Clustering multivariate functional data using unsupervised binary trees

TL;DR

This paper introduces a model-based clustering method using binary trees for multivariate functional data, accommodating noisy, discretely observed curves or images, with data-driven group determination and applications to vehicle trajectory analysis.

Contribution

It presents a novel binary tree clustering algorithm for complex multivariate functional data that is interpretable, fast, and adaptable to various data types and noise conditions.

Findings

Good performance on simulated datasets

Effective in complex clustering scenarios

Applied successfully to vehicle trajectory data

Abstract

We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout.