Representation based classification methods, such as Sparse Representation Classification (SRC) and Linear Regression Classification (LRC) have been developed for face recognition problem successfully. However, most of these methods use the original face images without any preprocessing for recognition. Thus, their performances may be affected by some problematic factors (such as illumination and expression variances) in the face images. In order to overcome this limitation, a novel supervised filter learning algorithm is proposed for representation based face recognition in this paper. The underlying idea of our algorithm is to learn a filter so that the within-class representation residuals of the faces' Local Binary Pattern (LBP) features are minimized and the between-class representation residuals of the faces' LBP features are maximized. Therefore, the LBP features of filtered face images are more discriminative for representation based classifiers. Furthermore, we also extend our algorithm for heterogeneous face recognition problem. Extensive experiments are carried out on five databases and the experimental results verify the efficacy of the proposed algorithm.