MATHEMATICAL PROGRAMMING APPLICATIONS IN MACHINE LEARNING by RESHMA KHEMCHANDANI

This thesis deals with the development of novel algorithms for the problems of binary classification and regression. These algorithms are in the support vector machines framework, which consists of constructing a separating surface that can discriminate between points of one class from the other, or a regressor which tries to fit the given data. These algorithms are generally very efficient and robust. All the proposed formulations result into the mathematical programming problems such as linear programming, quadratic programming or certain specialized convex programming problems e.g., semi-definite programming and second order cone programming. A novel idea is the introduction of Twin Support Vector Machines (TWSVMs) for handling large datasets. Twin support vector machines aim at generating two non-parallel planes, such that each plane is closer to one of the two classes and is as far as possible from the other. In TWSVMs, we solve a pair of quadratic programming problems (QPPs), whereas in Support Vector Machines (SVMs), we solve a single QPP. Thus, TWSVM is almost four times faster as compared to conventional SVMs. Incremental TWSVMs have been proposed for reducing memory and time requirements of the learning algorithm when dealing with large datasets. Further, fuzzy membership is introduced in Incremental TWSVM which allows us to improve the overall error rate, since each of the two problems being solved can be associated with a different set of fuzzy memberships, thereby