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2016 | OriginalPaper | Buchkapitel

Adaptive Hausdorff Distances and Tangent Distance Adaptation for Transformation Invariant Classification Learning

verfasst von : Sascha Saralajew, David Nebel, Thomas Villmann

Erschienen in: Neural Information Processing

Verlag: Springer International Publishing

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Abstract

Tangent distances (TDs) are important concepts for data manifold distance description in machine learning. In this paper we show that the Hausdorff distance is equivalent to the TD for certain conditions. Hence, we prove the metric properties for TDs. Thereafter, we consider those TDs as dissimilarity measure in learning vector quantization (LVQ) for classification learning of class distributions with high variability. Particularly, we integrate the TD in the learning scheme of LVQ to obtain a TD adaption during LVQ learning. The TD approach extends the classical prototype concept to affine subspaces. This leads to a high topological richness compared to prototypes as points in the data space. By the manifold theory of TDs we can ensure that the affine subspaces are aligned in directions of invariant transformations with respect to class discrimination. We demonstrate the superiority of this new approach by two examples.

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Vorheriges Kapitel Collaborative Filtering, Matrix Factorization and Population Based Search: The Nexus Unveiled

Nächstes Kapitel Semi-supervised Classification by Nuclear-Norm Based Transductive Label Propagation

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Titel: Adaptive Hausdorff Distances and Tangent Distance Adaptation for Transformation Invariant Classification Learning
verfasst von: Sascha Saralajew
David Nebel
Thomas Villmann
Verlag: Springer International Publishing
Buch: Neural Information Processing
Print ISBN: 978-3-319-46674-3

Electronic ISBN: 978-3-319-46675-0

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-46675-0_40

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