An active set strategy is applied to the dual of a simple reformulation of the standard quadratic program of a linear support vector machine. This application generates a fast new dual algorithm that consists of solving a finite number of linear equations, with a typically large dimensionality equal to the number of points to be classified. However, by making novel use of the Sherman-Morrison-Woodbury formula, a much smaller matrix of the order of the original input space is inverted at each step. Thus, a problem with a 32-dimensional input space and 7 million points required inverting positive definite symmetric matrices of size 33 × 33 with a total running time of 96 minutes on a 400 MHz Pentium II. The algorithm requires no specialized quadratic or linear programming code, but merely a linear equation solver which is publicly available.
['Olvi L. Mangasarian', 'David R. Musicant']
Active Support Vector Machine Classification