This paper studies the following problem: Given an SVM (kernel)based binary classifier C as a black-box oracle, how much can we learn of its internal working by querying it? Specifically, we assume the feature space R is known and the kernel machine has m support vectors such that d > m (or d >> m), and in addition, the classifier C is laconic in the sense that for a feature vector, it only pro...

This Research presents the effects of interaction between various Kernel functions and different Feature Selection Techniques for improving the learning capability of Support Vector Machine (SVM) in detecting email spams. The interaction of four Kernel functions of SVM i. e. "Normalised Polynomial Kernel (NP)", "Polynomial Kernel (PK)", "Radial Basis Function Kernel (RB...

The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...

The aim of this article is to present the potential of Kernel Principal Component Analysis (Kernel PCA) in the field of vision based robot localization. Using Kernel PCA we can extract features from the visual scene of a mobile robot. The analysis is applied only to local features so as to guarantee better computational performance as well as translation invariance. Compared with the classical ...

The presence of fluctuations and nonlinear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise....

We illustrate a relationship between reproducing kernel spaces and orthogonal polynomials via a general structure theorem. The Christofell–Darboux formula emerges as a limit case. c © 1998 Elsevier Science B.V. All rights reserved.

Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions jx1jã1 Ð Ð Ð jxdjãd on the unit sphere Sd 1 in Rd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.

A key result in the field of kernelization, a subfield of parameterized complexity, states that the classic Disjoint Cycle Packing problem, i.e. finding k vertex disjoint cycles in a given graph G, admits no polynomial kernel unless NP ⊆ coNP/poly. However, very little is known about this problem beyond the aforementioned kernelization lower bound (within the parameterized complexity framework)...

This paper proposes an efficient online method that trains a classifier with many conjunctive features. We employ kernel computation called kernel slicing, which explicitly considers conjunctions among frequent features in computing the polynomial kernel, to combine the merits of linear and kernel-based training. To improve the scalability of this training, we reuse the temporal margins of part...

Abstract. We obtain expressions for the Christoffel–Darboux kernel of antisymmetric multivariable orthogonal polynomials as determinants and pfaffians. These kernels include correlation functions of orthogonal polynomial ensembles (with β = 2). In subsequent work, our results are applied in combinatorics (enumeration of marked shifted tableaux) and number theory (representation of integers as s...