Understanding Published Literatures on Persistent Homology using Social Network Analysis
DOI:
https://doi.org/10.11113/mjfas.v18n4.2418Keywords:
Persistent Homology, Topological Data Analysis, Bibliometric Analysis, Social Network AnalysisAbstract
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.
References
Y. Du, M. Zhang, G. Stonis, and S. Juan, “Topological Data Analysis on Magnetic Resonance Image Biomarkers,” 2019, pp. 1185–1187, doi: 10.1109/BIBM47256.2019.8983312.
M. Olejniczak, A. Severo Pereira Gomes, and J. Tierny, “A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations,” Int. J. Quantum Chem., vol. 120, no. 8, p. e26133, Apr. 2020, doi: https://doi.org/10.1002/qua.26133.
S. Agami and R. J. Adler, “Modeling of persistent homology,” Commun. Stat. - Theory Methods, vol. 49, no. 20, pp. 4871–4888, 2020, doi: 10.1080/03610926.2019.1615091.
N. Otter, M. A. Porter, U. Tillmann, P. Grindrod, and H. A. Harrington, “A roadmap for the computation of persistent homology,” EPJ Data Sci., vol. 6, no. 1, pp. 1–45, 2017, doi: 10.1140/epjds/s13688-017-0109-5.
K. Turner, S. Mukherjee, and D. M. Boyer, “Persistent homology transform for modeling shapes and surfaces,” Inf. Inference, vol. 3, no. 4, pp. 310–344, 2014, doi: 10.1093/imaiai/iau011.
D. Bhaskar et al., “Analyzing collective motion with machine learning and topology,” Chaos, vol. 29, no. 12, pp. 123125-1-12315–12, 2019, doi: 10.1063/1.5125493.
M. E. Aktas, E. Akbas, and A. El Fatmaoui, “Persistence homology of networks: methods and applications,” Appl. Netw. Sci., vol. 4, no. 1, pp. 1–28, 2019, doi: 10.1007/s41109-019-0179-3.
M. Offroy and L. Duponchel, “Topological data analysis: A promising big data exploration tool in biology, analytical chemistry and physical chemistry,” Anal. Chim. Acta, vol. 910, pp. 1–11, 2016, doi: 10.1016/j.aca.2015.12.037.
A. Zomorodian and G. Carlsson, “Computing persistent homology,” in Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG’04), 2004, pp. 347–356, doi: 10.1145/997817.997870.
C. S. Pun, K. Xia, and S. X. Lee, “Persistent-Homology-Based Machine Learning and Its Applications -- A Survey,” SSRN Electron. J., 2018, doi: 10.2139/ssrn.3275996.
F. Altındiş, B. Yılmaz, S. Borisenok, and K. İçöz, “Parameter investigation of topological data analysis for EEG signals,” Biomed. Signal Process. Control, vol. 63, 2021, doi: 10.1016/j.bspc.2020.102196.
Y. Wang, H. Ombao, and M. K. Chung, “Statistical Persistent Homology of Brain Signals,” 2019, vol. 2019-May, pp. 1125–1129, doi: 10.1109/ICASSP.2019.8682978.
E. Merelli, M. Piangerelli, M. Rucco, and D. Toller, “A topological approach for multivariate time series characterization: The epileptic brain,” 2015, doi: 10.4108/eai.3-12-2015.2262525.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Muhamad Luqman Sapini, Mohd Salmi Md Noorani, Mohd Salmi Md Noorani, Fatimah Abdul Razak, Fatimah Abdul Razak, Mohd Almie Alias, Mohd Almie Alias, Norliza Muhamad Yusof, Norliza Muhamad Yusof
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
