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Advances in Self-Organizing Maps and Learning Vector Quantization pp 317–327Cite as

Functional Representation of Prototypes in LVQ and Relevance Learning

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 428)

Abstract

We present a framework for distance-based classification of functional data. We consider the analysis of labeled spectral data by means of Generalized Matrix Relevance Learning Vector Quantization (GMLVQ) as an example. Feature vectors and prototypes are represented as functional expansions in order to take advantage of the functional nature of the data. Specifically, we employ truncated Chebyshev series in the context of several spectral datasets available in the public domain. GMLVQ is applied in the space of expansion coefficients and its performance is compared with the standard approach in original feature space, which ignores the functional nature of the data. Data smoothing by polynomial expansion alone is also considered for comparison. Computer experiments show that, beyond the reduction of dimensionality and computational effort, the method offers the potential to improve classification performance significantly.

Keywords

  • Classification
  • Supervised learning
  • Functional data
  • Learning vector quantization
  • Relevance learning
  • Dimensionality reduction

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Acknowledgments

F. Melchert thanks for support through an Ubbo-Emmius Sandwich Scholarship by the Faculty of Mathematics and Natural Sciences.

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Authors and Affiliations

  1. University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, P.O. Box 407, 9700, Groningen, AK, The Netherlands

    Friedrich Melchert & Michael Biehl

  2. Fraunhofer Institute for Factory Operation and Automation IFF, Sandtorstrasse 22, 39106, Magdeburg, Germany

    Friedrich Melchert & Udo Seiffert

Authors
  1. Friedrich Melchert
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  2. Udo Seiffert
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  3. Michael Biehl
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Corresponding authors

Correspondence to Friedrich Melchert , Udo Seiffert or Michael Biehl .

Editor information

Editors and Affiliations

  1. Department of Statistics, Rice University, Houston, Texas, USA

    Erzsébet Merényi

  2. Department of Electrical and Computer En, Air Force Institute of Technology, Wright-Patterson AFB, Ohio, USA

    Michael J. Mendenhall

  3. Applied Physics, Rice University, Houston, Texas, USA

    Patrick O'Driscoll

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Melchert, F., Seiffert, U., Biehl, M. (2016). Functional Representation of Prototypes in LVQ and Relevance Learning. In: Merényi, E., Mendenhall, M., O'Driscoll, P. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-319-28518-4_28

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  • DOI: https://doi.org/10.1007/978-3-319-28518-4_28

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