Analysis of multiple classifier system using product and modified product rules

One of the key factors in designing a successful multiple classifier system (MCS) is choosing an appropriate combining rule. Many theoretical and experimental efforts have been focused on estimating the probability of classification error for different combining rules. In this work, assuming N classifiers and two independent and identically distributed classes, we investigate using product and modified product rules and derive formulas to estimate their classification error probability under two class distributions, Gaussian and uniform. We also validate our derivations with computer simulations. The performance results of product, modified product, average, and majority vote rules are compared. The comparisons are done in term of probability of classification error as a function of class variance and number of classifiers. The results show that the modified product rule outperforms others while the product rule ranks last.