Penalized Clustering of Large Scale Functional Data with Multiple Covariates

TL;DR

This paper introduces a flexible penalized clustering method for large-scale functional data with multiple covariates, utilizing nonparametric multivariate functions, functional ANOVA, and a novel EM algorithm for improved clustering accuracy.

Contribution

It develops a new penalized mixed-effect clustering approach for functional data with multiple covariates, incorporating functional ANOVA and a rejection-controlled EM algorithm.

Findings

Effective in modeling complex functional features like jumps and periodicity

Demonstrates superior clustering performance in simulations and real data

Provides open-source R package for implementation

Abstract

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling a variety of function features, such as jump points, branching, and periodicity. Functional ANOVA is employed to further decompose multivariate functions in a reproducing kernel Hilbert space and provide associated notions of main effect and interaction. Parsimonious random effects are used to capture various correlation structures. The mixed-effect models are nested under a general mixture model, in which the heterogeneity of functional data is characterized. We propose a penalized Henderson's likelihood approach for model-fitting and design a rejection-controlled EM algorithm for the estimation. Our method selects smoothing parameters through generalized cross-validation. Furthermore, the Bayesian confidence intervals are used to measure the clustering uncertainty. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Open-source code is available in the R package MFDA.