Face Verification using Locally Linear Discriminant Models

When linear discriminant analysis (LDA) is employed, the correct classification of a sample heavily depends on having an adequately large training set. This is often not possible in practical applications, such as person verification, where the lack of sufficient training samples causes improper estimation of a linear separation hyper-plane between the two classes. To overcome this shortcoming a novel algorithm that can handle the verification problem more efficiently than traditional LDA is presented. The dimensionality of the samples is reduced by breaking them down, thus creating subsets of smaller dimensionality feature vectors, and applying discriminant analysis on each subset. The resulting discriminant weight sets are themselves weighted under a normalization criterion, making the discriminant functions continuous in this sense. A series of simulations that formulate the face verification problem illustrate the cases for which our method outperforms traditional LDA and various statistical observations are made about the discriminant coefficients that are generated.