We show that dually supervised manifold embedding can improve the performance of machine learning based person-independent and thus calibration-free gaze estimation. For this purpose, we perform a manifold embedding for each person in the training dataset and then learn a linear transformation that aligns the individual, person-dependent manifolds. We evaluate the effect of manifold alignment on the recently presented Columbia dataset, where we analyze the influence on 6 regression methods and 8 feature variants. Using manifold alignment, we are able to improve the person-independent gaze estimation performance by up to 31.2 % compared to the best approach without manifold alignment.