dissertation

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\documentclass[ % the name of the author
                    author={Ivor Shanik Dassenaike},
                % the name of the supervisor
                supervisor={Prof. Bogdan Warinschi},
                % the degree programme
                    degree={BSc},
                % the dissertation    title (which cannot be blank)
                     title={Topological Data Analysis and its Application to Image Data},
                % the dissertation subtitle (which can    be blank)
                  subtitle={},
                % the dissertation     type
                %  type={},
                % the year of submission
                      year={2018} ]{dissertation}

\begin{document}

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\iffalse
\section*{Prelude}
\thispagestyle{empty}

A typical dissertation will be structured according to (somewhat) standard
sections, described in what follows.  However, it is hard and perhaps even
counter-productive to generalise: the goal is {\em not} to be prescriptive,
but simply to act as a guideline.  In particular, each page count given is
important but {\em not} absolute: their aim is simply to highlight that a
clear, concise description is better than a rambling alternative that makes
it hard to separate important content and facts from trivia.

You can use this document as a \LaTeX-based~\cite{latexbook1,latexbook2}
template for your own dissertation by simply deleting extraneous sections
and content; keep in mind that the associated {\tt Makefile} could be of
use, in particular because it automatically executes \mbox{BibTeX} to
deal with the associated bibliography.

You can, on the other hand, opt {\em not} to use this template; this is a
perfectly acceptable approach.  Note that a standard cover and declaration
of authorship may still be produced online via
\[
\mbox{\url{http://www.cs.bris.ac.uk/Teaching/Resources/cover.html}}
\]

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% dissertation, but if you do not require the latter they can be suppressed
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\newpage
\section*{Acknowledgments}
I want to thank Professor Bogdan Warinschi, not only for being my project supervisor and providing useful help in a timely manner, despite the field of research of this thesis still being in its infancy, but also for being my personal tutor throughout my time at this University and helping me in my university career whenever I needed it. I doubt I would have made it through so happily without him.
\newpage

\section*{Abstract}
Topological data analysis is an emergent field, and was recently invented as a tool to be used for data analysis. It provides a novel way of learning about or uncovering the structures underpinning data, by transforming the data into a topological shape to analyse it. Its key insight is that data fundamentally has shape, and that this shape matters. Topological data analysis can be used to find out information about the data that is obscured from other methods of analysis, for example hidden patterns. Moreover, a lot of data is very high-dimensional, and as such is very sparse; topological data analysis has an immediate advantage over more traditional analysis techniques in that it assumes its input data is already high-dimensional, so does not have to rely heavily on dimensionality reduction and chosen metrics in order to say anything useful about the data.

This thesis will investigate the idea that topological data analysis provides a new and useful way to consider and analyse image data and to learn from it, or about how different content changes the underlying structure of image data. We will use and extend work already done on topological data analysis by applying it to image data, and in doing so find out in a more concrete fashion whether topological data analysis can be used in such a context, and if so, how representing the data in different ways affects how topological data analysis sees the data, if it indeed affects it at all.

There are three major parts to do the above: reviewing the state of the art and understanding better exactly what topological data analysis is and how it works; implementing and applying topological data analysis to image data by combining and extending existing techniques to create a toolchain; and analysing the results we get to draw conclusions about how well topological data analysis works using the toolchain created.

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