Exploring the applicability of functional data analysis (FDA) for dimension reduction in bigdata applications

Abstract

In this thesis we use Functional Data Analysis (FDA) methods to explore space and time variations in climate patterns from historical data of 16 locations spread across South Africa. Specifically, we focus on maximum monthly temperature data for the period 1965 to 2010 with 5 years of intervals. We explore this data with methods of aligning curves, the phaseplane analysis, functional Principal Component Analysis (fPCA), and functional clustering. The purpose of this exercise is to investigate within the FDA framework how the temperature patterns may have changed over time and space for the data analysed. To the best of our knowledge this is the first attempt to understand maximum temperature over 40+ years from South Africa using FDA methods.