Learning with preknowledge: Clustering with point and graph matching distance measures

Prior knowledge constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2D point sets and graphs are learned by clustering with point-matching and graph-matching distance measures. The point-matching distance measure is approximately invariant under affine transformations-translation, rotation, scale, and shear-and permutations. It operates between noisy images with missing and spurious points. The graph-matching distance measure operates on weighted graphs and is invariant under permutations. Learning is formulated as an optimization problem. Large objectives so formulated (similar to million variables) are efficiently minimized using a combination of optimization techniques-softassign, algebraic transformations, clocked objectives, and deterministic annealing.