An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. This leads to the minimization of an unconstrained di erentiable convex ...

The multiple instance classification problem [6,2,12] is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite dimensional (noninteger) real space subject to linear and bilinear ...

A highly accurate algorithm, based on support vector machines formulated as linear programs [13, 1], is proposed here as a completely unconstrained minimization problem [15]. Combined with a chunking procedure [2] this ...

Slice models are collections of mathematical programs with the same structure but di erent data. Examples of slice models appear in Data Envelopment Analysis, where they are used to evaluate e ciency, and cross-validation, ...

An implicit Lagrangian [19] formulation of a support vector machine classi er that led to a highly e ective iterative scheme [18] is solved here by a nite Newton method. The proposed method, which is extremely fast and ...

An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset ...

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 ...

An e ective method for selecting features in clustering unlabeled data is proposed based on changing the objective function of the standard k-median clustering algorithm. The change consists of perturbing the objective ...

Using a recently introduced proximal support vector ma- chine classi er [4], a very fast and simple incremental support vector machine (SVM) classi er is proposed which is capable of modifying an existing linear classi ...

We outline a new approach for radiosurgery treatment planning, based on solving a series of optimization problems. We consider a speci c treat- ment planning problem for a specialized device known as the Gamma Knife, ...