For many years now, there is a growing interest around ROC curve for characterizing machine learning performances. This is particularly due to the fact that in real-world problems misclassification costs are not known and thus, ROC curve and related metrics such as the Area Under ROC curve (AUC) can be a more meaningful performance measures. In this paper, we propose a SVMs based algorithm for ...

Support vector machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed support vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularizat...

We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the non...

In this paper, a fast bounded parametric margin  -support vector machine (BP- SVM) for classification is proposed. Different from the parametric margin  -support vector machine (par- -SVM), the BP- -SVM maximizes a bounded parametric margin, and consequently the successive overrelaxation (SOR) technique could be used to solve our dual problem as opposed solving the standard quadratic progr...

A new smoothing strategy for solving 2-support vector regression (2-SVR), tolerating a small error in fitting a given dataset linearly or nonlinearly, is proposed in this paper. Conventionally, 2-SVR is formulated as a constrained minimization problem, namely a convex quadratic programming problem. We apply the smoothing techniques that have been used for solving the support vector machine for ...

In least squares support vector machine (LS-SVM) classi-ers the original SVM formulation of Vapnik is modiied by considering equalit y constraints within a form of ridge regression instead of inequality constraints. As a result the solution follows from solving a set of linear equations instead of a quadratic programming problem. Ho wever, a d r a wback is that sparseness is lost in the LS-SVM ...

Support Vector Machines are a family of algorithms for the analysis of data based on convex Quadratic Programming. We derive randomized algorithms for training SVMs, based on a variation of Random Sampling Techniques; these have been successfully used for similar problems. We formally prove an upper bound on the expected running time which is quasilinear with respect to the number of data point...

A generalized Persidskii-like theorem is derived and shown to be applicable to the stability analysis of a class of gradient dynamical systems with discontinuous right hand sides. These dynamical systems arise from the steepest descent technique applied to a variety of problems suitably formulated as constrained minimization problems. The problems susceptible to this approach include linear pro...

In this paper, we formulate a least squares version of the one-class support vector fuzzy machine (LS one-class SVFM) which is combined with the fuzzy set theory. The parameters in the proposed algorithm, such as weight vector and bias term, are fuzzy numbers. Our model only needs to solve a system of linear equations, instead of a complex quadratic programming problem (QPP) solved in one-class...

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...