Applied Modeling Techniques and Data Analysis 1 : Computational Data Analysis Methods and Tools

Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- PART 1: Computational Data Analysis -- 1 A Variant of Updating PageRank in Evolving Tree Graphs -- 1.1. Introduction -- 1.2. Notations and definitions -- 1.3. Updating the transition matrix -- 1.4. Updating the PageRank of a tree graph -- 1.4.1. Updating the PageRank of tree graph when a batch of edges changes -- 1.4.2. An example of updating the PageRank of a tree -- 1.5. Maintaining the levels of vertices in a changing tree graph -- 1.6. Conclusion -- 1.7. Acknowledgments -- 1.8. References -- 2 Nonlinearly Perturbed Markov Chains and Information Networks -- 2.1. Introduction -- 2.2. Stationary distributions for Markov chains with damping component -- 2.2.1. Stationary distributions for Markov chains with damping component -- 2.2.2. The stationary distribution of the Markov chain X0,n -- 2.3. A perturbation analysis for stationary distributions of Markov chains with damping component -- 2.3.1. Continuity property for stationary probabilities -- 2.3.2. Rate of convergence for stationary distributions -- 2.3.3. Asymptotic expansions for stationary distributions -- 2.3.4. Results of numerical experiments -- 2.4. Coupling and ergodic theorems for perturbed Markov chains with damping component -- 2.4.1. Coupling for regularly perturbed Markov chains with damping component -- 2.4.2. Coupling for singularly perturbed Markov chains with damping component -- 2.4.3. Ergodic theorems for perturbed Markov chains with damping component in the triangular array mode -- 2.4.4. Numerical examples -- 2.5. Acknowledgments -- 2.6. References -- 3 PageRank and Perturbed Markov Chains -- 3.1. Introduction -- 3.2. PageRank of the first-order perturbed Markov chain -- 3.3. PageRank of the second-order perturbed Markov chain.