Semi-Supervised Learning with Conditional Harmonic Mixing
Burges Christopher J. C., Platt John C. · The MIT Press eBooks · 2006
This chapter introduces a general probabilistic formulation called conditional harmonic mixing (CHM), in which the links are directed, a conditional probability matrix is associated with each link, and where the numbers of classes can vary from node to node. The posterior class probability at each node is updated by minimizing the Kullback-Leibler (KL) divergence between its distribution and that predicted by its neighbors. It is shown here that for arbitrary graphs, as long as each unlabeled point is reachable from at least one training point, a solution always exists, is unique, and can be found by solving a sparse linear system iteratively. This result holds even if the graph contains loops, or if the conditional probability matrices are not consistent. It is also shown how CHM can learn its transition probabilities. Using the Reuters database, it is shown here that CHM improves the accuracy of the best available classifier.