21st Ecmi Modelling Week Final Report Team 2 Data Mining in an Online Encyclopedia

We have surveyed and implemented different mathematical models to find the most relevant pages pertaining to some query for the case of an online encyclopedia. We have used the concepts of the webpage ranking to determine the ranking of the different topics and hence find the most important topics. The pages of an online encyclopedia are hyperlinked and this is represented by a directed graph and a corresponding matrix. The ranking of the relevant topics turns out to be an eigenvector problem. We show the existence and uniqueness of the solution and use both the power method and the linear system approach to solve this eigenvector problem. We also investigate the effect of α, a parameter used in the formation of the famous Google matrix from the adjacency matrix obtained from the directed graph, on the convergence rate of the power method. Rankings of the topics based on the three models have been implemented and obtained.