Adam M . Johansen and Ludger Evers 2007

MSc in Bioinformatics: Statistical Data Mining

Localized regression on principal manifolds

We consider nonparametric dimension reduction techniques for multivariate regression problems in which the variables constituting the predictor space are strongly nonlinearly related. Specifically, the predictor space is approximated via “local” principal manifolds, based on which a kernel regression is carried out.

Some Non-Standard Sequential Monte Carlo Methods and Their Applications

On Extended State-Space Constructions for Monte Carlo Methods

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”, “disconnected”, “bended”, “curved”, “heterogeneous”, or, more general, “complex”. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far...