Robust optimization in support-vector machines and applications.

Abstract

The main objective of this work is to investigate the robustness and stability of the behavior of the solutions of the Support Vector Machines model under bounded perturbations of the input data in the feature space. The resulting optimization model is equivalent to a second order cone-programming problem. Specifically those techniques are used both for pattern classification and regression analysis.

In the theory of support vector machines learning, it is assumed that the data are precise. However, real world data have uncertainties both in their inputs and outputs. Robust optimization techniques recently have attracted a lot of researchers who are interested in finding solutions to problems dealing with uncertainty, erroneous, or incomplete data. In this dissertation, robust optimization techniques are investigated in the support vector machine approach, with uncertainties in the data in feature space.

Computational results are provided both for synthetic problems such as the AND function and the XOR and real world problems such as the echocardiogram and the breast cancer in the classification case. Also in the regression analysis case, a synthetic problem was created to illustrate the stability of the resulting model. Real world problems (e.g lynx data) were examined. In both classification and regression cases, the obtained results were consistent with the goal of this dissertation.