The generalization performance of machine learning methods depends heavily on the quality of data representation. However, existing researches rarely consider representation learning from the perspective of generalization error. In this paper, we prove that generalization error of representation learning function can be estimated effectively by solving two convex optimization problems. Based on it, we propose a general representation learning framework. And then, we apply the proposed framework to two most commonly used nonlinear mapping methods, i.e., kernel based method and deep neural network (DNN), and thus design a kernel selection method and a DNN boosting framework, correspondingly. Finally, extensive experiments verify the effectiveness of the proposed methods.