On Extensions to Fishers Linear Discriminant Function,

This Memorandum describes how Fishers Linear Discriminant can be combined with the Fukunaga-Koontz transform to give a useful technique for reduction f feature space from many to two or three dimensions. Performance is seen to be superior in general to the Foley-Sammon extension to fishers method. The technique is then extended to show how a new radius vector or pair of radius vectors can be combined with fishers vector to produce a classifier with even more power of discrimination. Illustrations of the technique show that good discrimination can be obtained even if there is considerable overlap of classes in any single projection. Keywords include Index Terms Dimensionality reduction, Discriminant vectors, Feature selection, Fisher criterion, Linear transformations, Separability. Great Britain