Abstract:

In this talk we present an interesting connection between various
algorithms from the field of machine learning and statistical data
analysis and the theory of diffusion and stochastic processes. In
particular we show that some common data mining algorithms, such as
spectral clustering, kernel based non-linear dimensionality
reduction and semi-supervised learning, can be analyzed by standard
tools of applied mathematics, including asymptotic analysis and the
theory of stochastic processes. Conversely, we also show that
problems in the study of stochastic dynamical systems, such as
dimensional reduction of high dimensional dynamical systems and
estimation of effective macroscopic dynamics, can be analyzed by
applying data analysis tools inspired by spectral clustering.

Joint work with Ronald Coifman (Yale), Stephane Lafon (Google),
Mauro Maggioni (Duke) and Ioannis Kevrekidis (Princeton).