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Neural Computation

May 15, 1996, Vol. 8, No. 4, Pages 787-804
(doi: 10.1162/neco.1996.8.4.787)
© 1996 Massachusetts Institute of Technology
Learning with Preknowledge: Clustering with Point and Graph Matching Distance Measures
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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 (∼ million variables) are efficiently minimized using a combination of optimization techniques—softassign, algebraic transformations, clocked objectives, and deterministic annealing.