Chairs: Andreas Bittracher, Stefan Klus, Christof Schütte

Over the last years, several kernel-based methods for the analysis of high-dimensional data sets have been developed, many of which can be seen as nonlinear extensions of classical linear methods, e.g., kernel principal component analysis (kPCA), kernel canonical correlation analysis (kCCA), and kernel time-lagged independent component analysis (kTICA). The basic idea behind these methods is to represent data by elements in reproducing kernel Hilbert spaces associated with positive definite kernels and to then apply classical linear methods to these elements.

Other methods, such as kernel extended dynamic mode decomposition (kEDMD), use reproducing kernel Hilbert spaces as rich, possibly infinite-dimensional embedding spaces for the representation of complex functions. Inner products between embedded functions can be computed by cheap kernel evaluations, without ever explicitly constructing the embedding. Kernel methods are well suited for feature extraction, clustering, and dimensionality reduction of multiscale systems, as attested by numerous application to molecular dynamics and turbulent flows. This minisymposium aims to bring together experts from different fields in order to discuss recent advances of kernel-based methods, as well as applications to multiscale problems.

Find abstracts for all talks here or linked individually below.