Random Feature Maps for Dot Product Kernels

Purushottam Kar, Harish Karnick
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:583-591, 2012.

Abstract

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-kar12, title = {Random Feature Maps for Dot Product Kernels}, author = {Kar, Purushottam and Karnick, Harish}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {583--591}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/kar12/kar12.pdf}, url = {https://proceedings.mlr.press/v22/kar12.html}, abstract = {Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.} }
Endnote
%0 Conference Paper %T Random Feature Maps for Dot Product Kernels %A Purushottam Kar %A Harish Karnick %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-kar12 %I PMLR %P 583--591 %U https://proceedings.mlr.press/v22/kar12.html %V 22 %X Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.
RIS
TY - CPAPER TI - Random Feature Maps for Dot Product Kernels AU - Purushottam Kar AU - Harish Karnick BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-kar12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 583 EP - 591 L1 - http://proceedings.mlr.press/v22/kar12/kar12.pdf UR - https://proceedings.mlr.press/v22/kar12.html AB - Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence. ER -
APA
Kar, P. & Karnick, H.. (2012). Random Feature Maps for Dot Product Kernels. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:583-591 Available from https://proceedings.mlr.press/v22/kar12.html.

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