Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 4,094 papers for “Multiple kernel learning”

Multiple kernel learning.

Shengbing Ren (8697819), Fa Liu (1321878), Weijia Zhou (1391845) et al. · Figshare · 2020

Cited by 0Open access

On multiple kernel learning

O. Chapelle · 2013

Multiple kernel learning has recently been a topic of interest [3, 4]. The setting is the following: given p kernel functions K1,..., Kp that are potentially well suited for a given problem, find a linear combination of these kernels such that the resutling kernel K = ∑ λpKp is ”optimal ” in some sense. The aim of this presentation is to revisit some of the proposed approaches and to give both a well founded theoretical justification as well as a en efficient algorithm to learn this linear combination of kernels. Theoretical justification Margin has been argued to be a good quantity to maximize and that is the reason why the objective function that (hard margin) SVMs minimize is the invert squared margin. Let us define M(K) as the minimum of this objective function for a kernel K. Based on this motivation, it has often been suggested to find the kernel matrix by minimizing M. We would like to point out that one has to be cautious with this approach. Indeed, the SVM objective function has been derived to find the hyperplane given a kernel, but there is no guarantee that

Cited by 0

Localized multiple kernel learning

Mehmet Gönen, Ethem Alpaydın · 2008

Recently, instead of selecting a single kernel, multiple kernel learning (MKL) has been proposed which uses a convex combination of kernels, where the weight of each kernel is optimized during training. However, MKL assigns the same weight to a kernel over the whole input space. In this paper, we develop a localized multiple kernel learning (LMKL) algorithm using a gating model for selecting the appropriate kernel function locally. The localizing gating model and the kernel-based classifier are coupled and their optimization is done in a joint manner. Empirical results on ten benchmark and two bioinformatics data sets validate the applicability of our approach. LMKL achieves statistically similar accuracy results compared with MKL by storing fewer support vectors. LMKL can also combine multiple copies of the same kernel function localized in different parts. For example, LMKL with multiple linear kernels gives better accuracy results than using a single linear kernel on bioinformatics data sets.

Cited by 284

Kernel Matrix-Based Heuristic Multiple Kernel Learning

Stanton R. Price, Stanton R. Price, Derek T. Anderson et al. · Mathematics · 2022

Kernel theory is a demonstrated tool that has made its way into nearly all areas of machine learning. However, a serious limitation of kernel methods is knowing which kernel is needed in practice. Multiple kernel learning (MKL) is an attempt to learn a new tailored kernel through the aggregation of a set of valid known kernels. There are generally three approaches to MKL: fixed rules, heuristics, and optimization. Optimization is the most popular; however, a shortcoming of most optimization approaches is that they are tightly coupled with the underlying objective function and overfitting occurs. Herein, we take a different approach to MKL. Specifically, we explore different divergence measures on the values in the kernel matrices and in the reproducing kernel Hilbert space (RKHS). Experiments on benchmark datasets and a computer vision feature learning task in explosive hazard detection demonstrate the effectiveness and generalizability of our proposed methods.

Cited by 5Open access

Multiple kernel learning by empirical target kernel

Peiyan Wang, Dongfeng Cai · International Journal of Wavelets Multiresolution and Information Processing · 2019

Multiple kernel learning (MKL) aims at learning an optimal combination of base kernels with which an appropriate hypothesis is determined on the training data. MKL has its flexibility featured by automated kernel learning, and also reflects the fact that typical learning problems often involve multiple and heterogeneous data sources. Target kernel is one of the most important parts of many MKL methods. These methods find the kernel weights by maximizing the similarity or alignment between weighted kernel and target kernel. The existing target kernels implement a global manner, which (1) defines the same target value for closer and farther sample pairs, and inappropriately neglects the variation of samples; (2) is independent of training data, and is hardly approximated by base kernels. As a result, maximizing the similarity to the global target kernel could make these pre-specified kernels less effectively utilized, further reducing the classification performance. In this paper, instead of defining a global target kernel, a localized target kernel is calculated for each sample pair from the training data, which is flexible and able to well handle the sample variations. A new target kernel named empirical target kernel is proposed in this research to implement this idea, and three corresponding algorithms are designed to efficiently utilize the proposed empirical target kernel. Experiments are conducted on four challenging MKL problems. The results show that our algorithms outperform other methods, verifying the effectiveness and superiority of the proposed methods.

Cited by 2

Multiple Operator-valued Kernel Learning

Hachem Kadri, Alain Rakotomamonjy, Francis Bach et al. · arXiv (Cornell University) · 2012

Positive definite operator-valued kernels generalize the well-known notion of\nreproducing kernels, and are naturally adapted to multi-output learning\nsituations. This paper addresses the problem of learning a finite linear\ncombination of infinite-dimensional operator-valued kernels which are suitable\nfor extending functional data analysis methods to nonlinear contexts. We study\nthis problem in the case of kernel ridge regression for functional responses\nwith an lr-norm constraint on the combination coefficients. The resulting\noptimization problem is more involved than those of multiple scalar-valued\nkernel learning since operator-valued kernels pose more technical and\ntheoretical issues. We propose a multiple operator-valued kernel learning\nalgorithm based on solving a system of linear operator equations by using a\nblock coordinatedescent procedure. We experimentally validate our approach on a\nfunctional regression task in the context of finger movement prediction in\nbrain-computer interfaces.\n

Cited by 7Open access

Veto-Consensus Multiple Kernel Learning

Yuxun Zhou, Ninghang Hu, Costas J. Spanos · Proceedings of the AAAI Conference on Artificial Intelligence · 2016

We propose Veto-Consensus Multiple Kernel Learning (VCMKL), a novel way of combining multiple kernels such that one class of samples is described by the logical intersection (consensus) of base kernelized decision rules, whereas the other classes by the union (veto) of their complements. The proposed configuration is a natural fit for domain description and learning with hidden subgroups. We first provide generalization risk bound in terms of the Rademacher complexity of the classifier, and then a large margin multi-ν learning objective with tunable training error bound is formulated. Seeing that the corresponding optimization is non-convex and existing methods severely suffer from local minima, we establish a new algorithm, namely Parametric Dual Descent Procedure (PDDP) that can approach global optimum with guarantees. The bases of PDDP are two theorems that reveal the global convexity and local explicitness of the parameterized dual optimum, for which a series of new techniques for parametric program have been developed. The proposed method is evaluated on extensive set of experiments, and the results show significant improvement over the state-of-the-art approaches.

Cited by 30Open access

Kernel-based multiple-instance learning

Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 2006

Kernel-based multiple-instance learning by Pak-Ming Cheung thesis 2006 x, 47 leaves : ill. ; 30 cm In recent years, the Multiple-Instance Learning (MIL) problem is becoming more and more popular in the machine learning community. Each training object (bag) of…Read more ›

Cited by 0

Non-sparse multiple kernel learning

Marius Kloft, Ulf Brefeld, Pavel Laskov et al. · 2008

Approaches to multiple kernel learning (MKL) employ ℓ1-norm constraints on the mixing coefficients to promote sparse kernel combinations. When features encode orthogonal characterizations of a problem, sparseness may lead to discarding useful information and may thus result in poor generalization performance. We study non-sparse multiple kernel learning by imposing an ℓ2-norm constraint on the mixing coefficients. Empirically, ℓ2-MKL proves robust against noisy and redundant feature sets and significantly improves the promoter detection rate compared to ℓ1-norm and canonical MKL on large scales.

Cited by 0

Sparsity in multiple kernel learning

Koltchinskii, Vladimir, Yuan, Ming · arXiv (Cornell University) · 2012

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical $L_2$ 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.

Cited by 0Open access

Absent Multiple Kernel Learning Algorithms

Xinwang Liu, Lei Wang, Xinzhong Zhu et al. · IEEE Transactions on Pattern Analysis and Machine Intelligence · 2019

Multiple kernel learning (MKL) has been intensively studied during the past decade. It optimally combines the multiple channels of each sample to improve classification performance. However, existing MKL algorithms cannot effectively handle the situation where some channels of the samples are missing, which is not uncommon in practical applications. This paper proposes three absent MKL (AMKL) algorithms to address this issue. Different from existing approaches where missing channels are first imputed and then a standard MKL algorithm is deployed on the imputed data, our algorithms directly classify each sample based on its observed channels, without performing imputation. Specifically, we define a margin for each sample in its own relevant space, a space corresponding to the observed channels of that sample. The proposed AMKL algorithms then maximize the minimum of all sample-based margins, and this leads to a difficult optimization problem. We first provide two two-step iterative algorithms to approximately solve this problem. After that, we show that this problem can be reformulated as a convex one by applying the representer theorem. This makes it readily be solved via existing convex optimization packages. In addition, we provide a generalization error bound to justify the proposed AMKL algorithms from a theoretical perspective. Extensive experiments are conducted on nine UCI and six MKL benchmark datasets to compare the proposed algorithms with existing imputation-based methods. As demonstrated, our algorithms achieve superior performance and the improvement is more significant with the increase of missing ratio.

Cited by 78