Evaluation metric plays a critical role in achieving the optimal classifier during the classification training. Thus, a selection of suitable evaluation metric is an important key for discriminating and obtaining the optimal classifier. This paper systematically reviewed the related evaluation metrics that are specifically designed as a discriminator for optimizing generative classifier. Generally, many generative classifiers employ accuracy as a measure to discriminate the optimal solution during the classification training. However, the accuracy has several weaknesses which are less distinctiveness, less discriminability, less informativeness and bias to majority class data. This paper also briefly discusses other metrics that are specifically designed for discriminating the optimal solution. The shortcomings of these alternative metrics are also discussed. Finally, this paper suggests five important aspects that must be taken into consideration in constructing a new discriminator metric.