Spectral graph-based semi-supervised learning for imbalanced classes

Semi-supervised learning makes the realistic assumptions that labelled data is typically rare, and that unlabelled data that are similar are likely to belong to the same class. Unlabelled data are assigned the labels associated with their “most similar” labelled neighbors. For graph-based semi-supervised learning, “most similar” is defined by weighted multipath path length in a graph. When classes are of different sizes, or the number of labelled nodes per class is not the same across classes, the performance of existing graph-based algorithms degrades sharply. We develop a new algorithm that creates representative nodes for each class, connects them to the labelled nodes of that class, adds negative edges between them, embeds the resulting graph using a signed graph Laplacian technique, and then predicts the unlabelled nodes using distance-based techniques in the geometry of the embedding. Its performance matches current algorithms for balanced datasets, but is much better for datasets where the classes, or the number of labelled records, differ in size.