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2004
Springer

On Kernels, Margins, and Low-Dimensional Mappings

11 years 10 months ago
On Kernels, Margins, and Low-Dimensional Mappings
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 the result is linearly-separable by a large margin γ. However, the JohnsonLindenstrauss 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/γ2 ). In this paper, we explore the question of whether one can efficiently produce such low-dimensional mappings, using only black-box access to a kernel function. That is, given just a program that computes K(x, y) on inputs x, y of our choosing, can we efficiently construct an explicit (small) set of features that effectively capture the power of the implicit high-dimensional space? We answer this question in the affirmative if our method is also allowed black-box access to the underlying data distribution (i.e., unlabeled examples). We ...
Maria-Florina Balcan, Avrim Blum, Santosh Vempala
Added 14 Mar 2010
Updated 14 Mar 2010
Type Conference
Year 2004
Where ALT
Authors Maria-Florina Balcan, Avrim Blum, Santosh Vempala
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