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.