APPLICATIONS OF PERSISTENT HOMOLOGY IN FINITE METRIC SPACES AND CLUSTERING

Main Article Content

A. M. RASHAD
H. N. ALAA
M. S. MOHAMMED

Abstract

Finite data sets are considered as metric spaces with defining the dissimilarity measure between the data points of them. In this work, we describe the persistent homology flowchart (PHF) in detail and study the persistence barcodes of Vietoris-Rips. PHF starts with a finite metric space and ends with a persistence diagram encoding features of the input data set. We compute  and -dimensional persistence diagrams and barcodes of the -point metric space, . Finally, as an application on PH flowchart, we interpret the single linkage clustering of    via -dimensional persistence diagram , we then deduce that persistent homology generalizes clustering.

Keywords:
Persistent homology, metric spaces, clustering and diagrams.

Article Details

How to Cite
RASHAD, A. M., ALAA, H. N., & MOHAMMED, M. S. (2020). APPLICATIONS OF PERSISTENT HOMOLOGY IN FINITE METRIC SPACES AND CLUSTERING. Asian Journal of Mathematics and Computer Research, 27(1), 14-27. Retrieved from http://www.ikprress.org/index.php/AJOMCOR/article/view/4959
Section
Original Research Article

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