Abstract

This thesis deals with a particular problem of binary classification case in the framework of support vector machine. The case displays observations from two classes, and uniformly distributed on a space so that linear separation by a hyperplane is only possible in tiny cubes (or rectangles) of that space. The general approach to classification in the input space is then extended with the design of a new ad hoc kernel that is expected to perform better in the feature
space than the most common kernels found in the literature. Theoretical discussions to support the validity, the convergence to Bayes classifier of the new designed kernel and its application to simulated dataset will be our core
contribution to one a way we can approach a classification problem.
In order to make our way to this goal and grasp the necessary mathematical tools and concepts in support vector machine, a literature review is provided
with some applications in the first four sections of this document. The last and fifth section brings an answer the question that motivates this research.