Multilevel Functional Clustering Analysis

• Activity Number: 227
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Nicoleta Serban*+ and Huijing Jiang
• Companies: Georgia Institute of Technology and IBM T. J. Watson Research Center
• Keywords: Cluster analysis ; Functional ANOVA ; Hard clustering ; Microarray analysis ; Multilevel functional data ; Multilevel principal component analysis

Abstract

In this research, we investigate clustering methods for multilevel functional data, which consist of repeated random functions observed for a large number of units (e.g. genes) at multiple sub-units (e.g. bacteria types). To describe the within- and between-variability induced by the hierarchical structure in the data, we take a multilevel functional principal components (MFPCA) approach. We develop and compare a hard clustering method applied to the scores derived from the MFPCA and a soft clustering method using an MFPCA decomposition. In a simulation study, we assess the estimation accuracy of the clustering membership and the cluster patterns under a series of settings: small vs. moderate number of time points; various noise levels and varying number of subunits per unit. We demonstrate the applicability of the clustering analysis to a real data set consisting of expression pro files from genes activated by immunity system cells.