GenSVM: A Generalized Multiclass Support Vector Machine. 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 called GenSVM is proposed, which can be used for classification problems where the number of classes K is larger than or equal to 2. In the proposed method, classification boundaries are constructed in a K - 1 dimensional space. The method is based on a convex loss function, which is flexible due to several different weightings. An iterative majorization algorithm is derived that solves the optimization problem without the need of a dual formulation. The method is compared to seven other multiclass SVM approaches on a large number of datasets. 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