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SupMaxK is a family of anti-monotonic measures of discriminative power, which can be used for  the efficient discovery of discriminative patterns from biological data with high density and high dimensionality (e.g. Gene Expression data), and especially for the discovery of those patterns with relatively low-support but high discriminative power (e.g. odds ratio, information gain, p-value etc), which complements existing discriminative pattern mining algorithms. Several experiments on a cancer gene expression dataset demonstrate that there are low-support patterns that can be discovered using SMP (SupMaxPair), but not by existing approaches, and that these patterns are statistically significant and biologically relevant.