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The Geometry of Data: Distance on Data Manifolds

The increasing importance of data in the modern world has created a need for new mathematical techniques to analyze this data. We explore and develop the use of geometry—specifically differential geometry—as a means for such analysis, in two parts. First, we provide a general framework to discover patterns contained in time series data using a geometric framework of assigning distance, clustering, and then forecasting. Second, we attempt to define a Riemannian metric on the space containing the data in order to introduce a notion of distance intrinsic to the data, providing a novel way to probe the data for insight.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1088
Date01 January 2016
CreatorsChu, Casey
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceHMC Senior Theses
Rightsdefault

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