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Feature selection is viewed as an important preprocessing step for pattern recognition, machine learning, and data mining. Neighborhood is one of the most important concepts in classification learning and can be used to distinguish samples with different decisions. In this paper, a neighborhood discrimination index is proposed to characterize the distinguishing information of a neighborhood relation. It reflects the distinguishing ability of a feature subset. The proposed discrimination index is computed by considering the cardinality of a neighborhood relation rather than neighborhood similarity classes. Variants of the discrimination index, including joint discrimination index, conditional discrimination index, and mutual discrimination index, are introduced to compute the change of distinguishing information caused by the combination of multiple feature subsets. They have the similar properties as Shannon entropy …