One of the central problems in the study of Support vector machine (SVM) is kernel selection, that’s based essentially on the problem of choosing a kernel function for a particular task and dataset. By contradiction to other machine learning algorithms, SVM focuses on maximizing the generalisation ability, which depends on the empirical risk and the complexity of the machine. In the following p...

We show that the k-Dominating Set problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude Ki,j as a subgraph, for any fixed i, j ≥ 1. This strictly includes every class of graphs for which this problem has been previously shown to have FPT algorithms and/or polynomial kernels. In particular, our result implies that the problem restricted to bo...

We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix A ∈ Rm×n, the kernel problem requires a positive vector in the kernel of A, and the image problem requires a positive vector in the image of A. Both algorithms iterate between simple first order steps and rescaling steps. These rescalings steps improve natural geometric potentials in the domain ...

ABSTRACT. We consider the nearest-neighbor simple random walk on Zd, d ≥ 4, driven by a field of i.i.d. random nearest-neighbor conductances ωxy ∈ [0, 1]. Our aim is to derive estimates of the heat-kernel decay in a case where ellipticity assumption is absent. We consider the case of independant conductances with polynomial tail near 0 and obtain for almost every environment an anomalous lower ...

Magnetic Resonance (MR) Imaging has come up as widely accepted and revolutionary innovation in field of medical science and brain imaging especially. A new method is proposed here for MRI brain image classification using Polynomial Kernel Principle Component Analysis (KPCA) with Neural Network. In this paper, we are having various stages namely pre-processing, feature extraction, feature reduct...

small area estimation is a technique used to estimate parameters of subpopulations with small sample sizes.  small area estimation is needed  in obtaining information on a small area, such as sub-district or village.  generally, in some cases, small area estimation uses parametric modeling.  but in fact, a lot of models have no linear relationship between the small area average and the covariat...

In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic assumptions. We build upon recent results ...

We establish the asymptotical equivalence between L-spline smoothing and kernel estimation. The equivalent kernel is used to derive the asymptotic mean squared error of the L-smoothing spline estimator. The paper extends the corresponding results for polynomial spline smoothing.

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for β = 2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I ⊂ R can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for β = 2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I ⊂ R can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.