All positive examples are alike; each negative example is negative in its own way. During interactive multimedia information retrieval, the number of training samples fed-back by the user is usually small; furthermore, they are not representative for the true distributions-especially the negative examples. Adding to the difficulties is the nonlinearity in real-world distributions. Existing solutions fail to address these problems in a principled way. This paper proposes biased discriminant analysis and transforms specifically designed to address the asymmetry between the positive and negative examples, and to trade off generalization for robustness under a small training sample. The kernel version, namely "BiasMap", is derived to facilitate non-linear biased discrimination. Extensive experiments are carried out for performance evaluation as compared to the state-of-the-art methods.