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.
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Backhaus, A.: Wettbewerb Detektion von defekten Bohnen im Rohkaffee. Fraunhofer Inst. for Factory Operation and Automation, Biosystems Engineering (2012)
Backhaus, A., Seiffert, U.: Classification in high-dimensional spectral data: accuracy vs. interpretability vs. model size. Neurocomputing 131, 15–22 (2014)
Biehl, M.: A no-nonsense beginner’s tool for GMLVQ. University of Groningen. http://www.cs.rug.nl/~biehl/gmlvq
Biehl, M., Hammer, B., Verleysen, M., Villmann, T. (eds.): Similarity Based Clustering. Springer Lecture Notes in Artificial Intelligence, vol. 5400 (2009)
Biehl, M., Hammer, B., Villmann, T.: Distance measures for prototype based classfication. In: Grandinetti, L., Petkov, N., Lippert, T. (eds.) BrainComp 2013, Proceedings of the International Workshop on Brain-Inspired Computing, Cetraro/Italy, 2013. Lecture Notes in Computer Science, vol. 8603, pp. 100–116. Springer (2014)
Biehl, M., Schneider, P., Bunte, K.: Relevance and Matrix adaptation in Learning Vector Quantization (GRLVQ, GMLVQ and LiRaM LVQ). University of Gronignen. http://matlabserver.cs.rug.nl/gmlvqweb/web/
Bunte, K., Schneider, P., Hammer, B., Schleif, F.M., Villmann, T., Biehl, M.: Limeted rank matrix learning, discriminative dimension reduction and visualization. Neural Netw. 26, 159–173 (2012)
Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13(1), 21–27 (1967)
Driscoll, T.A., Hale, N., Trefethen, L.N.: Chebfun Guide. Pafnuty Publications (2014)
Duda, R., Hart, P., Stork, D.: Pattern Classification. Wiley (2000)
Kästner, M., Hammer, B., Biehl, M., Villmann, T.: Generalized functional relevance learning vector quantization. In: Verleysen, M. (ed.) Proceedings of the European Symposium on Artificial Neural Networks (ESANN), pp. 93–98. d-side (2011)
Kohonen, T.: Self-organizing Maps. Springer, Berlin (1995)
Krier, C., François, D., Rossi, F., Verleysen, M., et al.: Supervised variable clustering for classification of nir spectra. In: Verleysen, M. (ed.) Proceedings of the European Symposium on Artificial Neural Networks (ESANN), pp. 263–268. d-side (2009)
Lee, J.A., Verleysen, M.: Generalization of the Lp norm for time series and its application to self-organizing maps. In: Cottrell, M. (Eds.): Proceedings of the Workshop on Self-Organizing Maps (WSOM) 2005, pp. 733–740. Paris, Sorbonne (2005)
Meurens, M.: Orange juice near-infrared spectra dataset and wine mean infrared spectra dataset. University of Louvain. http://mlg.info.ucl.ac.be/index.php?page=DataBases
Papari, G., Bunte, K., Biehl, M.: Waypoint averaging and step size control in learning by gradient descent. Machine Learning Reports MLR-06/2011, vol. 16 (2011)
Ramsay, J., Silverman, B.: Functional Data Analysis. Springer (2006)
Sato, A., Yamada, K.: Generalized learning vector quantization. In: Tesauro, G., Touretzky, D., Leen, T. (eds.) Advances in Neural Information Processing Systems. vol. 7, pp. 423–429. MIT Press (1995)
Schneider, P., Biehl, M., Schleif, F.M., Hammer, B.: Advanced metric adaptation in Generalized LVQ for classification of mass spetrometry data. In: Proceedings of the 6th International Workshop on Self-Organizing-Maps (WSOM), 5 pp. Bielefeld University (2007)
Schneider, P., Biehl, M., Hammer, B.: Adaptive relevance matrices in Learning Vector Quantization. Neural Comput. 21, 3532–3561 (2009)
Seo, S., Bode, M., Obermayer, K.: Soft nearest prototype classification. IEEE Trans. Neural Netw. 14(2), 390–398 (2003)
The Chebfun Developers: Chebfun—Numerical Computing with functions. University of Oxford. http://www.chebfun.org
Thodberg, H.H.: Tecator meat sample dataset. StatLib Datasets Archive. http://lib.stat.cmu.edu/datasets/tecator
Villmann, T., Hammer, B.: Functional principal component learning using Oja’s method and Sobolev norms. In: J. Princip, R. Miikulainen (eds.): Advances in Self-Organizing Maps—Proceedings of the Workshop on Self-Organizing Maps (WSOM) 2009. Springer Lecture Notes on Computer Science 5629: 325–333 (2009)
Weinberger, K., Saul, L.: Distance metric learning for large margin classification. J. Mach. Learn. Res. 10, 207–244 (2009)
Acknowledgments
F. Melchert thanks for support through an Ubbo-Emmius Sandwich Scholarship by the Faculty of Mathematics and Natural Sciences.
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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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