Appearance-based methods have been proven to be useful for face recognition tasks. The main problem with appearance-based methods originates from the multimodality of face images. It is known that images of different people in the original data space are more closely located to each other than those of the same person under different imaging conditions. In this paper, we propose a novel approach based on the nonlinear manifold embedding to define a linear subspace for illumination variations. This embedding based framework utilizes an optimization scheme to calculate the bases of the subspace. Since the optimization problem does not rely on the physical properties of the factor, the framework can also be used for other types of factors such as pose and expression. We obtained some promising recognition results under changing illumination conditions. Our error rates are comparable with state of art methods.