Trainable classifier: Fisher's Least Square Linear Discriminant
W = FISHERC(A)
Finds the linear discriminant function between the classes in the dataset A by minimizing the errors in the least square sense. This is a multi-class implementation using the one-against-all strategy. It results in a set of linear base classifiers, one for every class. The final result may be improved significantly by using a non-linear trained combiner, e.g. by calling W = A*(FISHERC*QDC(,,1e-6);
For high dimensional datasets or small sample size situations, the Pseudo-Fisher procedure is used, which is based on a pseudo-inverse.
This classifier, like all other non-density based classifiers, does not use the prior probabilities stored in the dataset A. Consequently, it is just for two-class problems and equal class prior probabilities equivalent to LDC, which assumes normal densities with equal covariance matrices.
Note that A*(KLMS(,N)*NMC) performs a very similar operation, but uses the prior probabilities to estimate the mean class covariance matrix used in the pre-whitening operation performed by KLMS. The reduced dimensionality N controls some regularisation.
1. R.O. Duda, P.E. Hart, and D.G. Stork, Pattern classification, 2nd ed. John Wiley and Sons, New York, 2001.