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Abstract: Kernel functions are typically viewed as providing an implicit mapping of points into a high-dimensional space, with the ability to gain much of the power of that space without incurring a high cost if data is separable in that space by a large margin . However, the Johnson-Lindenstrauss lemma suggests that in the presence of a large margin, a kernel function can also be viewed as a mapping to a low- dimensional space, one of dimension only ~ O(1= ). In this paper, we explore the... (Update)
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BibTeX entry: (Update)
@misc{ balcan-kernels,
author = "Maria-Florina Balcan and Avrim Blum and Santosh Vempala",
title = "On Kernels, Margins, and Low-dimensional Mappings",
url = "citeseer.ist.psu.edu/694855.html" }
Citations (may not include all citations):947 Statistical Learning Theory (context) - Vapnik - 1998
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227 An elementary proof of the Johnson-Lindenstrauss Lemma - Dasgupta, Gupta - 1999
79 Extensions of Lipschitz mappings into a Hilbert space (context) - Johnson, Lindenstrauss - 1984
63 Generalization Performance of Support Vector Machines and Ot.. - Bartlett, Shawe-Taylor - 1999
52 A Training Algorithm for Optimal Margin Classi ers (context) - Boser, Guyon et al. - 1992
50 An Introduction to kernel-based learning algorithms (context) - Muller, Mika et al. - 2001
36 Structural Risk Minimization over Data-Dependent Hierarchies (context) - Shawe-Taylor, Bartlett et al. - 1998
25 Database-friendly Random Projections - Achlioptas - 2001
21 Large Margin Classi cation Using the Perceptron Algorithm (context) - Freund, Schapire - 1999
7 Limitations of Learning Via Embeddings in Euclidean Half-Spa.. (context) - Ben-David, Eiron et al. - 2002
5 Support Vector Machines (context) - Scholkopf, Smola et al. - 2002
4 Advances in Large Margin Classi ers (context) - Smola, Bartlett et al. - 2000
3 A Priori Generalization Bounds for Kernel Based Learning (context) - Ben-David - 2001
1 ithmic theory of learning, Robust concepts and random projec.. (context) - Arriaga, Vempala et al. - 1999
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