A simple and efficient supervised method for spatially weighted PCA in face image analysis

Principal Component Analysis (PCA) is an example of a successful unsupervised statistical dimensionality reduction method, especially in small sample size problems. Despite the well-known attractive properties of PCA, the traditional approach does not incorporate prior information extracted from a specific domain knowledge. The development of techniques that bring together dimensionality reduction and prior knowledge can be performed in the framework of supervised learning methods, like Fisher Discriminant Analysis. Semi-supervised methods can also be applied if only a small number of labeled samples is available. In this paper, we propose a simple and efficient supervised method that allows PCA to incorporate explicitly domain knowledge and generates an embedding space that inherits its optimality properties for dimensionality reduction. The method relies on discriminant weights given by separating hyperplanes to generate the spatially weighted PCA. Several experiments using 2D frontal face images and different data sets have been carried out to illustrate the usefulness of the method for dimensionality reduction, classification and interpretation of face images