PhD Comprehensive Seminar | Justin Shaw, A Simple Example of Dimension Reduction

MC 6460

Candidate

Justin Shaw
Applied Mathematics, University of Waterloo

Title

A Simple Example of Dimension Reduction

Abstract

We are overwhelmed with information, but raw data by itself is generally not helpful.  We need a way to make sense of information by determining which part of it is the most important for a given application.  There are numerous mathematical methods which can be used to extract features from a dataset.  In this talk we will use wavelet and empirical orthogonal function (EOF) methods to examine in situ measurements from Honeoye Lake in upstate New York.   These two methods identify features on different timescales.  We will then show how EOFs can be used to represent the original data by a simple reduced order model.  This model, while having half the dimension of the original data, retains enough information to accurately construct the time series for the Wedderburn number and the Schmidt Stability Index with a small RMS error.   The more general problem, along with possible directions for future work, will then be discussed.