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|Title:||Persistent Homology and Machine Learning|
|Advisor:||McNicholas, Sharon M.|
Nicas, Andrew J.
|Department:||Mathematics and Statistics|
|Keywords:||Algebraic Topology;Machine Learning;Applied Topology;Persistent Homology|
|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.|
|Appears in Collections:||Open Access Dissertations and Theses|
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|Tan_Anthony_FinalSubmission202006_MScStats.pdf||999.91 kB||Adobe PDF||View/Open|
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