The Geometry of Data: Distance on Data Manifolds
Open Access Senior Thesis
Bachelor of Science
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.
Chu, Casey, "The Geometry of Data: Distance on Data Manifolds" (2016). HMC Senior Theses. 74.