Multiple kernel learning

About: Multiple kernel learning is a research topic. Over the lifetime, 1630 publications have been published within this topic receiving 56082 citations.

An Extended Level Method for Efficient Multiple Kernel Learning

Abstract: We consider the problem of multiple kernel learning (MKL), which can be formulated as a convex-concave problem. In the past, two efficient methods, i.e., Semi-Infinite Linear Programming (SILP) and Subgradient Descent (SD), have been proposed for large-scale multiple kernel learning. Despite their success, both methods have their own shortcomings: (a) the SD method utilizes the gradient of only the current solution, and (b) the SILP method does not regularize the approximate solution obtained from the cutting plane model. In this work, we extend the level method, which was originally designed for optimizing non-smooth objective functions, to convex-concave optimization, and apply it to multiple kernel learning. The extended level method overcomes the drawbacks of SILP and SD by exploiting all the gradients computed in past iterations and by regularizing the solution via a projection to a level set. Empirical study with eight UCI datasets shows that the extended level method can significantly improve efficiency by saving on average 91.9% of computational time over the SILP method and 70.3% over the SD method.

Learning Sparse SVM for Feature Selection on Very High Dimensional Datasets

Abstract: A sparse representation of Support Vector Machines (SVMs) with respect to input features is desirable for many applications. In this paper, by introducing a 0-1 control variable to each input feature, l0-norm Sparse SVM (SSVM) is converted to a mixed integer programming (MIP) problem. Rather than directly solving this MIP, we propose an efficient cutting plane algorithm combining with multiple kernel learning to solve its convex relaxation. A global convergence proof for our method is also presented. Comprehensive experimental results on one synthetic and 10 real world datasets show that our proposed method can obtain better or competitive performance compared with existing SVM-based feature selection methods in term of sparsity and generalization performance. Moreover, our proposed method can effectively handle large-scale and extremely high dimensional problems.

Sparsity in multiple kernel learning

Abstract: The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the problem is sparse. The goal is to establish oracle inequalities for the excess risk of the resulting prediction rule showing that the method is adaptive both to the unknown design distribution and to the sparsity of the problem.

Group-sensitive multiple kernel learning for object categorization

Abstract: In this paper, we propose a group-sensitive multiple kernel learning (GS-MKL) method to accommodate the intra-class diversity and the inter-class correlation for object categorization. By introducing an intermediate representation “group” between images and object categories, GS-MKL attempts to find appropriate kernel combination for each group to get a finer depiction of object categories. For each category, images within a group share a set of kernel weights while images from different groups may employ distinct sets of kernel weights. In GS-MKL, such group-sensitive kernel combinations together with the multi-kernels based classifier are optimized in a joint manner to seek a trade-off between capturing the diversity and keeping the invariance for each category. Extensive experiments show that our proposed GS-MKL method has achieved encouraging performance over three challenging datasets.

A General and Efficient Multiple Kernel Learning Algorithm

Abstract: While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constraint 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 a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning result and works for hundred thousands of examples or hundreds of kernels to be combined.