Title

The Geometry of Data: Distance on Data Manifolds

Graduation Year

2016

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Weiqing Gu

Reader 2

Dagan Karp

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Abstract

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.