non-linear combination of variables to obtain new ones

#1
Hi,

I have the following doubt:

let's imagine I have a matrix of data with N variables (columns) and M rows (individuals, examples, etc...). Is there any technique/tool of feature extraction (i.e.,the generation of new variables from original ones) that takes into account the, for example, ratio of 2 original variables as a new one? For example, PCA only allows you to obtain a linear combination of the original variables to obtain the principal components, but I am looking for something more general than that, so I can consider no-linear combinations of the original variables to obtain new ones.

Regards.