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Functional Representation of Prototypes in LVQ and Relevance Learning

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


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.


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

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

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Correspondence to Friedrich Melchert , Udo Seiffert or Michael Biehl .

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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.

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