This paper investigates the correspondence matching of point-sets using spectral graph analysis. In particular, we are interested in the problem of how the modal analysis of point-sets can be rendered robust to contamination and dropout. We make three contributions. First, we show how the modal structure of point-sets can be embedded within the framework of the EM algorithm. Second, we present several methods for computing the probabilities of point correspondences using the point proximity matrix. Third, we consider alternatives to the Gaussian proximity matrix. We evaluate the new method on both synthetic and real-world data. Here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50%.