Embedding and function extension on directed graph

Abstract

In this paper, we propose a novel technique for finding the graph embedding and function extension for directed graphs. We assume that the data points are sampled from a manifold and the similarity between the points is given by an asymmetric kernel. We provide a graph embedding algorithm which is motivated by Laplacian type operator on manifold. We also introduce a Nyström type eigenfunctions extension which is used both for extending the embedding to new data points and to extend an empirical function on new data set. For extending the eigenfunctions to new points, we assume that only the distances of the new points from the labelled data are given. Simulation results demonstrate the performance of the proposed method in recovering the geometry of data and extending a function on new data points.