Time-varying clustering of multivariate longitudinal observations

TL;DR

This paper introduces a novel time-varying clustering method for multivariate longitudinal data, combining a modified K-means algorithm with vector autoregressive models to capture evolving cluster structures over time.

Contribution

It extends classical K-means with a time-varying component and models cluster centroid evolution using VAR, providing a new approach for dynamic clustering analysis.

Findings

Successfully applied to human development data

Effectively captures temporal changes in clusters

Demonstrates improved clustering over static methods

Abstract

We propose a statistical method for clustering of multivariate longitudinal data into homogeneous groups. This method relies on a time-varying extension on the classical K-means algorithm, where a multivariate vector autoregressive model is additionally assumed for modeling the evolution of clusters' centroids over time. We base the inference on a least squares specification of the model and coordinate descent algorithm. To illustrate our work, we consider a longitudinal dataset on human development. Three variables are modeled, namely life expectancy, education and gross domestic product.