Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/25538
Title: | Persistent Homology and Machine Learning |
Authors: | Tan, Anthony |
Advisor: | McNicholas, Sharon M. Nicas, Andrew J. |
Department: | Mathematics and Statistics |
Keywords: | Algebraic Topology;Machine Learning;Applied Topology;Persistent Homology |
Publication Date: | 2020 |
Abstract: | Persistent homology is a technique of topological data analysis that seeks to understand the shape of data. We study the effectiveness of a single-layer perceptron and gradient boosted classification trees in classifying perhaps the most well-known data set in machine learning, the MNIST-Digits, or MNIST. An alternative representation is constructed, called MNIST-PD. This construction captures the topology of the digits using persistence diagrams, a product of persistent homology. We show that the models are more effective when trained on MNIST compared to MNIST-PD. Promising evidence reveals that the topology is learned by the algorithms. |
URI: | http://hdl.handle.net/11375/25538 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Tan_Anthony_FinalSubmission202006_MScStats.pdf | 999.91 kB | Adobe PDF | View/Open |
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