In mathematics, a ridge function is any function
that can be written as the composition of an univariate function
, that is called a profile function, with an affine transformation, given by a direction vector
Then, the ridge function reads
Coinage of the term 'ridge function' is often attributed to B.F. Logan and L.A.
[1] A ridge function is not susceptible to the curse of dimensionality[clarification needed], making it an instrumental tool in various estimation problems.
This is a direct result of the fact that ridge functions are constant in
independent vectors that are orthogonal to
, such that these vectors span
In other words, any shift of
in a direction perpendicular to
Ridge functions play an essential role in amongst others projection pursuit, generalized linear models, and as activation functions in neural networks.
For a survey on ridge functions, see.
[2] For books on ridge functions, see.