Abstract We introduce a method for the nonlinear dimension reduction of high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with prescribed intermediate $m\ll d$, so that $u$ can be well approximated by $f\circ g$ some profile $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. propose build ...

Nonlinear dimensionality reduction (DR) techniques offer the possibility to visually inspect a high-dimensional data set in two dimensions, and such methods have recently been extended to also visualize class boundaries as induced by a trained classifier on the data. In this contribution, we investigate the effect of two different ways to shape the involved dimensionality reduction technique in...