Kernel functions are used in support vector machines (SVMs) to compute dot product in a higher dimensional space. The performance of classification depends on the chosen kernel. Each kernel function is suitable for some tasks. In order to obtain a more flexible kernel function, a family of RBF kernels is proposed. Multi-scale RBF kernels are combined by including weights. These kernels allow be...

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is critical method used find global optimum of black-box functions. Kernel play an important role shaping estimated functi...

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank, and in practice, these methods are effective even for high-dimensional datasets. The practical success has elicited the theoretical analysis of the function rank in this paper, which is an upper bound of...

To enhance the accuracy of protein–protein interaction function prediction, a 2-order graphic neighbor information feature extraction method based on undirected simple graph is proposed in this paper , which extends the 1-order graphic neighbor featureextraction method. And the chi-square test statistical method is also involved in feature combination. To demonstrate the effectiveness of our 2-...

The local radial basis function (RBF) interpolation method enables very large-scale data sets to be handled efficiently, overcoming the drawbacks of global interpolation which produces highly ill-conditioned linear systems. Whereas there have been intensive studies on the accuracy of global RBF interpolation, the error analysis of local RBF interpolation is much less investigated. In this regar...

Support vector regression (SVR) has been regarded as a state-of-the-art method for approximation and regression. The importance of kernel function, which is so-called admissible support vector kernel (SV kernel) in SVR, has motivated many studies on its composition. The Gaussian kernel (RBF) is regarded as a “best” choice of SV kernel used by non-expert in SVR, whereas there is no evidence, exc...

Convolutional Radial Basis Function (RBF) networks are introduced for smoothing out irregularly sampled signals. Our proposed technique involves training a RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need t...

The use of kernels is a key factor in the success of many classification algorithms by allowing nonlinear decision surfaces. Radial basis function (RBF) kernels are commonly used but often associated with dense Gram matrices. We consider a mathematical operator to sparsify any RBF kernel systematically, yielding a kernel with a compact support and sparse Gram matrix. Having many zero elements i...

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or polynomial kernels, there are also specific kernels tailored to consider structure in the data for similarity assessment. In this article, we will capture structure...

Biometric systems can be used for the identification or verification of humans based on their physiological or behavioral features. In these systems the biometric characteristics such as fingerprints, palm-print, iris or speech can be recorded and are compared with the samples for the identification or verification. Multimodal biometrics is more accurate and solves spoof attacks than the single...