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This paper presents a novel approach to classification of decomposed cortical evoked potentials (EPs). The decomposition is based on learning of a sparse set of basis functions using an artificial neural network (ANN). The basis functions are generated according to a probabilistic model of the data. In contrast to the traditional signal decomposition techniques (i.e. principle component analysis or independent component analysis), this allows for an overcomplete representation of the data (i.e. number of basis functions that is greater than the dimensionality of the input signals). Obviously, this can be of a great advantage. However, there arises an issue of selecting the most significant components from the whole collection. This is especially important in classification problems based upon the decomposed representation of the data, where only those components that provide a substantial discernibility between EPs of different groups are relevant. To deal with this problem, we propose an approach based on the rough set theory's (RS) feature selection mechanisms. We design a sparse coding- and RS-based hybrid system capable of signal decomposition and, based on a reduced component set, signal classification.