Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Computer Engineering
Topological Hierarchies And Decomposition: From Clustering To Persistence, Kyle A. Brown
Topological Hierarchies And Decomposition: From Clustering To Persistence, Kyle A. Brown
Browse all Theses and Dissertations
Hierarchical clustering is a class of algorithms commonly used in exploratory data analysis (EDA) and supervised learning. However, they suffer from some drawbacks, including the difficulty of interpreting the resulting dendrogram, arbitrariness in the choice of cut to obtain a flat clustering, and the lack of an obvious way of comparing individual clusters. In this dissertation, we develop the notion of a topological hierarchy on recursively-defined subsets of a metric space. We look to the field of topological data analysis (TDA) for the mathematical background to associate topological structures such as simplicial complexes and maps of covers to clusters in …