Multiclass Classification with Multi-Prototype Support Vector Machines

Winner-take-all multiclass classifiers are built on the top of a set of prototypes each representing one of the available classes. A pattern is then classified with the label associated to the most 'similar' prototype. Recent proposal of SVM extensions to multiclass can be considered instances of the same strategy with one prototype per class. The multi-prototype SVM proposed in this paper extends multiclass SVM to multiple prototypes per class. It allows to combine several vectors in a principled way to obtain large margin decision functions. For this problem, we give a compact constrained quadratic formulation and we propose a greedy optimization algorithm able to find locally optimal solutions for the non convex objective function. This algorithm proceeds by reducing the overall problem into a series of simpler convex problems. For the solution of these reduced problems an efficient optimization algorithm is proposed. A number of pattern selection strategies are then discussed to speed-up the optimization process. In addition, given the combinatorial nature of the overall problem, stochastic search strategies are suggested to escape from local minima which are not globally optimal. Finally, we report experiments on a number of datasets. The performance obtained using few simple linear prototypes is comparable to that obtained by state-of-the-art kernel-based methods but with a significant reduction (of one or two orders) in response time.