A topological approach to data visualization

Abstract: Barcoding is a mathematical tool, to analyze data, which is based on the theory of persistent homology. In this thesis both Hierarchical Clustering and Barcoding are defined and analyzed according to three criterion: Continuity, Computability and Visualizability. It is also presented how the two methods, barcoding and hierarchical clustering, are connected and why barcoding, in some cases, is a generalized method of hierarchical clustering. Lastly some more question of interest, for better understanding barcoding, are stated.