Elastic-Net Multiple Kernel Learning: Combining Multiple Data Sources for Prediction

Janaina Mourão-Miranda; Zakria Hussain; Konstantinos Tsirlis; Christophe Phillips; John Shawe-Taylor

Paper

Elastic-Net Multiple Kernel Learning: Combining Multiple Data Sources for Prediction

Abstract

Multiple Kernel Learning (MKL) models combine several kernels in supervised and unsupervised settings to integrate multiple data representations or sources, each represented by a different kernel. MKL seeks an optimal linear combination of base kernels that maximizes a generalized performance measure under a regularization constraint. Various norms have been used to regularize the kernel weights, including

and

, as well as the "elastic-net" penalty, which combines

- and

-norm to promote both sparsity and the selection of correlated kernels. This property makes elastic-net regularized MKL (ENMKL) especially valuable when model interpretability is critical and kernels capture correlated information, such as in neuroimaging. Previous ENMKL methods have followed a two-stage procedure: fix kernel weights, train a support vector machine (SVM) with the weighted kernel, and then update the weights via gradient descent, cutting-plane methods, or surrogate functions. Here, we introduce an alternative ENMKL formulation that yields a simple analytical update for the kernel weights. We derive explicit algorithms for both SVM and kernel ridge regression (KRR) under this framework, and implement them in the open-source Pattern Recognition for Neuroimaging Toolbox (PRoNTo). We evaluate these ENMKL algorithms against

-norm MKL and against SVM (or KRR) trained on the unweighted sum of kernels across three neuroimaging applications. Our results show that ENMKL matches or outperforms

-norm MKL in all tasks and only underperforms standard SVM in one scenario. Crucially, ENMKL produces sparser, more interpretable models by selectively weighting correlated kernels.