  Multiple time scale stochastic dynamical systems are ubiquitous in science
and engineering, and the reduction of such systems and their models to only
their slow components is often essential for scientific computation and further
analysis. Rather than being available in the form of an explicit analytical
model, often such systems can only be observed as a data set which exhibits
dynamics on several time scales. We will focus on applying and adapting data
mining and manifold learning techniques to detect the slow components in such
multiscale data. Traditional data mining methods are based on metrics (and
thus, geometries) which are not informed of the multiscale nature of the
underlying system dynamics; such methods cannot successfully recover the slow
variables. Here, we present an approach which utilizes both the local geometry
and the local dynamics within the data set through a metric which is both
insensitive to the fast variables and more general than simple statistical
averaging. Our analysis of the approach provides conditions for successfully
recovering the underlying slow variables, as well as an empirical protocol
guiding the selection of the method parameters.
