Next: Ensemble Learning Up: Linear and Nonlinear Factor Previous: Linear and Nonlinear Factor

## Model structure

According to the general FA model the data has been generated by factors s through mapping f:

 (3)

where x is a data vector, s is a factor vector, is a parameter vector and e is a noise vector. The factors and the noise are assumed to be independent and Gaussian:
 sl(t) (4) ek(t)

The linear mapping f used in FA is

 (5)

The model is similar to principal component analysis except that FA includes the noise term and the factors have a Gaussian distribution. In NFA, the function f is allowed to be nonlinear. We use the method proposed in [6], where the MLP network

 (6)

is used to model the nonlinearity. The parameter vector  contains both A and b.

In NFA the data is modelled by a high dimensional manifold created by function  f from a prior Gaussian distribution. It can be compared to the self-organising map (SOM) [5], but the number of parameters scale more like in FA. The SOM scales exponentially as function of the dimensionality of the underlying data manifold. A small number of parameters keeps the modelled manifold smooth. We find the parameter vector  using ensemble learning.

Next: Ensemble Learning Up: Linear and Nonlinear Factor Previous: Linear and Nonlinear Factor
Tapani Raiko
2001-09-26