In this paper, we present an extension of the state-of-the-art normalized graph cut method based on asymmetry of the affinity matrix. We provide algorithms for classification and clustering problems and show how our method can improve solutions for unequal and overlapped data distributions. The proposed approaches are based on the theoretical relation between classification accuracy, mutual information and normalized graph cut. The first method requires a priori known class labeled data that can be utilized, e.g., for a calibration phase of a brain-computer interface (BCI). The second one is a hierarchical clustering method that does not involve any prior information on the dataset.