Multidimensional splines with infinite number of knots as SVM kernels

Improving the kernel regularized least squares method for small-sample regression

“…In Ref. [7], a multidimensional spline kernel was proposed as the multiplication of one-dimensional kernels (11) corresponding to each dimension of the data. 1 The authors also propose normalizing it to mitigate (but not avoid) numerical difficulties.…”

“…[7], the kernel in Expression (12) was experimentally evaluated only on SVM classification. In this work, we evaluate it on KRLS regression.…”

“…When combined with cross-validation and small training sets, RBF kernels have a great potential for overfitting. Recently, there has been a renewed interest in developing kernels with less potential for overfitting while retaining a good approximation property [7]. The kernel regularized least squares method is computationally efficient in small sample situations, although it may be rendered ineffective by the issues plaguing the popular combination of cross-validation and RBF kernels.…”

“…The kernel regularized least squares method is computationally efficient in small sample situations, although it may be rendered ineffective by the issues plaguing the popular combination of cross-validation and RBF kernels. Having that in mind, in this paper we follow [7] and investigate the use of splines as a safer choice to compose a multidimensional kernel function. We go one step further in this work and propose the use of additive spline kernels instead of multiplicative ones.…”

Online sequential prediction of bearings imbalanced fault diagnosis by extreme learning machine

“…The first point is to choose a proper baseline algorithm for online sequential setting, and the second is to reconstruct a new balanced dataset with the raw distribution of online sequential data unchanged. As a classical learning algorithm SVM [12] is widely applied. However, it mainly tackles the small-scale learning problem, and is computationally expensive when facing large-scale data, especially in sequential learning settings.…”