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Neural Computing and Applications

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01.04.2010 | Original Article

Feature space versus empirical kernel map and row kernel space in SVMs

verfasst von: Xun Liang

Erschienen in: Neural Computing and Applications | Ausgabe 3/2010

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Abstract

In machine-learning technologies, the support vector machine (SV machine, SVM) is a brilliant invention with many merits, such as freedom from local minima, the widest possible margins separating different clusters, and a solid theoretical foundation. In this paper, we first explore the linear separability relationships between the high-dimensional feature space H and the empirical kernel map U as well as between H and the space of kernel outputs K. Second, we investigate the relations of the distances between separating hyperplanes and SVs in H and U, and derive an upper bound for the margin width in K. Third, as an application, we show experimentally that the separating hyperplane in H can be slightly adjusted through U. The experiments reveal that existing SVM training can linearly separate the data in H with considerable success. The results in this paper allow us to visualize the geometry of H by studying U and K.

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Titel: Feature space versus empirical kernel map and row kernel space in SVMs
verfasst von: Xun Liang
Publikationsdatum: 01.04.2010
Verlag: Springer-Verlag
Erschienen in: Neural Computing and Applications / Ausgabe 3/2010
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-010-0337-0

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