Quotient vs. difference: Comparison between the two discriminant criteria

Two discriminant criteria—quotient and difference, are commonly used in linear discriminant analysis. In the paper, we experiment with the CENPARMI handwritten numeral database, the NUST603 handwritten Chinese character database, the ORL face image database and the FERET face image database and find that the quotient criterion is better than the difference criterion for large sample size problems such as the character recognition, while the difference criterion is better for small sample size problems such as face recognition. Through theoretical analysis, the defect of the difference criterion—the correlation among discriminant vectors is revealed, and it is testified that the quotient criterion is superior to the difference criterion in general, if the instability of denominator can be overcome. Otherwise, the difference criterion might be better. Finally, the two criteria (quotient and difference) are unified into one framework in the paper.