this talk, we will address the following question raised in the literature. Since PCA is used to capture the directions of greatest variability in the data, this variability is not necessarily to reflect the variability of between hidden clusters or transforming the data into principal components may obscure rather than revealing group of interest as in Chang (1983, Applied Statistics) and Yeung and Ruzzo (2001, Bioinformatics).Conditions in terms of eigenanalysis of between group variation and eigenanalysis of combined group within-cluster covariance structure will be given to ensure the?feasibility of straightforward eigenanalysis with k-means clustering procedure can be counted on to reveal cluster structure for latent variable models. In addition, the ?limitation on discovering hidden cluster structure will also be addressed.