Cited by 1,453Advanced Optimization Algorithms ResearchStochastic Gradient Optimization TechniquesMachine Learning and Algorithms

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Multiple kernel learning, conic duality, and the SMO algorithm

Bach, Francis R., Lanckriet, Gert R. G., Jordan, Michael I.·2004·Twenty-first international conference on Machine learning - ICML '04

DOI 10.1145/1015330.1015424

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Abstract

While classical kernel-based classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points; moreover, the sequential minimal optimization (SMO) techniques that are essential in large-scale implementations of the SVM cannot be applied because the cost function is non-differentiable. We propose a novel dual formulation of the QCQP as a second-order cone programming problem, and show how to exploit the technique of Moreau-Yosida regularization to yield a formulation to which SMO techniques can be applied. We present experimental results that show that our SMO-based algorithm is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes.

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Authors: Bach, F. R., Lanckriet, G. R. G., & Jordan, M. I.
Affiliations: University of California, Berkeley (US)
ORCID: Bach, Francis R.
Jordan, Michael I.
Venue: Twenty-first international conference on Machine learning - ICML '04
Publisher: ACM Press
Published: 2004
Pages: 6
DOI: 10.1145/1015330.1015424
OpenAlex: W2031823405
Semantic Scholar: 141e6c1dd532504611266d08458dbe2a0dbb4e98
Cited by: 1,453
References: 13
Citations by year: 2026: 7 · 2025: 4 · 2024: 19 · 2023: 20 · 2022: 22 · 2021: 36 · 2020: 52 · 2019: 84 · 2018: 89 · 2017: 86 · 2016: 84 · 2015: 116 · 2014: 136 · 2013: 123 · 2012: 132
Type: conference abstract
Language: en
Open access: closed
Licence: www.acm.org/publications/policies/copyright_policy#Background (vor)
Locations: International Conference on Machine Learning (publishedVersion)
Funders: Intel Corporation
Microsoft Research
Topics: Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
Keywords: multiple kernel learning, support vector machine, sequential minimal optimization, second-order cone programming, Moreau-Yosida regularization, quadratically constrained quadratic programming, non-differentiable cost functions

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Multiple kernel learning, conic duality, and the SMO algorithm

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