Supervised locally linear embedding with probability-based distance for classification

We present a novel dimension reduction method for classification based on probability-based distance and the technique of locally linear embedding (LLE). Logistic Discrimination (LD) is adopted for estimating the probability distribution as well as for classification on the reduced data. Different from the supervised locally linear embedding (SLLE) that is only used for the dimension reduction of training data, our probability-based locally linear embedding (PLLE) can be applied on both training and testing data. Five microarray data sets in high-dimensional spaces, the IRIS data, and a real set of handwritten digits are experimented. The numerical results show the proposed methodology performs better, compared with the LD classifiers applied on the lower-dimensional embedding coordinates computed by LLE or SLLE.