Clustering Methods for Correlated Data

Abstract

Hierarchical Clustering is one of the most popular unsupervised clustering methods.Using a simple agglomerative algorithm, it iteratively combines similar clusters together forming cohesive groups of observations. This work focuses on Hierarchical Clustering and how it may be adapted to accommodate correlated observations. Chapter 2 investigates how to develop a statistical framework for Hierarchical Clustering so we may derive statistical properties from the clustering method. In Chapter 3, a new method, Hierarchical Cohesion Clustering is proposed. This method is a modification of the traditional methods which aims to accommodate correlated observations. This approach explores how repeated measurements may be preprocessed into intermediate clusters to improve clustering outcomes. The method is applied to a sequence-based time use dataset about how people spend their time throughout the day. In Chapter 4, we focus on how to incorporate spatial adjacency data when clustering. We continue to investigate Hierarchical Clustering methods, with a special focus on Hierarchical Cohesion Clustering. Applying the collection of methods to COVID-19 case rate data within counties, a comparison of the methods is performed with summaries of their respective strengths and weaknesses. Spatial simulations are included to better determine each approach’s efficacy and when certain approaches are preferable.