Pseudo-inverse linear discriminants for the improvement of overall classification accuracies

This paper studies the learning and generalization performances of pseudo-inverse linear discriminant (PILDs) based on the processing minimum sum-of-squared error (MS(2)E) and the targeting overall classification accuracy (OCA) criterion functions. There is little practicable significance to prove the equivalency between a PILD with the desired outputs in reverse proportion to the number of class samples and an FLD with the totally projected mean thresholds. When the desired outputs of each class are assigned a fixed value, a PILD is partly equal to an FLD. With the customarily desired outputs {1, -1}, a practicable threshold is acquired, which is only related to sample sizes. If the desired outputs of each sample are changeable, a PILD has nothing in common with an FLD. The optimal threshold may thus be singled out from multiple empirical ones related to sizes and distributed regions. Depending upon the processing MS(2)E criteria and the actually algebraic distances, an iterative learning strategy of PILD is proposed, the outstanding advantages of which are with limited epoch, without learning rate and divergent risk. Enormous experimental results for the benchmark datasets have verified that the iterative PILDs with optimal thresholds have good learning and generalization performances, and even reach the top OCAs for some datasets among the existing classifiers.