Classification into Two Groups with different Cost of Misclassification Ratios

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Nigerian Association of Mathematical Physics


Fisher’s Linear Discriminant and Bayesian Classification procedures were compared when the assumption of equal cost of misclassification is violated. The comparison was carried out at various sample sizes and different misclassification cost ratios. Data were simulated to consist two groups (populations) of four variables each from two multivariate normal populations. The homogeneity of the variance-covariance matrices of the two groups was tested using Box’s M-Test. The apparent Error Rate as the estimate of the Actual Error Rate was used to judge the performance of both procedures at different misclassification cost ratios (1:1, 1:2, , , 4:5) and sample sizes (10, 20, 30, 40, , , 100). The results show that at equal cost ratio (1:1), both approaches produced almost the same error rate at different sample sizes. With difference in misclassification cost ratio, the Bayesian approach generally has higher proportion of misclassification than the Fisher at various ratios and sample sizes. The Fisher performed better in small sample cases (n < 50) under all cost ratios considered except 1:2 and 1:5. For large sample cases (n > 50), the performance was better at cost ratios 2:3, 2:4 and 2:5



Fisher’s Linear Discriminant Function, Baye’s Classification Rule, Apparent Error Rates, Cost of Misclassification, Cost Adjusted Prior Probabilities, Cost Matrix


Journal of the Nigerian Association of Mathematical Physics