title: A scatter-based prototype framework and multi-class extension of support vector machines.
abstract: We provide a novel interpretation of the dual of support vector machines (SVMs) in terms of scatter with respect to class prototypes and their mean. As a key contribution, we extend this framework to multiple classes, providing a new joint Scatter SVM algorithm, at the level of its binary counterpart in the number of optimization variables. This enables us to implement computationally efficient solvers based on sequential minimal and chunking optimization. As a further contribution, the primal problem formulation is developed in terms of regularized risk minimization and the hinge loss, revealing the score function to be used in the actual classification of test patterns. We investigate Scatter SVM properties related to generalization ability, computational efficiency, sparsity and sensitivity maps, and report promising results.
authors.affiliation: Department of Physics and Technology, University of Tromsø, Tromsø, Norway. robert.jenssen@uit.no
authors.forename: Robert
authors.initials: R
authors.lastname: Jenssen
authors.forename: Marius
authors.initials: M
authors.lastname: Kloft
authors.forename: Alexander
authors.initials: A
authors.lastname: Zien
authors.forename: Sören
authors.initials: S
authors.lastname: Sonnenburg
authors.forename: Klaus-Robert
authors.initials: KR
authors.lastname: Müller
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003627:Data Interpretation, Statistical; D006801:Humans; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated; D060388:Support Vector Machine