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Title: Clustering time series data by analysing graphical models of connectivity and the application to diagnosis of brain disorders
Author: Wolstenholme, Robert
ISNI:       0000 0004 6496 2890
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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In this thesis we investigate clustering and classification techniques applied to time series data from multivariate stochastic processes. In particular we focus on extracting features in the form of graphical models of conditional dependence between the process components. The motivation is to use the techniques on brain EEG data measured from multiple patients and investigate whether it can be used in areas such as medical diagnosis. We look at both the case where the graphical model is estimated based on time series recorded on the scalp and also where the graphical model is estimated based on source signals within the brain. In the first case we use a multiple hypothesis testing approach to build the graphical models and a learning algorithm based on random forests to find patterns within multiple graphical models. In the second case we use independent component analysis (ICA) to extract the source time series and estimate the conditional dependence graphs using partial mutual information. It is of particular note that in this case due to the indeterminacy issues associated with ICA we only know the conditional dependence graphs up to some unknown permutation of the nodes. To solve this issue we use novel methods based on an extension of graph matching to multiple inputs in order to develop a new clustering algorithm. Finally, we show how this algorithm can be combined with further information obtained during the ICA phase contained in columns of the unmixing matrix, to create a more powerful method.
Supervisor: Walden, Andrew Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral