Graph transduction methods label input data by learning a classification function that is regularized to exhibit smoothness along a graph over labeled and unlabeled samples. In practice, these algorithms are sensitive to the initial set of labels provided by the user. For instance, classification accuracy drops if the training set contains weak labels, if imbalances exist across label classes or if the labeled portion of the data is not chosen at random. This paper introduces a propagation algorithm that more reliably minimizes a cost function over both a function on the graph and a binary label matrix. The cost function generalizes prior work in graph transduction and also introduces node normalization terms for resilience to label imbalances. We demonstrate that global minimization of the function is intractable but instead provide an alternating minimization scheme that incrementally adjusts the function and the labels towards a reliable local minimum. Unlike prior methods, the res...