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The proposed feature number determining method for the ranking-based feature selection problem builds a convex hull in high-dimensional space for each category in the training dataset and estimates the discriminative degree by calculating the overlapped proportion of these high-dimensional convex hulls. Normalising these discriminative degrees, an initial selected feature number can be determined, then a local optimal result is output by using the hill climbing algorithm. This approach reduces the time consumed by the existing many ranking-based feature selection methods. Classification results on three data sets using three major feature ranking and selection criteria and an SVM classifier show considerable improvement in time consumed of feature selection and comparable accuracy.