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

  • Sascha Saralajew
  • David Nebel
  • Thomas VillmannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9949)

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.

Keywords

Hausdorff Distance Classification Learning Dissimilarity Measure Learn Vector Quantization Affine Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Sascha Saralajew
    • 1
  • David Nebel
    • 2
  • Thomas Villmann
    • 2
    • 3
    Email author
  1. 1.Electrical/Electronics Engineering - Driver Assistance Platform/SystemsDr. Ing. h.c. F. Porsche AGWeissachGermany
  2. 2.Computational Intelligence GroupUniversity of Applied Sciences MittweidaMittweidaGermany
  3. 3.Institut für Computational Intelligence und Intelligente Datenanalyse Mittweida (CIID) e.V.MittweidaGermany

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