Analysis of Markov Influence Graphs

References

• Abbas K, Berkhout J, Heidergott BF (2016) A critical account of perturbation analysis of Markov chains. Markov Processes Related Fields. 22(2):227–266.Google Scholar
• Agharkar P, Patel R, Bullo F (2014) Robotic surveillance and Markov chains with minimal first passage time. 53rd IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 6603–6608.Crossref, Google Scholar
• Barabási A, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512.Crossref, Google Scholar
• Berkhout J (2016) Google’s PageRank algorithm for ranking nodes in general networks. Proc. 13th Internat. Workshop Discrete Event Systems (WODES 2016) (IEEE, Piscataway, NJ), 153–158.Crossref, Google Scholar
• Berkhout J, Heidergott BF (2019) The jump start power method: A new approach for computing the ergodic projector of a finite Markov chain. J. Sci. Comput. 78(3):1691-1723.Crossref, Google Scholar
• Berkhout J, Heidergott BF (2017) Ranking nodes in general networks: A Markov multi-chain approach. Discrete Event Dyn. Systems 28(1):3–33.Crossref, Google Scholar
• Borkar VS, Ejov V, Filar JA, Nguyen GT (2012) Hamiltonian Cycle Problem and Markov Chains (Springer-Verlag, New York).Crossref, Google Scholar
• Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput. Networks ISDN Systems 30(1-7):107–117.Crossref, Google Scholar
• Catral M, Kirkland S, Neumann M, Sze NS (2010) The Kemeny constant for finite homogeneous ergodic Markov chains. J. Sci. Comput. 45(1-3):151–166.Crossref, Google Scholar
• Coolen-Schrijner P, van Doorn EA (2002) The deviation matrix of a continuous-time Markov chain. Probab. Engrg. Inform. Sci. 16(3):351–366.Crossref, Google Scholar
• Crisostomi E, Kirkland S, Shorten R (2011) A Google-like model of road network dynamics and its application to regulation and control. Internat. J. Control. 84(3):633–651.Crossref, Google Scholar
• DeGroot MH (1974) Reaching a consensus. J. Amer. Statist. Assoc. 69(345):118–121.Crossref, Google Scholar
• D’Souza RM, Nagler J (2015) Anomalous critical and supercritical phenomena in explosive percolation. Nature Phys. 11(7):531–538.Crossref, Google Scholar
• Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Proc. 2nd Internat. Conf. Knowledge Discovery Data Mining (AAAI Press, Palo Alto, CA), 226–231.Google Scholar
• Fox BL, Landi DM (1968) An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix. Comm. ACM. 11(9):619–621.Crossref, Google Scholar
• Glynn PW (1984) Some asymptotic formulas for Markov chains with applications to simulation. J. Statist. Comput. Simulation 19(2):97–112,Crossref, Google Scholar
• Golub B, Jackson MO (2010) Naïve learning in social networks and the wisdom of crowds. Amer. Econom. J. Microeconom. 2(1):112–149.Crossref, Google Scholar
• Heidergott BF, Hordijk A, Leder N (2010) Series expansions for continuous-time Markov processes. Oper. Res. 58(3):756–767.Link, Google Scholar
• Heidergott BF, Hordijk A, van Uitert M (2007) Series expansions for finite-state Markov chains. Probab. Engrg. Inform. Sci. 21(3):381–400.Crossref, Google Scholar
• Hunter JJ (1982) Generalized inverses and their application to applied probability problems. Linear Algebra Appl. 45:157–198.Crossref, Google Scholar
• Hunter JJ (2005) Stationary distributions and mean first passage times of perturbed Markov chains. Linear Algebra Appl. 410:217–243,Crossref, Google Scholar
• Hunter JJ (2014) The role of Kemeny’s constant in properties of Markov chains. Comm. Statist. Theory Methods 43(7):1309–1321.Crossref, Google Scholar
• Kemeny JG, Snell JL (1976) Finite Markov Chains: With a New Appendix “Generalization of a Fundamental Matrix” (Springer, New York).Google Scholar
• Kirkland S (2010) Fastest expected time to mixing for a Markov chain on a directed graph. Linear Algebra Appl. 433(11–12):1988–1996.Crossref, Google Scholar
• Kirkland S (2014) On the Kemeny constant and stationary distribution vector for a Markov chain. Electron. J. Linear Algebra 27(1):354–372.Crossref, Google Scholar
• Kleinberg JM (2000) Navigation in a small world. Nature 406(6798):845.Crossref, Google Scholar
• Koole GM, Spieksma FM (2001) On deviation matrices for birth-death processes. Probab. Engrg. Inform. Sci. 15(2):239–258.Crossref, Google Scholar
• Langville AN, Meyer CD (2011) Google’s PageRank and Beyond: The Science of Search Engine Rankings (Princeton University Press, Princeton, NJ).Google Scholar
• Levene M, Loizou G (2002) Kemeny’s constant and the random surfer. Amer. Math. Monthly 109(8):741–745.Crossref, Google Scholar
• Litvak N, Ejov V (2009) Markov chains and optimality of the Hamiltonian cycle. Math. Oper. Res. 34(1):71–82.Link, Google Scholar
• Luxburg UV (2006) A tutorial on spectral clustering a tutorial on spectral clustering. Statist. Comput. 17(4):395–416.Crossref, Google Scholar
• Mcpherson M, Smith-lovin L, Cook JM (2001) Birds of a feather: Homophily in social networks. Annual Rev. Soc. 27(1):415–444.Crossref, Google Scholar
• Meyer CD (1975) The role of the group generalized inverse in the theory of finite Markov chains. SIAM Rev. 17(3):443–464.Crossref, Google Scholar
• Meyer CD (1982) Analysis of finite Markov chains by group inversion techniques. Campbell SL, ed. Recent Applications of Generalized Inverses, Research Notes in Math, vol. 66 (Pitman, Boston), 50–81.Google Scholar
• Meyer CD (1989) Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems. SIAM Rev. 31(2):240–272.Crossref, Google Scholar
• Meyer CD, Race S, Valakuzhy K (2013) Determining the number of clusters via iterative consensus clustering. Proc. 2013 SIAM Internat. Conf. Data Mining (Society for Industrial and Applied Mathematics, Philadelphia), 94–102.Crossref, Google Scholar
• Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, et al.. (2011) Scikit-learn machine learning in Python. J. Machine Learn. Res. 12:2825–2830.Google Scholar
• Puterman ML (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming (Wiley, New York).Crossref, Google Scholar
• Schweitzer PJ (1968) Perturbation theory and finite Markov chains. J. Appl. Probab. 5(2):401–413.Crossref, Google Scholar
• Scikit-learn (2017) Comparing different clustering algorithms on toy datasets. Retrieved May 9, 2017, http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html,Google Scholar
• Stewart WJ (1994) Introduction to the Numerical Solution of Markov Chains (Princeton University Press, Princeton, NJ).Google Scholar
• Taylor A, Higham DJ (2009) CONTEST. ACM Trans. Math. Software 35(4):1–17.Crossref, Google Scholar
• Whitt W (1992) Asymptotic formulas for Markov processes with applications to simulation. Oper. Res. 40(2):279–291.Link, Google Scholar
• Winkelmann A, Haselmann T (2010) Ein konzeptionelles model auf basis von Markov-ketten zur berechnung und bewertung von persönlichen kompetenzen in sozialen netzwerken. Proc. Multikonferenz Wirtschaftsinformatik (MKWI) (Leuphana Universität Lüneburg, Lüneburg, Germany), 1317–1328.Google Scholar
• Zachary WW (1977) An information flow model for conflict and fission in small groups. J. Anthropological Res. 33(4):452–473.Crossref, Google Scholar