The DOI matches its Crossref record; 12 of the 13 references it cites were found in a registry or an index.
Multiple kernel learning, conic duality, and the SMO algorithm
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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“Let us first assume that each memory unit has a frozen value extraction function ψ.The training procedure can still make each memory unit statistically more efficient by tuning the parameters of the key extraction function φ, that is, by learning how to compare the current prediction context (x T , x T -1 , x T -2 . . . ) with past prediction contexts (x t , x t-1 , x t-2 . . . ) for t < T .”
From Memory Mosaics (2024) · cites this paper as Bach et al., 2004
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Cites
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Fast Training of Support Vector Machines Using Sequential Minimal Optimization
Platt, J. C. (1998) · The MIT Press eBooks · doi:10.7551/mitpress/1130.003.0016 · Cited by 5,501
Algorithms for Minimization Without Derivatives
G., D., & Brent, R. P. (1974) · Mathematics of Computation · doi:10.2307/2005713 · Cited by 2,914
Applications of second-order cone programming
Lobo, M. S., Vandenberghe, L., Boyd, S., & Lebret, H. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10032-0 · Cited by 2,405
Choosing Multiple Parameters for Support Vector Machines
Chapelle, O., Vapnik, V. N., Bousquet, O., & Mukherjee, S. (2002) · Machine Learning · doi:10.1023/a:1012450327387 · Cited by 2,232
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Keerthi, S. S., Shevade, S., Bhattacharyya, C., & Murthy, K. R. K. (2001) · Neural Computation · doi:10.1162/089976601300014493 · Cited by 1,791
Making Large-Scale Support Vector Machine Learning Practical
Joachims, T. (1998) · The MIT Press eBooks · doi:10.7551/mitpress/1130.003.0015 · Cited by 1,639
Feature Selection via Concave Minimization and Support Vector Machines
Bradley, P. S., & Mangasarian, O. L. (1998) · Cited by 984
Andersen, E. D., & Andersen, K. D. (2000) · Applied Optimization · doi:10.1007/978-1-4757-3216-0_8 · Cited by 766
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
Lemaréchal, C., & Sagastizábal, C. A. (1997) · SIAM Journal on Optimization · doi:10.1137/s1052623494267127 · Cited by 242
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A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization
Abernethy, J., Bach, F., Evgeniou, T., & Vert, J.-P. (2008) · arXiv · doi:10.48550/arxiv.0802.1430 · Cited by 210
Self-citation
Metadata
- Authors
- Bach, F. R., Lanckriet, G. R. G., & Jordan, M. I.
- Affiliations
- University of California, Berkeley (US)
- Venue
- Twenty-first international conference on Machine learning - ICML '04
- Publisher
- ACM Press
- Published
- 2004
- Pages
- 6
- 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
- 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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