A0467
Title: The MEM algorithm and modal clustering of functional data
Authors: Adhiraj Mandal - University of Glasgow (United Kingdom) [presenting]
Abstract: Functional data analysis (popularly abbreviated as FDA) is a branch of statistics that attempts to analyse information on a process that varies over a continuum. Such processes are often considered to be functions of time, though they can also be any other domain, such as energy, spatial location, wavelength, etc. In the FDA, each curve is considered to be an individual entity instead of a number of individual observations along the curve. Though this is a rich source of information about the process of generating the data, it also makes both theoretical and computational work centered on functional data challenging. The main focus of my research is to develop a framework for modal clustering for clustering functional data. The discussion starts with the MEM (modal expectation maximization) algorithm for multivariate data on a finite-dimensional space, followed by the HMAC (hierarchical mode association clustering) and PHMAC (parallel HMAC) algorithms for clustering functional data. The MEM algorithm plays a crucial role in the functionality and effectiveness of the HMAC and PHMAC algorithms. The benefits and drawbacks of the algorithms are discussed, and how these techniques might be applied for clustering functional data is investigated. In order to observe the clustering outcomes, the identical algorithms are applied to two data sets: one simulated and one real-world.
