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Learning Equivariant Functions with Matrix Valued Kernels

Published: 01 December 2007 Publication History

Abstract

This paper presents a new class of matrix valued kernels that are ideally suited to learn vector valued equivariant functions. Matrix valued kernels are a natural generalization of the common notion of a kernel. We set the theoretical foundations of so called equivariant matrix valued kernels. We work out several properties of equivariant kernels, we give an interpretation of their behavior and show relations to scalar kernels. The notion of (ir)reducibility of group representations is transferred into the framework of matrix valued kernels. At the end to two exemplary applications are demonstrated. We design a non-linear rotation and translation equivariant filter for 2D-images and propose an invariant object detector based on the generalized Hough transform.

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  • (2023)Approximation-generalization trade-offs under (approximate) group equivarianceProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668830(61936-61959)Online publication date: 10-Dec-2023
  • (2013)A unifying framework for vector-valued manifold regularization and multi-view learningProceedings of the 30th International Conference on International Conference on Machine Learning - Volume 2810.5555/3042817.3042905(II-100-II-108)Online publication date: 16-Jun-2013
  • (2008)Universal Multi-Task KernelsThe Journal of Machine Learning Research10.5555/1390681.14427859(1615-1646)Online publication date: 1-Jun-2008

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cover image The Journal of Machine Learning Research
The Journal of Machine Learning Research  Volume 8, Issue
12/1/2007
2736 pages
ISSN:1532-4435
EISSN:1533-7928
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JMLR.org

Publication History

Published: 01 December 2007
Published in JMLR Volume 8

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Cited By

View all
  • (2023)Approximation-generalization trade-offs under (approximate) group equivarianceProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668830(61936-61959)Online publication date: 10-Dec-2023
  • (2013)A unifying framework for vector-valued manifold regularization and multi-view learningProceedings of the 30th International Conference on International Conference on Machine Learning - Volume 2810.5555/3042817.3042905(II-100-II-108)Online publication date: 16-Jun-2013
  • (2008)Universal Multi-Task KernelsThe Journal of Machine Learning Research10.5555/1390681.14427859(1615-1646)Online publication date: 1-Jun-2008

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