Persistent Homology : A Modern Application of Algebraic Topology in Data Analysis

Sammanfattning: Topological data analysis emerged as a field in the 2000s and has proven very useful for examining the shape of data sets. Using persistent homology as their main methodology researchers has succesfully applied the theory presented in this paper to study as varied subjects as robot motion, brain connectivity, network theory, finger print analysis and computer vision.  The mathematical theory behind persistent homology has traditionally required training far beyond what an average engineer would have. Therefore much theory is usually left out of presentations meant for an audience outside of a mathematics department. This paper contains a novel approach to the presentation of this theory, maintaining mathematical rigour while only using linear algebra as its building blocks.