The Persistence of Data: A Road Map
Date
2022-04-22
Authors
Pothagoni, Shrunal
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Abstract
The purpose of data mining is to use advanced mathematical and statistical techniques to extract quantitative information from large data sets. These tools are incredibly powerful and in conjunction with machine learning algorithms allow for extremely accurate pattern prediction. However, there are various datasets that have qualitative properties that cannot be discerned using classic data mining techniques. Topological Data Analysis (TDA) is a field developed within the last two decades that uses methods in topology to extract such qualitative features. In this paper we will study how to use abstract simplicial complexes on point cloud data sets to find their most ‘optimal’ topology using computational homology.
Description
Honors Thesis
Keywords
Persistence theory, TDA, Computational homology