Clustering Gaussian Processes: A Modified EM Algorithm for Functional Data Analysis with Application to British Columbia Coastal Rainfall Patterns

Abstract

Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the lo- cation for a function’s value. In this thesis Gaussian processes, a generalization of the multivariate normal distribution to function space, are used. When multiple processes are observed on a comparable interval, clustering them into sub-populations can provide significant insights. A modified EM algorithm is developed for cluster- ing processes. The model presented clusters processes based on how similar their underlying covariance kernel is. In other words, cluster formation arises from modelling correlation between inputs (as opposed to magnitude between process values). The method is applied to both simulated data and British Columbia coastal rainfall patterns. Results show clustering yearly processes can accurately classify extreme weather patterns.