Today I submitted my Masters of Mathematics thesis. I embarked on this journey 3 years ago and today marks an end to that journey. The title of my thesis is ‘Optimal Cycle Representatives in Persistent Homology’.
It is essentially mainly a Pure Mathematics thesis, exploring a problem present in statistical data analysis, and it culminates in an application to image analysis – so it’s pretty much a chimera of pure, applied and stats.
Here is the abstract of my thesis:
This thesis presents current research on computing optimal cycle representatives in persistent homology, a critical topic in Topological Data Analysis. Persistent homology provides a mathematical framework for studying the multi-scale topological features of data, capturing essential structures such as connected components, holes, and cavities. However, the cycle representatives calculated in persistent homology are not always the best representation of these topological features and thus requires optimisation. This thesis explores the current methods as well as their limitations in computing persistent homology cycle representatives and concludes with an application to image analysis.
And below is an upload of the thesis document.
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