Abstract
We consider distance-based similarity measures for real-valued vectors of interest in kernel-based machine learning algorithms. In particular, a truncated Euclidean similarity measure and a self-normalized similarity measure related to the Canberra distance. It is proved that they are positive semi-definite (p.s.d.), thus facilitating their use in kernel-based methods, like the Support Vector Machine, a very popular machine learning tool. These kernels may be better suited than standard kernels (like the RBF) in certain situations, that are described in the paper. Some rather general results concerning positivity properties are presented in detail as well as some interesting ways of proving the p.s.d. property.
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© 2008 Springer-Verlag Berlin Heidelberg
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Belanche, L., Vázquez, J.L., Vázquez, M. (2008). Distance-Based Kernels for Real-Valued Data. In: Preisach, C., Burkhardt, H., Schmidt-Thieme, L., Decker, R. (eds) Data Analysis, Machine Learning and Applications. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78246-9_1
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DOI: https://doi.org/10.1007/978-3-540-78246-9_1
Publisher Name: Springer, Berlin, Heidelberg
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