Spectral clustering and downsampling-based model selection for functional data

Al Alawi, Maryam (2021) Spectral clustering and downsampling-based model selection for functional data. PhD thesis, University of Glasgow.

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Functional data analysis is a growing field of research and has been employed in a wide range of applications ranging from genetics in biology to stock markets in economics. A crucial but challenging problem is clustering of functional data. In this thesis, we review the main contributions in this field and discuss the strengthens and weaknesses of the different clustering functional data approaches. We propose a new framework for clustering functional data and a new paradigm for model selection that is specifically designed for functional data, which are designed to address many of the weaknesses of existing techniques. Our clustering framework is based on first reducing the infinite dimensional space of functional data to a finite dimensional space by smoothing and basis expansion. Then we implement the spectral clustering approach by designing a new distance measure which has the flexibility of using the distance between the original trajectories and/or their derivatives. In addition, we develop a new model selection criterion, by introducing a technique called ‘downsampling’, which allows us to create lower resolution replicates of the observed curves. These replicates can then be used to examine the clustering stability of the existing clustering functional data approaches and select the optimal number of clusters. Further, we combine the two proposed techniques to develop an integrated clustering framework to estimate the number of clusters inherently and accordingly cluster the functional data. An extensive simulation study with existing clustering functional data methods show a superior performance of our clustering framework and reliable results of the proposed model selection criteria. The usefulness of these new approaches is also illustrated through applications to real data.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
Supervisor's Name: Ray, Professor Surajit and Gupta, Dr. Mayetri
Date of Award: 2021
Depositing User: Theses Team
Unique ID: glathesis:2021-82568
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 18 Nov 2021 14:40
Last Modified: 08 Apr 2022 17:08
Thesis DOI: 10.5525/gla.thesis.82568
URI: http://theses.gla.ac.uk/id/eprint/82568

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