Jennifer G. DyProfessor
Department of Electrical and Computer Engineering
Support Vector Machine:
Support vector machines (SVM) were originally cast for two-class problems; however, several real applications deal with multiple classes. We developed algorithms for extending support vector machines to multi-class problems. Another limitation of SVMs, and machine learning algorithms in general, was that they assume that data samples are independent. We developed algorithms on batch-wise classification applied to computer aided diagnosis problems. This work is in collaboration with Glenn Fung, Balaji Krishnapuram, and Bharat Rao of Siemens Medical Solutions. We re-designed logistic regression and SVMs to incorporate dependencies among samples within a batch during training and testing. SVM is a supervised learning algorithm, however manual labeling is expensive. We also formulated a semi-supervised SVM classifier that took advantage of spatial information and enforced smoothness constraints to leverage the unlabeled data. We proposed different objective function formulations in an inductive setting for various norms (1-, 2-, and infinity-norm). The 1-norm formulation became a linear programming problem with the advantage of generating sparse solutions. The 2-norm resulted in an unconstrained quadratic problem for which solutions can be obtained by solving a simple system of linear equations.
Publications in Support Vector Machine:
V. Vural, G. Fung, R. Rosales, J. G. Dy, "Multi-Class Classifiers and their Underlying Shared Structure," Proceeding s of the International Joint Conferences on Artificial Intelligence (IJCAI), pp. 1267-1272, 2009. (pdf version).
V. Vural, G. Fung, B. Krishnapuram, J. G. Dy, and B. Rao, "Using Local Dependencies within Batches to Improve Large Margin Classifiers," Journal of Machine Learning Research, 10(Feb):183--206, 2009. (pdf version).
V. Vural, G. Fung, J. G. Dy, and B. Rao, "Fast Semi-Supervised Classifiers Using A-priori Metric Information," Optimization Methods and Software on Mathematical Programming in Machine Learning and Data Mining, to appear.
V. Vural, G. Fung, B. Krishnapuram, J. Dy, and B. Rao, "Batch Classification with Applications in Computer Aided Diagnosis," Proceedings of the Seventeenth European Conference on Machine Learning, vol. 4212, p. 449-460, Berlin, Germany, Sept. 18-22, 2006. (pdf version).
V. Vural and J. G. Dy, "A Hierarchical Method for Multi-Class Support Vector Machines," Proceedings of the 21st International Conference on Machine Learning, pages 831-838, July, 2004, Banff, Alberta, Canada. (pdf version).
The student working on this project is: