Sergei Silvestrov

Xiaomin Qi, Sergei Silvestrov, Talat Nazir

In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide various examples to support our results.

Christopher Engström, Sergei Silvestrov

In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving the linear system. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.