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In this article, 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 subunits (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 component analysis (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 versus 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 profiles from genes activated by immunity system cells. Prevalent response patterns are identified by clustering the expression profiles using our multilevel clustering analysis.

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This paper introduces a spatio-temporal statistical analysis approach appropriate for monitoring or managing a physical system in which measurements are taken over dense time resolution but at sparse locations. The proposed approach is designed for implementation in an automated and efficient operation with manual intervention required only for scenario analysis. The method is based on a modeling framework for complex predictor-response and spatio-temporal relationships, and issues model-based prediction intervals. To accommodate varying practical situations, the method also includes an automated decision criterion for choosing between parametric and nonparametric spatial covariance models. The approach is illustrated using a data center thermal management problem.