An approach for solving the problem of dataset reduction is considered. The problem of selection an optimal subset of features and objects is an important task for every classification algorithm. Having smaller and more informative dataset one can perform training operation faster and study data visually. However nowadays most of algorithms select features and objects separately and are based on statistical or logical base. In this paper a method for training set reduction is presented. Using

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... tes for each class in calculation estimation algorithm a bilinear form is constructed. Having optimized bilinear form one can find an optimal subset for features and objects at once. In order to fasten optimization a technique for linear local optimization is proposed. During bilinear form optimization one can select an optimal iteration with smaller dataset and acceptable classification quality. Prospects of this approach are confirmed by a series of experiments on various practical tasks.