Faster Functional Clustering via Gaussian Mixture Models

TL;DR

This paper introduces a Gaussian mixture model-based method for functional data clustering that significantly improves computational efficiency over traditional linear mixed-effects models, demonstrated on biological data.

Contribution

The paper presents a novel GMM-based approach for functional clustering that is faster and easier to implement than existing MLMM methods.

Findings

GMM approach offers improved computational speed.

The method is effective on calcium imaging data.

Theoretical analysis supports the approach.

Abstract

Functional data analysis (FDA) is an important modern paradigm for handling infinite-dimensional data. An important task in FDA is model-based clustering, which organizes functional populations into groups via subpopulation structures. The most common approach for model-based clustering of functional data is via mixtures of linear mixed-effects models. The mixture of linear mixed-effects models (MLMM) approach requires a computationally intensive algorithm for estimation. We provide a novel Gaussian mixture model (GMM) characterization of the model-based clustering problem. We demonstrate that this GMM-based characterization allows for improved computational speeds over the MLMM approach when applied via available functions in the R programming environment. Theoretical considerations for the GMM approach are discussed. An example application to a dataset based upon calcium imaging in the larval zebrafish brain is provided as a demonstration of the effectiveness of the simpler GMM approach.