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Nonlinear mapping

An obvious way to extend the representational power of the linear factor analysis model is to consider the case where the factors can have a nonlinear effect on the observations

x(t) = f(s(t)) + n(t). (31)

Here we replaced the affine mapping As + a by an arbitrary function f(s).

The nonlinear mapping does not change the considerations about the density of the factors. With the Gaussian model for the factors, the nonlinear mapping yields an extension of the ordinary factor analysis, that is, there is the same indeterminacy relative to the rotation of the factors. Nonlinear mapping with non-Gaussian model for the factors yields an extension of independent factor analysis which is able to recover the underlying factors if they exist.


Harri Valpola