Semi-Supervised Nonparametric Discriminant Analysis

We extend the Nonparametric Discriminant Analysis (NDA) algorithm to a semi-supervised dimensionality reduction technique, called Semi-supervised Nonparametric Discriminant Analysis (SNDA). SNDA preserves the inherent advantages of NDA, that is, relaxing the Gaussian assumption required for the traditional LDA-based methods. SNDA takes advantage of both the discriminating power provided by the NDA method and the locality-preserving power provided by the manifold learning. Specifically, the labeled data points are used to maximize the separability between different classes and both the labeled and unlabeled data points are used to build a graph incorporating neighborhood information of the data set. Experiments on synthetic as well as real datasets demonstrate the effectiveness of the proposed approach.