Worst-case discriminative feature selection

Feature selection plays a critical role in data mining, driven by increasing feature dimensionality in target problems. In this paper, we propose a new criterion for discriminative feature selection, worst-case discriminative feature selection (WDFS). Unlike Fisher Score and other methods based on the discriminative criteria considering the overall (or average) separation of data, WDFS adopts a new perspective called worst-case view which arguably is more suitable for classification applications. Specifically, WDFS directly maximizes the ratio of the minimum of between-class variance of all class pairs over the maximum of within-class variance, and thus it duly considers the separation of all classes. Otherwise, we take a greedy strategy by finding one feature at a time, but it is very easy to implement and effective. Moreover, we utilize the correlation between features to help reduce the redundancy, and then WDFS is extended to uncorrelated WDFS (UWDFS). To evaluate the effectiveness of the proposed algorithm, we conduct classification experiments on many real data sets. In the experiment, we respectively use the original features and the score vectors of features over all class pairs to calculate the correlation coefficients, and analyze the experimental results in these two ways. Experimental results demonstrate the effectiveness of WDFS and UWDFS.