Biclustering analysis of functionals via penalized fusion

In biomedical data analysis, clustering is commonly conducted. Biclustering analysis conducts clustering in both the sample and covariate dimensions and can more comprehensively describe data heterogeneity. In most of the existing biclustering analyses, scalar measurements are considered. In this study, motivated by time-course gene expression data and other examples, we take the "natural next step" and consider the biclustering analysis of functionals under which, for each covariate of each sample, a function (to be exact, its values at discrete measurement points) is present. We develop a doubly penalized fusion approach, which includes a smoothness penalty for estimating functionals and, more importantly, a fusion penalty for clustering. Statistical properties are rigorously established, providing the proposed approach a strong ground. We also develop an effective ADMM algorithm and accompanying R code. Numerical analysis, including simulations, comparisons, and the analysis of two time-course gene expression data, demonstrates the practical effectiveness of the proposed approach.