This thesis is a mathematical exposition of the theory behind Topological Data Analysis
(TDA) complemented by two applications in medicine and financial realm. We start
by establishing the foundation of homology theory, ...
Clustering is one of the most widely researched areas in unsupervised learning, where the main aim is to find structures in unlabelled data sets. This is done by partitioning data
set into smaller groups or clusters so ...
This thesis aims to serve as an introduction to Topological Data Analysis (TDA), a collection
of methods that seek to quantify the topological and geometric features of data using
algebraic topology. The theory behind ...