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Trainable classifier: Fisher's Least Square Linear Discriminant

    W = FISHERC(A)

 A Dataset

 W Fisher's linear classifier


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);

 FISHERC also works for soft and target labels.

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.
2. A. Webb, Statistical Pattern Recognition, Wiley, New York, 2002.
3. S. Raudys and R.P.W. Duin, On expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix, Pattern Recognition Letters, vol. 19, no. 5-6, 1998, 385-392.

See also

mappings, datasets, testc, ldc, nmc, fisherm,

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