# Large Scale Multiple Kernel Learning

@article{Sonnenburg2006LargeSM, title={Large Scale Multiple Kernel Learning}, author={S{\"o}ren Sonnenburg and Gunnar R{\"a}tsch and Christin Sch{\"a}fer and Bernhard Sch{\"o}lkopf}, journal={J. Mach. Learn. Res.}, year={2006}, volume={7}, pages={1531-1565} }

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to…

## 1,401 Citations

### A General and Efficient Multiple Kernel Learning Algorithm

- Computer ScienceNIPS
- 2005

The formulation and method can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations and generalized to a larger class of problems, including regression and one-class classification.

### Y.: SimpleMKL

- Computer Science
- 2008

This paper proposes an algorithm, named SimpleMKL, for solving this MKL problem and provides a new insight on MKL algorithms based on mixed-norm regularization by showing that the two approaches are equivalent.

### Building Sparse Multiple-Kernel SVM Classifiers

- Computer ScienceIEEE Transactions on Neural Networks
- 2009

Experiments on a large number of toy and real-world data sets show that the resultant classifier is compact and accurate, and can also be easily trained by simply alternating linear program and standard SVM solver.

### More generality in efficient multiple kernel learning

- Computer ScienceICML '09
- 2009

It is observed that existing MKL formulations can be extended to learn general kernel combinations subject to general regularization while retaining all the efficiency of existing large scale optimization algorithms.

### An efficient multiple-kernel learning for pattern classification

- Computer ScienceExpert Syst. Appl.
- 2013

### Multiple kernel learning based on local and nonlinear combinations

- Computer Science2012 XXXVIII Conferencia Latinoamericana En Informatica (CLEI)
- 2012

A new MKL method is proposed, which is based on a local and nonlinear combination of different kernels using a gating model for selecting the appropriate kernel function and has performed better than the other methods analyzed.

### Learning SVM with Complex Multiple Kernels Evolved by Genetic Programming

- Computer ScienceInt. J. Artif. Intell. Tools
- 2010

The numerical experiments show that the SVM involving the evolutionary complex multiple kernels perform better than the classic simple kernels and on the considered data sets, the new multiple kernels outperform both the cLMK and eLMK — linear multiple kernels.

### Multiple kernel learning using nonlinear lasso

- Computer ScienceIEEJ Transactions on Electrical and Electronic Engineering
- 2018

A novel MKL model based on a nonlinear Lasso, that is, the Hilbert–Schmidt independence criterion (HSIC) Lasso is developed, which has a clear statistical interpretation that minimum redundant kernels with maximum dependence on output labels are found and combined.

### Spectral Projected Gradient Descent for Efficient and Large Scale Generalized Multiple Kernel Learni

- Computer Science
- 2012

This work addresses the problem of learning the kernel in a Support Vector Machine framework from training data by developing a Spectral Projected Gradient descent optimizer which takes into account second order information in selecting step sizes and employs a nonmonotone step size selection criterion requiring fewer function evaluations.

### Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming

- Computer ScienceKDD '07
- 2007

This paper proposes a Quadratically Constrained Quadratic Programming (QCQP) formulation for the kernel learning problem, which can be solved more efficiently than SDP and shows that the QCQP formulation can be extended naturally to the multi-class case.

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