Probability-Based Locally Linear Embedding for Classification

We propose a novel dimension reduction method for classification using a 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 for the reduced data. Different to 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 that our method performs better, compared with the LD classifiers applied on the LLE or SLLE mapped lower dimensional data.