## GenSVM: A Generalized Multiclass Support Vector Machine

*Gerrit J.J. van den Burg, Patrick J.F. Groenen*; 17(225):1−42, 2016.

### Abstract

Traditional extensions of the binary support vector machine
(SVM) to multiclass problems are either heuristics or require
solving a large dual optimization problem. Here, a generalized
multiclass SVM is proposed called GenSVM. In this method
classification boundaries for a $K$-class problem are
constructed in a $(K-1)$-dimensional space using a simplex
encoding. Additionally, several different weightings of the
misclassification errors are incorporated in the loss function,
such that it generalizes three existing multiclass SVMs through
a single optimization problem. An iterative majorization
algorithm is derived that solves the optimization problem
without the need of a dual formulation. This algorithm has the
advantage that it can use warm starts during cross validation
and during a grid search, which significantly speeds up the
training phase. Rigorous numerical experiments compare linear
GenSVM with seven existing multiclass SVMs on both small and
large data sets. These comparisons show that the proposed method
is competitive with existing methods in both predictive accuracy
and training time, and that it significantly outperforms several
existing methods on these criteria.

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