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Casey Chu

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The Geometry of Data: Distance on Data Manifolds

Weiqing Gu
Second Reader(s)
Dagan Karp


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.

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