Geometric and Topological Approaches to Mode Clustering

Hong, Hyunmin (2021) Geometric and Topological Approaches to Mode Clustering. Bachelor's Thesis, Mathematics.

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Abstract

Clustering is one of the most significant tasks nowadays, but the mathematics behind defining clusters are vastly different depending on the choice of metric. Thus, this thesis will focus on density-based clustering which usually fails to give good quality clustering result in high dimensions. We improve the classical density-based clustering into two varying fields of mathematics: geometry and topology. This thesis begins with geometric clustering approach called enhanced mode clustering (EMC). This approach will be provided with some enhancements to mode clustering. Following this, we present topological clustering approach that combines the classical hill climbing algorithm and topological persistence. That is, topological mode analysis tool (ToMATo). Lastly, two implementations of the ToMATo and EMC will be presented in high dimensional data to see if these clustering methods improved the remaining problem from the classical density-based clustering.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Hirsch, C.P. and Grzegorczyk, M.A.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	16 Jul 2021 08:07
Last Modified:	16 Jul 2021 08:07
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/25029

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