We propose a novel method for improving Wi-Fi positioning accuracy while reducing the energy consumption of mobile devices. Our method presents three contributions. First, we jointly and intelligently select the optimal subset of access points for positioning via maximum mutual information criterion. Second, we further propose local discriminant embedding algorithm for nonlinear discriminative feature extraction, a process that cannot be effectively handled by existing linear techniques. Third, to reduce complexity and make input signal space more compact, we incorporate clustering analysis to localize the positioning model. Experiments in realistic environments demonstrate that the proposed method can lower energy consumption while achieving higher accuracy compared with previous methods. The improvement can be attributed to the capability of our method to extract the most discriminative features for positioning as well as require smaller computation cost and shorter sensing time.