Understanding Published Literatures on Persistent Homology using Social Network Analysis

Abstract

In several fields, topology is well adapted for analyzing big data and much more potent than conventional data analysis methods. Persistent Homology is an algebraic method used in topological data analysis for measuring shapes and functions. This paper aimed to analyze literature on Persistent Homology. From its inception (2004) to 6th November 2020, we comprehensively searched the Scopus science database. This paper records the document and source types, year of publication, languages of documents, subject areas, author’s keywords, country/region, authors, institutions, and citations, utilizing standard bibliometric indicators. The VOSviewer applications were used for analysis through various network forms. Two network measurements were considered to analyze the network model, which are degree centrality and betweenness centrality. Additional analysis was undertaken using Persistent Homology itself to comprehend the co-authorship network better. The study found that the number of Persistent Homology research has risen dramatically since 2014. Globally, scholars in the area mainly come from the United States. Regarding the number of citations, with an average of 51.2 citations each year, the paper by Zomorodian and Carlsson (2005) appears as the most cited article. Much of the study on Persistent Homology was in the fields of computer science and mathematics. The most used keywords were “topological features” and “data handling”, which reflect the significant study fields covered in Persistent Homology. Overall, the increasing number of Persistent Homology publications reflects a growing knowledge of its meaning and unique demands.