Sufficient conditions are given for a classical dual exterior penalty function of a linear program to be independent of its penalty parameter. This ensures that an exact solution to the primal linear program can be obtained ...

We propose a novel privacy-preserving random kernel approximation based on a data matrix A ? Rm�n whose rows are divided into privately owned blocks. Each block of rows belongs to a different entity that is unwilling to ...

We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax ? |x| = b, where A is an n � n square matrix. The algorithm, which makes no ...

A fast Newton method is proposed for solving linear programs with a very large ( 106) number of constraints and a moderate ( 102) number of variables. Such linear programs occur in data mining and machine learning. ...

Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification problems as linear constraints in a linear program. The key tool in this incorporation is a theorem of the alternative for ...

We introduce a class of linear programs with constraints in the form of implications. Such linear programs arise in support vector machine classi cation, where in addition to explicit datasets to be classi ed, prior knowledge ...

A chunking procedure [2] utilized in [18] for linear classifiers is proposed here for nonlinear kernel classification of massive datasets. A highly accurate algorithm based on nonlinear support vector machines that ...

We show that the problem of minimizing the sum of arbitrary-norm real distances to misclassi ed points, from a pair of parallel bounding planes of a classi cation problem, divided by the margin (distance) be- tween the ...

The problem of tolerant data tting by a nonlinear surface, in- duced by a kernel-based support vector machine [24], is formulated as a linear program with fewer number of variables than that of other linear programming ...

Prior knowledge in the form of multiple polyhedral sets, each belonging to one of two categories, is introduced into a reformulation of a linear support vector machine classi er. The resulting formulation leads to a ...