Isograph: Neighbourhood Graph Construction Based on Geodesic Distance for Semi-supervised Learning

Semi-supervised learning based on manifolds has been the focus of extensive research in recent years. Convenient neighbourhood graph construction is a key component of a successful semi-supervised classification method. Previous graph construction methods fail when there are pairs of data points that have small Euclidean distance, but are far apart over the manifold. To overcome this problem, we start with an arbitrary neighbourhood graph and iteratively update the edge weights by using the estimates of the geodesic distances between points. Moreover, we provide theoretical bounds on the values of estimated geodesic distances. Experimental results on real-world data show significant improvement compared to the previous graph construction methods.