NEWS in the Department of Mathematics
Tegan Emerson - PhD preliminary examination
Date: Tuesday, September 20, 2016
Place: Weber 201
Time: 3:00 p.m.
Title: A Geometric and Topological Data Analysis Approach to Machine Learning and Data Mining in Medical and Biological Sensing
Advisor: Dr. Michael Kirby
Committee: Dr. Chris Peterson, Dr. Margaret Cheney, Dr. Jennifer Nyborg
Abstract: There are two ways to consider the "bigness" of data. First, we can consider data that is big with respect to the dimension of the ambient space in which it exists. That is to say, where many measurements or values are attributed to each sample or subject (the number of which may actually be quite small as in the case of medical data). Alternatively, one can have a "big" data set that is comprised of a small number of measurements for a large quantity of samples. My dissertation focuses on "big data" with respect to dimensionality. In particular, methods for reducing the dimension while preserving the ability to perform specific machine learning tasks on the data sets of interest. Dimensionality reduction can manifest in many ways from feature selection, to data visualization, to creating an ability to interpret resulting machine learning models. Of particular emphasis will be the proposed final project for my doctoral research which consists of exploring dimension reducing, nearly distance preserving maps between special manifolds. Applications discussed will include computer aided diagnostics, tracking and identification of aerosolized bio-agents, signal detection and estimation in signal processing, and the potential for mental task identification via multi-nodal ElectroEncephaloGram (EEG) data.