In this paper, we present recent solutions to the problem of approximating functions by polynomials for reducing in a substantial manner two well-known phenomena: Runge and Gibbs. The main idea is avoid resampling function or data relies on mapped “fake” nodes approach. This technique turns out be effective stability effect also presence discontinuities almost cancelling Gibbs phenomenon. very ...

The Remaining Useful Life (RUL) of Lithium-ion (Li-ion) batteries estimation is very important for the intelligent Battery Management System (BMS). With the arrival of the era of big data, data mining technology is becoming more and more mature, and the Li-ion batteries RUL estimation based on data-driven prognostics is more accurate. However, the Support Vector Machine (SVM) applying to predic...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

This paper presents a preliminary exploration showing the surprising effect of extreme parameter values used by Support Vector Machine (SVM) classifiers for identifying objects in images. The Radial Basis Function (RBF) kernel used with SVM classifiers is considered to be a state-of-the-art approach in visual object classification. Standard tuning approaches apply a relative narrow window of va...

We propose a new method for constructing hyperkenels and define two promising special cases that can be computed in closed form. These we call the Gaussian and Wishart hyperkernels. The former is especially attractive in that it has an interpretable regularization scheme reminiscent of that of the Gaussian RBF kernel. We discuss how kernel learning can be used not just for improving the perform...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and makes no assumptions regarding data normalization. The prediction speed of a...

As it is not clear how to choose an appropriate kernel function for a specific learning problem, this paper examines the performance of three kernel functions with varied parameters for online handwritten character recognition. The three kernel functions evaluated are the polynomial, complete polynomial, and radial basis functions. Results show that the three functions perform comparably with t...

Flow number of asphalt–aggregate mixtures as an explanatory factor has been proposed in order to assess the rutting potential of asphalt mixtures. This study proposes a multiple–kernel based support vector machine (MK–SVM) approach for modeling of flow number of asphalt mixtures. The MK–SVM approach consists of weighted least squares–support vector machine (WLS–SVM) integrating two kernel funct...