Parameterized Appearance Models, such as Active Appearance Models (AAM), Morphable Models, or Boosted Appearance Models, have been extensively used for face alignment. Discriminative methods learn a mapping function between appearance features and shape parameters. Different mapping functions have been studied in the literature, including linear regression, which has proved to perform well when close to the true solution. Despite its easiness, it still suffers from two major drawbacks: 1) It takes the whole data without highlighting relations among different regions of the face, and 2) it is computationally expensive both in time and memory. In this paper, we analyze the covariance of the training data, and propose a way to find related information. By clustering those patches that are related, we reach a noise-reduced regression matrix. Then, we construct a clean mapping matrix, with reduced dimensionality, taking only the relevant training information. Experiments show that this method outperforms linear regression for face alignment.