Learning with Preknowledge: Clustering with Point and Graph Matching Distance Measures

Part of Advances in Neural Information Processing Systems 7 (NIPS 1994)

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Steven Gold, Anand Rangarajan, Eric Mjolsness


Prior constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2-D point sets and graphs are learned by clustering with point matching and graph matching dis(cid:173) tance measures. The point matching distance measure is approx. 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 per(cid:173) mutations. Learning is formulated as an optimization problem . Large objectives so formulated ('" million variables) are efficiently minimized using a combination of optimization techniques - alge(cid:173) braic transformations, iterative projective scaling, clocked objec(cid:173) tives, and deterministic annealing.