🍩 Database of Original & Non-Theoretical Uses of Topology

1. Hierarchical Clustering and Zeroth Persistent Homology (2020)

   İsmail Güzel, Atabey Kaygun

   Abstract

   In this article, we show that hierarchical clustering and the zeroth persistent homology do deliver the same topological information about a given data set. We show this fact using cophenetic matrices constructed out of the filtered Vietoris-Rips complex of the data set at hand. As in any cophenetic matrix, one can also display the inter-relations of zeroth homology classes via a rooted tree, also known as a dendogram. Since homological cophenetic matrices can be calculated for higher homologies, one can also sketch similar dendograms for higher persistent homology classes.

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   • Geography
   • Coordinates data
   • Point cloud
   • Dendrogram
   • Hierarchical clustering
   • Persistent homology