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Kernel Cuts: Kernel and Spectral Clustering Meet Regularization

Authors
  • Tang, Meng1
  • Marin, Dmitrii1, 2
  • Ben Ayed, Ismail3
  • Boykov, Yuri1
  • 1 University of Waterloo, Computer Science, Waterloo, Canada , Waterloo (Canada)
  • 2 Western University, Computer Science, London, Canada , London (Canada)
  • 3 ETS Montreal, Montreal, Canada , Montreal (Canada)
Type
Published Article
Journal
International Journal of Computer Vision
Publisher
Springer-Verlag
Publication Date
Sep 22, 2018
Volume
127
Issue
5
Pages
477–511
Identifiers
DOI: 10.1007/s11263-018-1115-1
Source
Springer Nature
Keywords
License
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Abstract

This work bridges the gap between two popular methodologies for data partitioning: kernel clustering and regularization-based segmentation. While addressing closely related practical problems, these general methodologies may seem very different based on how they are covered in the literature. The differences may show up in motivation, formulation, and optimization, e.g. spectral relaxation versus max-flow. We explain how regularization and kernel clustering can work together and why this is useful. Our joint energy combines standard regularization, e.g. MRF potentials, and kernel clustering criteria like normalized cut. Complementarity of such terms is demonstrated in many applications using our bound optimization Kernel Cut algorithm for the joint energy (code is publicly available). While detailing combinatorial move-making, our main focus are new linear kernel and spectral bounds for kernel clustering criteria allowing their integration with any regularization objectives with existing discrete or continuous solvers.

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