TITLE: Manifold Learning: Discovering Nonlinear Variation Patterns in Complex Data Sets

SPEAKER: Professor Daniel Apley

ABSTRACT:

In statistical analysis and data mining of multivariate data sets, many problems can be viewed as discovering variation patterns in a set of N observations of n variables. The term "variation pattern" refers to the structured, interdependent manner in which the n variables may vary over the N observations. In a very general mathematical representation we view each multivariate observation as a vector in n-dimensional space. Then over the set of N observations, we assume the data consist of a structured component plus noise, where the structured component lies on a p-dimensional manifold with p << n. The objective is to learn, or discover, the manifold based only on the set of data, with no prior knowledge of what to expect. Discovery of the manifold is useful in many different contexts:  Denoising noisy images and other multivariate data; dimensionality reduction of large data sets; extraction of important features for enhancing subsequent analyses; exploratory analyses for identifying and understanding relationships between variables; etc. In this talk, I will discuss the manifold learning problem, applications, and algorithms. Linear structured manifolds can be easily discovered with standard principal components and factor analyses. Consequently, this talk will focus on discovering nonlinear manifolds, which is a much more challenging and nuanced problem.

Bio:  Daniel W. Apley is an Associate Professor of Industrial Engineering & Management Sciences at Northwestern University. His research interests lie at the interface of engineering modeling, statistical analysis, and data mining, with particular emphasis on manufacturing variation reduction applications in which very large amounts of data are available. His research has been supported by numerous industries and government agencies. He received the NSF CAREER award in 2001, the IIE Transactions Best Paper Award in 2003, and the Wilcoxon Prize for best practical application paper appearing in Technometrics in 2008. He currently serves as Editor-in-Chief for the Journal of Quality Technology and has served as Chair of the Quality, Statistics & Reliability Section of INFORMS, Director of the Manufacturing and Design Engineering Program at Northwestern, and Associate Editor for Technometrics.