Asymmetric multidimensional scaling is a visualization method that reveals relations between objects using their asymmetric dissimilarity data as input. Such visualization is important in areas such as marketing science since it reveals consumer dynamics and brand competition. Large amounts of asymmetric dissimilarity data can be processed by modern information technology; nevertheless, it remains difficult to interpret the asymmetries between many objects. To overcome this problem, we propose a new visualization method called discriminant coordinates for asymmetric dissimilarity data, which interprets the relations between and within a set of object classes, given asymmetric dissimilarity data. The method easily interprets the estimated asymmetries between and within classes, even when the asymmetric dissimilarity data contain noise if some assumptions for asymmetric dissimilarity data is satisfied.