Weiging Gu's Abstract

 

Claremont Mathematics Weekend

 

Sponsored by Claremont Colleges

 

January 30 - 31, 2016

 

Speaker: Weiging Gu

Title: Differential Geometric Data to Decision
Abstract:

There are big data problems everywhere in this world.  There is an urgent need to apply new and advanced mathematical techniques to extract knowledge and insights from large and complex collections of digital data since traditional statistical methods do not suffice.  In this talk, I will present how to use the techniques in differential geometry especially using manifold and Lie group theories for approaching big data problem and for data-to-information and data-to-decision.  I will use two to three examples that I worked with three of my Claremont students to demonstrate how to use differential geometric techniques to visualize data, reduce data dimension, extract data features, and define appropriate distance functions to analyze time series data.   You will see Grassmann manifolds, Stiefel manifolds, and the Lie group of rigid motions play important roles in processing and analyzing big nonlinear dynamical data.