Advanced pseudo-inverse linear discriminants for the improvement of classification accuracies

There is very little practicable significance to prove the equivalency between a pseudo-inverse linear discriminant (PILD) with the desired outputs in reverse proportion to the number of within-class samples and a Fisher linear discriminant (FLD) with the totally projected mean thresholds which are disadvantageous to improve the overall classification accuracy. Even if so, several examples have borne out that a PILD is not wholly equivalent to an FLD. Consequently, the most often used total-projected-mean thresholds usually behave poor. Starting from the customarily desired targets {1, -1}, a simple practicable threshold is gotten, which is only related to sample sizes. By substituting the desired targets with the actually algebraic distances of all training samples, a new threshold is obtained. When the desired targets are different from each other, the weight vector and the threshold given by a PILD are not equal to the ones given by an FLD anymore. At the moment, a PILD is wholly different from an FLD.