An efficient multiple kernel learning in reproducing kernel Hilbert spaces (RKHS)

Abstract

The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel with a Hilbert space of functions. Recently, reproducing kernel Hilbert space (RKHS) has come wildly alive in the pattern recognition and machine learning community. In this paper, we propose a novel method named multiple kernel learning with reproducing property (MKLRP) to achieve some classification tasks. The MKLRP consists of two major steps. First, we find the basic solution of a generalized differential operator by delta function, and prove this basic solution is a new specific reproducing kernel called H 2 -reproducing kernel (HRK) in RKHS. Second, in RKHS, we prove that the HRK satisfies the condition of Mercer kernel. Furthermore, a novel specific multiple kernel learning (MKL) called MKLRP, which is based on reproducing kernel is proposed. We perform an extensive experimental evaluation on synthetic and real-world data, which shows the effectiveness of the proposed approach.

Kernel Matrix-Based Heuristic Multiple Kernel Learning

“…For completeness: SpicyMKL scales very well as the number of kernels increases and presents an iterative optimization strategy; GMKL extends traditional MKL formulations to generalized kernel combinations subject to regularization on the kernel parameters; and MRMKL put forth a closed-form solution for kernel weight assignment with a guarantee of global convergence. Xu et al put forth an efficient approach to MKL in the RKHS in [20], which identifies a new kernel, H 2 -reproducing kernel (HRK), in RKHS and satisfies Mercer's conditions. In [21], Banerjee and Das proposed multi-feature kernel learning (MFKL), a weight assignment technique that seeks to identify the optimal combination of feature kernels for a given classification task based upon Eigen-domain transformation in the RKHS.…”

A New L₁ Multi-Kernel Learning Support Vector Regression Ensemble Algorithm With AdaBoost

“…The criteria of mean absolute error (MAE) and root mean square error (RMSE) [34] are employed to validate the effectiveness of the models in this paper.…”

On the solutions of electrohydrodynamic flow with fractional differential equations by reproducing kernel method

“…Many problems such as population models and complex dynamics have been solved in the reproducing kernel spaces [7,17,26,27]. For more details of this method see [1,2,5,8,15,16,19,25,28,29].…”