  This paper studies the approximation of generalized ridge functions, namely
of functions which are constant along some submanifolds of $\mathbb{R}^N$. We
introduce the notion of linear-sleeve functions, whose function values only
depend on the distance to some unknown linear subspace $L$. We propose two
effective algorithms to approximate linear-sleeve functions
$f(x)=g(\text{dist}(x,L)^2)$, when both the linear subspace $L\subset
\mathbb{R}^N$ and the function $g\in C^s[0,1]$ are unknown. We will prove error
bounds for both algorithms and provide an extensive numerical comparison of
both. We further propose an approach of how to apply these algorithms to
capture general sleeve functions, which are constant along some lower
dimensional submanifolds.
