University of Oulu

C. Asirimath, J. Ratnayake, C. Weeraddana and N. Rajatheva, "Critical Points to Determine Persistence Homology," 2019 53rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 2019, pp. 2121-2126, doi: 10.1109/IEEECONF44664.2019.9048780

Critical points to determine persistence homology

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Author: Asirimath, Charmin1; Ratnayake, Jayampathy2; Weeraddana, Chathuranga3;
Organizations: 1Center for Machine Vision and Signal Analysis, University of Oulu, Finland
2Department of Mathematics, University of Colombo, Sri Lanka
3Department of Electronic and Telecommunication Engineering, University of Moratuwa, Sri Lanka
4Centre for Wireless Communications, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.8 MB)
Persistent link: http://urn.fi/urn:nbn:fi-fe2020060841123
Language: English
Published: Institute of Electrical and Electronics Engineers, 2020
Publish Date: 2020-06-08
Description:

Abstract

Computation of simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The sampling of the point cloud should minimally mutilate the features of the underlying object to enable effective “feature extraction” that lies at the center of modern data analysis techniques, e.g., machine learning. The study considers sampling critical points of a Morse function associated with a point cloud, to approximate the Vietoris-Rips complex and to compute persistence homology. The effectiveness of the approach is compared with the farthest point sampling (FPS), in the context of two classification problems. The empirical results suggest that sampling critical points of the Morse function can be more effective than FPS when determining the persistence homology for the cases where the critical points play a decisive role.

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Series: Asilomar Conference on Signals, Systems & Computers
ISSN: 1058-6393
ISSN-E: 1058-6393
ISSN-L: 1058-6393
ISBN: 978-1-7281-4300-2
ISBN Print: 978-1-7281-4301-9
Pages: 2121 - 2126
DOI: 10.1109/IEEECONF44664.2019.9048780
OADOI: https://oadoi.org/10.1109/IEEECONF44664.2019.9048780
Host publication: Conference Record of the Fifty-Third Asilomar Conference on Signals, Systems & Computers, November 3–6, 2019 Pacific Grove, California
Conference: Asilomar Conference on Signals, Systems & Computers
Type of Publication: A4 Article in conference proceedings
Field of Science: 213 Electronic, automation and communications engineering, electronics
Subjects:
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