In this paper, we propose a novel approach for visualizing and recognizing different emotion categories using facial expression images. Extended by the unsupervised nonlinear dimension reduction technique of locally linear embedding (LLE), we propose a supervised LLE (sLLE) algorithm utilizing emotion labels of face expression images. While existing works typically aim at training on such labeled data for emotion recognition, our approach allows one to derive subspaces for visualizing facial expression images within and across different emotion categories, and thus emotion recognition can be properly performed. In our work, we relate the resulting two-dimensional subspace to the valence-arousal emotion space, in which our method is observed to automatically identify and discriminate emotions in different degrees. Experimental results on two facial emotion datasets verify the effectiveness of our algorithm. With reduced numbers of feature dimensions (2D or beyond), our approach is shown to achieve promising emotion recognition performance.