In Support Vector Machines (SVM's), a non-linear model is estimated based on solving a Quadratic Programming (QP) problem. The quadratic cost function consists of a maximum likelihood cost term with constant variance and a regularization term. By specifying a diierence inclusion on the noise variance model, the maximum likelihood term is adopted for the case of heteroskedastic noise, which aris...

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions of a single quadratic form V → R in case the module V is free. Any (semi)module over a semiring gives rise to what we call its minimal ordering, which is a partial order iff the semiring is “upper bound.” Any polynomial map q (or quadratic...

The support vector machine (SVM) is a new and promising technique for pattern recognition. It requires the solution of a large dense quadratic programming problem. Traditional optimization methods cannot be directly applied due to memory restrictions. Up to now, very few methods can handle the memory problem and an important one is the "decomposition method." However, there is no convergence pr...

Resum Typically, the cash management literature focuses on optimizing cost, hence neglecting risk analysis. In this chapter, we address the cash management problem from a multiobjective perspective by considering not only the cost but also the risk of cash policies. We propose novel measures to incorporate risk analysis as an additional goal in cash management. Next, we rely on compromise progr...

By setting apart the two functions of a support vector machine: separation of points by a nonlinear surface in the original space of patterns, and maximizing the distance between separating planes in a higher dimensional space, we are able to deene indeenite, possibly discontinuous, kernels, not necessarily inner product ones, that generate highly nonlin-ear separating surfaces. Maximizing the ...

Resum Typically, the cash management literature focuses on optimizing cost, hence neglecting risk analysis. In this chapter, we address the cash management problem from a multiobjective perspective by considering not only the cost but also the risk of cash policies. We propose novel measures to incorporate risk analysis as an additional goal in cash management. Next, we rely on compromise progr...

Learning from positive and unlabeled examples (PU learning) is a special case of semi-supervised binary classification. The key feature of PU learning is that there is no labeled negative training data, which makes the traditional classification techniques inapplicable. Similar to the idea of Biased-SVM which is one of the most famous classifier, a biased least squares support vector machine cl...

Support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm classificat...

Twin support vector machine (TWSVM) was initially designed for binary classification. However, real-world problems often require the discrimination more than two categories. To tackle multi-class classification problem, in this paper, a multiple least squares twin support vector machine is proposed. Our Multi-LSTSVM solves K quadratic programming problems (QPPs) to obtain K hyperplanes, each pr...

Biosignal recordings are useful for extracting information about the functional state of an organism. For this reason, such recordings are widely used as tools for supporting medical decision. Nevertheless, reaching a diagnostic decision based on biosignal recordings normally requires analysis of long data records by specialized medical personnel. In several cases, specialized medical attention...