Factor analysis is widely used in the social sciences and there is an
extensive literature describing various methods for estimating the
factors and then rotating them in order to yield solutions which have
simple interpretations
[122,110,35,25,5]. Principal component
analysis (PCA) is often used as the first stage for finding the
factors [63,58]. We shall call PCA and related
methods signal transformation (ST) approaches. These methods define a
criterion on the factors and then find a transformation from
observations to factors which optimises the criterion. In PCA, the
criterion is that the resulting factors are uncorrelated and have
maximal variance. A further requirement of orthogonal
**A** is
required to make the problem well determined.

In many cases ST approaches yield a fair approximation to the result
which would be gained by the Bayesian approach to estimating the
factors. Almost always, however, the ST methods provide only point
estimates. From the point of view of this thesis, reference
[9] is relevant because it uses ensemble learning for
estimating the posterior probabilities of the factors and the mapping
**A**.

There are several criteria for the rotation. Varimax, one of the most
popular rotation criteria, aims at maximising the sparsity of the
matrix
**A**. In general, the goal of the rotation is to find a
meaningful interpretation of the resulting factors.