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# Bayesian Nonlinear Independent Component Analysis by
Multi-Layer Perceptrons

In *Advances in Independent Component Analysis*, ed. Mark
Girolami, pp. 93-121, Springer-Verlag, 2000.
**Harri Lappalainen - Antti Honkela**

Helsinki University of Technology, Neural Networks Research Centre, P.O. Box 5400, FIN-02015 HUT, Finland

### Abstract:

In this chapter, a nonlinear extension to independent
component analysis is developed. The nonlinear mapping from source
signals to observations is modelled by a multi-layer perceptron
network and the distributions of source signals are modelled by
mixture-of-Gaussians. The observations are assumed to be corrupted by
Gaussian noise and therefore the method is more adequately described
as nonlinear independent factor analysis. The nonlinear mapping, the
source distributions and the noise level are estimated from the data.
Bayesian approach to learning avoids problems with overlearning which
would otherwise be severe in unsupervised learning with flexible
nonlinear models.

*Harri Lappalainen*

*2000-03-03*