If I understand what you meant by "dimensional scaling" correctly,
then you probably want to do some sort of nonlinear projection, i.e.,
projection of high dimensional data to a low dimensional nonlinear
surface using neural networks.

There have been several attempts to do that such as nonlinear PCA
based on three-hidden layered neural networks. The hidden nodes at the
middle layer can be used as nonlinear principal components. But from
my personal experience, training such big neural networks is not easy
problem esp. when the dimension of input data is higher than 4~50.

Hope this would help,

Jay Liu
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