Invariance in kernel methods by haar-integration kernels

Authors:
B. Haasdonk;A. Vossen;H. Burkhardt
Affiliations:
Computer Science Department, Albert-Ludwigs-University Freiburg, Freiburg, Germany;Institute of Physics, Albert-Ludwigs-University Freiburg, Freiburg, Germany;Computer Science Department, Albert-Ludwigs-University Freiburg, Freiburg, Germany
Venue:
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Year:
2005

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Abstract

We address the problem of incorporating transformation invariance in kernels for pattern analysis with kernel methods. We introduce a new class of kernels by so called Haar-integration over transformations. This results in kernel functions, which are positive definite, have adjustable invariance, can capture simultaneously various continuous or discrete transformations and are applicable in various kernel methods. We demonstrate these properties on toy examples and experimentally investigate the real-world applicability on an image recognition task with support vector machines. For certain transformations remarkable complexity reduction is demonstrated. The kernels hereby achieve state-of-the-art results, while omitting drawbacks of existing methods.