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

  • Authors:
  • Steven Gold;Anand Rangarajan;Eric Mjolsness

  • Affiliations:
  • Department of Computer Science, Yale University, New Haven, CT 06520-8285 USA;Department of Diagnostic Radiology, Yale University, New Haven, CT 06520-8042 USA;Department of Computer Science and Engineering, University of California at San Diego (UCSD), La Jolla, CA 92093-0114 USA

  • Venue:
  • Neural Computation
  • Year:
  • 1996

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Abstract

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.