Optimization Methods in Massive Data Sets

P. S. Bradley, O. L. Mangasarian, and D. R. Musicant

We describe the role of generalized support vector machines in separating massive and complex data using arbitrary nonlinear kernels. Feature selection that improves generalization is implemented via an effective procedure that utilizes a polyhedral norm or a concave function minimization. Massive data is separated using a linear programming chunking algorithm as well as a successive overrelaxation algorithm, each of which is capable of processing data with millions of points.

Keywords: Vector machines, Nonlinear kernels, Polyhedral norm, Concave function minimization, Linear and quadratic programming, Linear separability, Lagrange multipliers.