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http://hdl.handle.net/123456789/3801
Title: | An Introduction to Persistent Homology and Simplicial Collapses |
Authors: | Bhalachandra, Abhijit. |
Keywords: | Homology Persistent Simplicial collapses |
Issue Date: | 28-Jul-2021 |
Publisher: | IISERM |
Abstract: | The explosion of data has brought in the fervent need to analyze large and higher-dimensional datasets accurately and fast. Conventional tools are quickly becoming redundant when the focus is on the speed of computation and the expectations of impactful insight. There is a vibrant community of researchers who are looking at topology-based tools which are able to extract shape-pertinent features of these large datasets. Looking at alternate and non-classical tools has led to the development of some of the most impactful sub-fields of mathematics, one being Topological Data Analysis, which has been widely accepted and noticed for its effectiveness on certain use cases. This thesis will focus on studying a method called Persistent Homology, which in a sense forms the vein of Topological Data Analysis. This thesis will build mathematical theory to understand Persistent Homology, and subse- quently proceed to comment on contemporary challenges with regard to the method, and novel techniques to overcome them including algorithmic approaches with experimental observations. |
URI: | http://hdl.handle.net/123456789/3801 |
Appears in Collections: | MS-16 |
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It is under embargo period.docx | 11.62 kB | Microsoft Word XML | View/Open |
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