Using SDP to Parameterize Universal Kernel Functions

Brendon K. Colbert, Matthew M. Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose a new class of universal kernel functions which admit a linear parametrization using positive semidefinite matrices. We refer to kernels of this class as Tessellated Kernels (TKs) due to the observation that if applied to kernel-based learning algorithms, the resulting discriminants are defined by continuous piecewise-polynomial functions with hyper-rectangular domains whose vertices are determined by the training data. The number of parameters used to define these TKs is determined by the length of an associated monomial basis. However, even for a single monomial basis function the TKs are universal in the sense that the resulting discriminants occupy a hypothesis space which is dense in L. This implies that the use of TKs for learning the kernel (aka kernel learning) can obviate the need for Gaussian kernels and associated problem of selecting bandwidth - a conclusion verified through extensive numerical testing on soft margin Support Vector Machine (SVM) problems. Furthermore, our results show that when the ratio of the number of training data to features is high, the proposed method will significantly outperform other algorithms for learning the kernel. Finally, TKs can be integrated efficiently with existing Multiple Kernel Learning (MKL) algorithms such as SimpleMKL.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4622-4629
Number of pages8
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Externally publishedYes
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Colbert, B. K., & Peet, M. M. (2019). Using SDP to Parameterize Universal Kernel Functions. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 4622-4629). [9030084] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9030084