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Nowadays, high throughput experimental techniques make it feasible to examine and collect massive data at the molecular level. These data, typically mapped to a very high dimensional feature space, carry rich information about functionalities of certain chemical or biological entities and can be used to infer valuable knowledge for the purposes of classification and prediction. Typically, a small number of features or feature combinations may play determinant roles in functional discrimination. The identification of such features or feature combinations is of great importance. In this paper, we study the problem of discovering compact and highly discriminative features or feature combinations from a rich feature collection. We employ the support vector machine as the classification means and aim at finding compact feature combinations. Comparing to previous methods on feature selection, which identify features solely based on their individual roles in the classification, our method is able to identify minimal feature combinations that ultimately have determinant roles in a systematic fashion. Experimental study on drug activity data shows that our method can discover descriptors that are not necessarily significant individually but are most significant collectively.