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Learning in high dimensions with projected linear discriminants

Durrant, Robert John (2013)
Ph.D. thesis, University of Birmingham.

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Abstract

The enormous power of modern computers has made possible the statistical modelling of data with dimensionality that would have made this task inconceivable only decades ago. However, experience in such modelling has made researchers aware of many issues associated with working in high-dimensional domains, collectively known as `the curse of dimensionality', which can confound practitioners' desires to build good models of the world from these data. When the dimensionality is very large, low-dimensional methods and geometric intuition both break down in these high-dimensional spaces. To mitigate the dimensionality curse we can use low-dimensional representations of the original data that capture most of the information it contained. However, little is currently known about the effect of such dimensionality reduction on classifier performance. In this thesis we develop theory quantifying the effect of random projection - a recent, very promising, non-adaptive dimensionality reduction technique - on the classification performance of Fisher's Linear Discriminant (FLD), a successful and widely-used linear classifier. We tackle the issues associated with small sample size and high-dimensionality by using randomly projected FLD ensembles, and we develop theory explaining why our new approach performs well. Finally, we quantify the generalization error of Kernel FLD, a related non-linear projected classifier.

Type of Work:Ph.D. thesis.
Supervisor(s):Kaban, Ata
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Computer Science
Subjects:QA75 Electronic computers. Computer science
Institution:University of Birmingham
ID Code:4218
This unpublished thesis/dissertation is copyright of the author and/or third parties.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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