Invariant kernel functions for pattern analysis and machine learning |
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Authors: | Bernard Haasdonk Hans Burkhardt |
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Affiliation: | 1.Applied Mathematics Department,Albert-Ludwigs-University Freiburg,Freiburg,Germany;2.Computer Science Department,Albert-Ludwigs-University Freiburg,Freiburg,Germany |
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Abstract: | In many learning problems prior knowledge about pattern variations can be formalized and beneficially incorporated into the
analysis system. The corresponding notion of invariance is commonly used in conceptionally different ways. We propose a more distinguishing treatment in particular in the active
field of kernel methods for machine learning and pattern analysis. Additionally, the fundamental relation of invariant kernels
and traditional invariant pattern analysis by means of invariant representations will be clarified. After addressing these
conceptional questions, we focus on practical aspects and present two generic approaches for constructing invariant kernels.
The first approach is based on a technique called invariant integration. The second approach builds on invariant distances.
In principle, our approaches support general transformations in particular covering discrete and non-group or even an infinite
number of pattern-transformations. Additionally, both enable a smooth interpolation between invariant and non-invariant pattern
analysis, i.e. they are a covering general framework. The wide applicability and various possible benefits of invariant kernels
are demonstrated in different kernel methods.
Editor: Phil Long. |
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Keywords: | Invariance Kernel methods Pattern recognition Pattern analysis Invariant features |
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