Frequent pattern mining is used widely in feature selection for classification problem.In order to provide theoretical basis for the application

we established the relationship between the classification discriminative ability and the support of the feature.Information gain was adopted as evaluation criteria

and we discussed the connection between the support of the feature and its discriminative ability.Firstly

we proved the information gain is a concave function about the support of the feature;secondly

we proved the conclusion that the feature with too-high or too-low support has limited discriminative ability under the two classes and multiple classes circumstances separately;Finally

simulation experiments validate our conclusions.And the conclusion provides a theoretical basis for the application of frequent pattern mining in classification problems.