Head pose estimation has been an integral problem in the study of face recognition systems andhuman-computer interfaces, as part of biometric applications. A fine estimate of the head poseangle is necessary and useful for several face analysis applications. To determine the head pose,face images with varying pose angles can be considered to be lying on a smooth low-dimensionalmanifold in high-dimensional image feature space. However, when there are face images of multipleindividuals with varying pose angles, manifold learning techniques often do not give accurateresults. In this work, we propose a framework for a supervised form of manifold learning calledBiased Manifold Embedding to obtain improved performance in head pose angle estimation. Thisframework goes beyond pose estimation, and can be applied to all regression applications. Thisframework, although formulated for a regression scenario, unifies other supervised approaches tomanifold learning that have been proposed so far. Detailed studies of the proposed method arecarried out on the FacePix database, which contains 181 face images each of 30 individuals withpose angle variations at a granularity of 1°. Since biometric applications in the real world maynot contain this level of granularity in training data, an analysis of the methodology is performedon sparsely sampled data to validate its effectiveness. We obtained up to 2° average pose angle estimation error in the results from our experiments, which matched the best results obtained forhead pose estimation using related approaches.