Abstract: An algorithm for fitting the entire regularization path of the support vector machine (SVM) was recently proposed by Hastie et al. (2004). It allows effective computation of solutions and greatly facilitates the choice of the regularization parameter that balances a trade-off between complexity of a solution and its fit to data. Extending the idea to more general setting of the multiclass case, we characterize the coefficient path of the multicategory SVM via the complementarity conditions for optimality. The extended algorithm provides a computational shortcut to attain the entire spectrum of solutions from the most regularized to the completely overfitted ones.
Key words and phrases: Classification, coefficient paths, Karush-Kuhn-Tucker condition, multicategory support vector machine.