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.
Publication types
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Research Support, Non-U.S. Gov't
MeSH terms
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Algorithms*
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Artificial Intelligence
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Data Interpretation, Statistical
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Humans
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Models, Theoretical*
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Pattern Recognition, Automated
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Support Vector Machine*
Grants and funding
This work was financed in part by the Research Council of Norway, grant 171125/V30, by the German Bundesministerium für Bildung und Forschung (BMBF) grant FKZ 01-IS07007A, and by the FP7-ICT Programme of the European Community, under the PASCAL2 Network of Excellence, ICT-216886. This work was also supported by the German Science Foundation (DFG MU 987/6-1, RA 1894/1-1) and by the World Class University Program through the National Research Foundation of Korea funded by the Ministry of Education, Science, and Technology, under Grant R31-10008. Sören Sonnenburg acknowledges financial support by the German Research Foundation (DFG) under the grant MU 987/6-1 and RA 1894/1-1; Marius Kloft acknowledges a research scholarship by the German Academic Exchange Service (DAAD). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.