Diffusion maps for dimensionality reduction with partially labeled samples

In this paper, we present a novel diffusion maps based semi-supervised algorithm for dimensionality reduction and data parameterization. Unlike previous works which use only geometric information for similarity metric construction, a distribution similarity metric is introduced to boost the classification accuracy in our algorithm. The metric is related to the posterior probability of the labels of each sample, which is learned through expectation maximization algorithm. The algorithm preserves the local manifold structure in addition to separating samples in different classes. Encouraging experimental results on Hand-written digits, Yale faces and UCI data sets show that the algorithm can improve the classification accuracy significantly.