[mluser]

Here's an attempt to visualize the nonlinear transformation->

Data without noise and before transformation:



Data with noise and before transformation:



Data without noise and after transformation. Taking only the last 3 dimensions (x1x2, x1^2, x2^2) as these seem to carry more weight:



Data with noise and after transformation. Taking only the last 3 dimensions (x1x2, x1^2, x2^2) as these seem to carry more weight: