Spectral learning

We present a simple, easily implemented spectral learning algorithm which applies equally whether we have no supervisory information, pairwise link constraints, or labeled examples. In the unsupervised case, it performs consistently with other spectral clustering algorithms. In the supervised case, our approach achieves high accuracy on the categorization of thousands of documents given only a few dozen labeled training documents for the 20 Newsgroups data set. Furthermore, its classification accuracy increases with the addition of unlabeled documents, demonstrating effective use of unlabeled data. By using normalized affinity matrices which are both symmetric and stochastic, we also obtain both a probabilistic interpretation of our method and certain guarantees of performance.