Christopher Engström

PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph

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 corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.

PageRank, Connecting a Line of Nodes with a Complete Graph

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most releva ...

Generalisation of the Damping Factor in PageRank for Weighted Networks

In this article we will look at the PageRank algorithm used to rank nodes in a network. While the method was originally used by Brin and Page to rank home pages in order of “importance”, since then many similar methods have been used for other networks such as financial or P2P networks. We will work with a non-normalised version of the usual PageRank definition which we will then generalise to enable better options, such as adapting the method or allowing more types of data. We will show what kind of effects the new options creates using examples as well as giving some thoughts on what it can be used for. We will also take a brief look at how adding new connections between otherwise unconnected networks can change the ranking.

Term Ranking Adaptation to the Domain: Genetic Algorithm-Based Optimisation of the C-Value

Term extraction methods based on linguistic rules have been proposed to help the terminology building from corpora. As they face the difficulty of identifying the relevant terms among the noun phrases extracted, statistical measures have been proposed. However, the term selection results may depend on corpus and strong assumptions reflecting specific terminological practice. We tackle this problem by proposing a parametrised C-Value which optimally considers the length and the syntactic roles of the nested terms thanks to a genetic algorithm. We compare its impact on the ranking of terms extracted from three corpora. Results show average precision increased by 9% above the frequency-based ranking and by 12% above the C-Value-based ranking.

Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms

In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of ...

Calculating PageRank in a Changing Network With Added or Removed Edges

PageRank was initially developed by S. Brinn and L. Page in 1998 to rank homepages on the Internet using the stationary distribution of a Markov chain created using the web graph. Due to the large ...

Graph Centrality Based Prediction of Cancer Genes

Current cancer therapies including surgery, radiotherapy and chemotherapy are often plagued by high failure rates. Designing more targeted and personalized treatment strategies requires a detailed understanding of druggable tumor driver genes. As a consequence, the detection of cancer driver genes has evolved to a critical scientific field integrating both high-throughput experimental screens as well as computational and statistical strategies. Among such approaches, network based prediction tools have recently been accentuated and received major focus due to their potential to model various aspects of the role of cancer genes in a biological system. In this chapter, we focus on how graph centralities obtained from biological networks have been used to predict cancer genes. Specifically, we start by discussing the current problems in cancer therapy and the reasoning behind using network based cancer gene prediction, followed by an outline of biological networks, their generation and properties. Finally, we review major concepts, recent results as well as future challenges regarding the use of graph centralities in cancer gene prediction.