Suomeksi
### Nonlinear factor analysis

The models typically used in unsupervised learning assume that the
observations have been generated by simple factors, which cannot be
directly measured but which influence the observations more or less
directly.
According to the model used in the traditional linear factor
analysis, the observations are generated by factors, which have
Gaussian distributions. The factors are assumed to generate the
observations through linear combinations. In addition, the
observations are assumed to have Gaussian noise. In many cases, the
linearity and gaussianity assumptions are not good at describing the
observations, but due to the ease of use, linear factor analysis is
widespread particularly in many humanistic sciences.

Unlike in factor analysis, in independent component analysis (ICA)
the factors are not assumed to have Gaussian distributions.
Computational efficient methods, which can be used instead of the
traditional factor analysis, have been developed in the ICA research group in the laboratory of
computer and information science.

Another important extension to the ordinary factor analysis is the
relaxation of the linearity assumption. In nonlinear factor analysis,
the observations are assumed to be generated from the factors through
a nonlinear mapping.

Last updated on 15th June, 1999.
<Harri.Lappalainen@hut.fi>