Kernel methods are used to tackle a variety of learning tasks including classification, regression, ranking, clustering, and dimensionality reduction. The appropriate choice of a kernel is often left to the user. But, poor selections may lead to a sub-optimal performance. Instead, sample points can be used to learn a kernel function appropriate for the task by selecting one out of a family of k...

Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as least-squares, Yule–Walker and Burg, as well as Durbin–Watson statistics, provide important examples of such ratios. The cumulative distribution function (c.d.f...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

In order to deal with known limitations of the hard margin support vector machine (SVM) for binary classification — such as overfitting and the fact that some data sets are not linearly separable —, a soft margin approach has been proposed in literature [2, 4, 5]. The soft margin SVM allows training data to be misclassified to a certain extent, by introducing slack variables and penalizing the ...

This paper presents a new formulation of multi-instance learning as maximum margin problem, which is an extension of the standard C-support vector classification. For linear classification, this extension leads to, instead of a mixed integer quadratic programming, a continuous optimization problem, where the objective function is convex quadratic and the constraints are either linear or bilinea...

We propose a new algorithm, a reeective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indeenite) quadratic function, for which a local minimizer subject to bounds is required, and is particularily suitable for the large-scale problem. Our new method exhibits strong conver...