Learning in high dimensions with projected linear discriminants

Durrant, Robert John (2013). Learning in high dimensions with projected linear discriminants. University of Birmingham. Ph.D.

PDF - Accepted Version

Download (1MB)


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: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Computer Science
Funders: None/not applicable
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
URI: http://etheses.bham.ac.uk/id/eprint/4218


Request a Correction Request a Correction
View Item View Item


Downloads per month over past year