The two classical steps of image or video classification are: image signature extraction and assignment of a class based on this image signature. The class assignment rule can be learned from a training set composed of sample images manually classified by experts. This is known as supervised statistical learning. The well-known Support Vector Machine (SVM) learning method was designed for two classes. Among the proposed extensions to multiclass (three classes or more), the one-versus-one and one-versus-all approaches are the most popular ones. This work presents an alternative approach to extending the original SVM method to multiclass. A tree of SVMs is built using a recursive learning strategy, achieving a linear worst-case complexity in terms of number of classes for classification. During learning, at each node of the tree, a bi-partition of the current set of classes is determined to optimally separate the current classification problem into two sub-problems. Rather than relying on an exhaustive search among all possible subsets of classes, the partition is obtained by building a graph representing the current problem and looking for a minimum cut of it. The proposed method is applied to classification of endomicroscopic videos and compared to classical multiclass approaches.