On the Consistency of Multithreshold Entropy Linear Classifier

Wojciech Marian Czarnecki

Titles

Abstract

Multithreshold Entropy Linear Classifier (MELC) is a recent classifier idea which employs information theoretic concept in order to create a multithreshold maximum margin model. In this paper we analyze its consistency over multithreshold linear models and show that its objective function upper bounds the amount of misclassified points in a similar manner like hinge loss does in support vector machines. For further confirmation we also conduct some numerical experiments on five datasets.

Keywords

entropy, consistency, classification theory, multithreshold classifier

multithreshold classifier, entropy, consistency, classification theory

References

[1] Sch¨olkopf B., Smola A.J., Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press, London, England, 2002.

[2] Steinwart I., On the inﬂuence of the kernel on the consistency of support vector machines. The Journal of Machine Learning Research, 2002, 2, pp. 67–93.

[3] Steinwart I., Consistency of support vector machines and other regularized kernel classiﬁers. IEEE Transactions on Information Theory, 2005, 51(1), pp. 128–142.

[4] Czarnecki W.M., Tabor J., Multithreshold entropy linear classiﬁer. arXiv preprint arXiv:1408.1054, 2014.

[5] Jenssen R., Principe J.C., Erdogmus D., Eltoft T., The cauchy–schwarz divergence and parzen windowing: Connections to graph theory and mercer kernels. Journal of the Franklin Institute, 2006, 343(6), pp. 614–629.

[6] Silverman B.W., Density estimation for statistics and data analysis. vol. 26. CRC press, Boca Raton 1986.

[7] Principe J.C., Information theoretic learning: R´enyi’s entropy and kernel perspectives. Springer, Gainesville 2010.

[8] Vapnik V., The nature of statistical learning theory. Springer, New York 2000.

[9] Ho T.K., Kleinberg E.M., Building projectable classiﬁers of arbitrary complexity. In: Proceedings of the 13th International Conference on Pattern Recognition, 1996. vol. 2., IEEE, 1996, pp. 880–885.

[10] LeCun Y., Cortes C., The mnist database of handwritten digits, 1998, http://yann.lecun.com/exdb/mnist/.

Information

Information: Schedae Informaticae, 2015, Volume 24, pp. 123 - 132

DOI: https://doi.org/10.4467/20838476SI.15.012.3034

Article type: Original article

Titles:

Polish:

On the Consistency of Multithreshold Entropy Linear Classifier

English:

On the Consistency of Multithreshold Entropy Linear Classifier

Authors

Wojciech Marian Czarnecki

Department of Mathematics Faculty of Mathematics and Computer Science Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland

Published at: 11.04.2016

Article status: Open

Licence: None

Percentage share of authors:

Wojciech Marian Czarnecki (Author) - 100%

Article corrections:

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Publication languages:

English

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