We present an approach to recognizing faces with varying appearances which also considers the relative probability of occurrence for each appearance. We propose and demonstrate extending dimensionality reduction using locally linear embedding (LLE), to model the local shape of the manifold using neighboring nodes of the graph, where the probability associated with each node is also considered. The approach has been implemented in software and evaluated on the Yale database of face images. Recognition rates are compared with non-weighted LLE and principal component analysis (PCA), and in our setting, weighted LLE achieves superior performance.