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Clustering multivariate and functional data using spatial rank functions

Baragilly, Mohammed Hussein Hassan (2016)
Ph.D. thesis, University of Birmingham.

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In this work, we consider the problem of determining the number of clusters in the multivariate and functional data, where the data are represented by a mixture model in which each component corresponds to a different cluster without any prior knowledge of the number of clusters. For the multivariate case, we propose a new forward search methodology based on spatial ranks. We also propose a modified algorithm based on the volume of central rank regions. Our numerical examples show that it produces the best results under elliptic symmetry and it outperforms the traditional forward search based on Mahalanobis distances.
In addition, a new nonparametric multivariate clustering method based on different weighted spatial ranks (WSR) functions is proposed. The WSR are completely data-driven and easy to compute without any need to parameter estimates of the underlying distributions, which make them robust against distributional assumptions. We have considered parametric and nonparametric weights for comparison. We give some numerical examples based on both simulated and real datasets to illustrate the performance of the proposed method.
Moreover, we propose two different clustering methods for functional data. The first method is an extension to the forward search based on functional spatial ranks (FSR) that we proposed for the multivariate case. In the second method, we extend the WSR method to the functional data analysis. The proposed weighted functional spatial ranks (WFSR) method is a filtering method based on FPCA. Comparison between the existing methods has been considered. The results showed that the two proposed methods give a competitive and quite reasonable clustering analysis.

Type of Work:Ph.D. thesis.
Supervisor(s):Chakraborty, Biman
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:7124
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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