How to Calculate the Barycenter of a Weighted Graph

Published Online:https://doi.org/10.1287/moor.2017.0896

References

  • Acemoğlu D, Fagnani F, Ozdağlar A, Como G (2013) Opinion fluctuations and disagreement in social networks. Math. Oper. Res. 38(1):1–27.LinkGoogle Scholar
  • Allassonnière S, Trouvé A, Kuhn E (2010) Construction of Bayesian deformable models via stochastic approximation algorithm: A convergence study. Bernoulli 16(3):641–678.CrossrefGoogle Scholar
  • Arnaudon M, Miclo L (2014) Means in complete manifolds: Uniqueness and approximation. ESAIM: Prob. Statist. 18:185–206.CrossrefGoogle Scholar
  • Arnaudon M, Miclo L (2014) A stochastic algorithm finding generalized means on compact manifolds. Stochastic Processes and Their Appl. 124:3463–3479.CrossrefGoogle Scholar
  • Arnaudon M, Miclo L (2016) A stochastic algorithm finding p-means on the circle. Bernoulli. 22(4):2237–2300.CrossrefGoogle Scholar
  • Bach F, Jordan M (2004) Learning spectral clustering. Advances in Neural Information Processing Systems, 305–312.Google Scholar
  • Bakry D, Ledoux M, Gentil I (2014) Analysis and Geometry of Markov Diffusion Operators. Grundlehren der mathematischen Wissenschaften, Vol. 348 (Springer, Cham, Switzerland).CrossrefGoogle Scholar
  • Barden D, Owen M, Le H (2013) Central limit theorems for Fréchet means in the space of phylogenetic trees. Electronic J. Probab. 18:1–25.CrossrefGoogle Scholar
  • Bhattacharya R, Patrangenaru V (2003) Large sample theory of intrinsic and extrinsic sample means on manifolds. Ann. Statist. 31(1):1–29.CrossrefGoogle Scholar
  • Bierkens J, Fearnhead P, Roberts G (2016) The zig–zag process and super-efficient sampling for Bayesian analysis of big data. Working paper, Delft University, Delft, Netherlands, arXiv:1607.03188.Google Scholar
  • Bigot J (2013) Fréchet means of curves for signal averaging and application to ECG data analysis. Ann. Appl. Statist. 7(4):1837–2457.CrossrefGoogle Scholar
  • Bigot J, Gadat S (2010) A deconvolution approach to estimation of a common shape in a shifted curves model. Ann. Statist. 38:224–243.CrossrefGoogle Scholar
  • Bigot J, Gendre X (2013) Minimax properties of Fréchet means of discretely sampled curves. Ann. Statist. 41:923–956.CrossrefGoogle Scholar
  • Bigot J, Klein T, Lopez A, Gouet R (2017) Geodesic PCA in the Wasserstein space by convex PCA. Annales de l’Institut Henri Poincaré B: Probab. Statist. 53(1):1–26.CrossrefGoogle Scholar
  • Bigot J, Lopez A, Gouet R (2013) Geometric PCA of images. SIAM J. Imaging Sci. 6(4):1851–1879.CrossrefGoogle Scholar
  • Bontemps D, Gadat S (2014) Bayesian methods for the shape invariant model. Electronic J. Statist. 8(1):1522–1568.CrossrefGoogle Scholar
  • Brezis H (1987) Analyse Fonctionelle (Masson, Paris).Google Scholar
  • Catoni O (1992) Rough large deviation estimates for simulated annealing: Application to exponential schedules. Ann. Probab. 20(3):1109–1146.CrossrefGoogle Scholar
  • Csiszár I (1967) Information-type measures of difference of probability distributions and indirect observations. Stud. Sci. Math. Hung. 2:299–318.Google Scholar
  • Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer. Math. 1(1):269–271.CrossrefGoogle Scholar
  • Dryden IL, Mardia KV (1998) Statistical Shape Analysis (John Wiley & Sons, New York).Google Scholar
  • Estrada E (2015) Introduction to Complex Networks. Structure and Dynamics. Evolutionary Equations with Applications to Natural Sciences (Springer International, Cham, Switzerland).Google Scholar
  • Ethier SN, Kurtz T (2005) Markov Processes. Characterization and Convergence, Wiley Series in Probability and Statistics (John Wiley & Sons, New York).Google Scholar
  • Fréchet M (1948) Les éléments aléatoires de nature quelconque dans un espace distancié. Annales de l’Institut Henri Poincaré (B) 10:215–310.Google Scholar
  • Freidlin M, Sheu SJ (2000) Diffusion processes on graphs: Stochastic differential equations, large deviation principle. Probab. Theory Related Fields 116(2):181–220.CrossrefGoogle Scholar
  • Freidlin MI, Wentzell AD (1979) Random perturbations of dynamical systems. Grundlehren der Mathematischen Wissenschaften, Vol. 260, 2nd ed. (Springer, New York). Translated from the 1979 Russian original by Joseph Szücs.Google Scholar
  • Freidlin MI, Wentzell AD (1995) Random perturbations of Hamiltonian systems. Memoirs of the American Mathematical Society, Vol. 523 (American Mathematical Society, Providence, RI).Google Scholar
  • Ginestet CE (2013) Strong consistency of set-valued Fréchet sample means in metric spaces. Working paper, Boston University, Boston.Google Scholar
  • Goldenberg A, Fienberg SE, Airoldi EM, Zheng AX (2010) A survey of statistical network models. Found. Trends Machine Learning 2(2):129–233.CrossrefGoogle Scholar
  • Gutjahr WJ, Pflug G (1996) Simulated annealing for noisy cost functions. J. Global Optim. 8(1):1–13.CrossrefGoogle Scholar
  • Hajeck B (1988) Cooling schedules for optimal annealing. Math. Oper. Res. 13(2):311–329.LinkGoogle Scholar
  • Hakimi SL (1983) On locating new facilities in a competitive environment. Eur. J. Oper. Res. 12(1):29–35.CrossrefGoogle Scholar
  • Holley R, Stroock D (1988) Simulated annealing via Sobolev inequalities. Comm. Math. Phys. 115(4):553–569.CrossrefGoogle Scholar
  • Holley R, Stroock D, Kusuoka D (1989) Asymptotics of the spectral gap with applications to the theory of simulated annealing. J. Funct. Anal. 83(2):333–347.CrossrefGoogle Scholar
  • Ikeda N, Watanabe S (1981) Stochastic Differential Equations and Diffusion Processes (North-Holland, Amsterdam).Google Scholar
  • Jackson MO (2008) Social and Economic Networks (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Klopp O, Tsybakov AB, Verzelen N (2017) Oracle inequalities for network models and sparse graphon estimation. Ann. Statist. 45(1):316–354.CrossrefGoogle Scholar
  • Kolaczyk ED (2009) Statistical Analysis of Network Data: Methods and Models, Springer Series in Statistics (Springer, New York).CrossrefGoogle Scholar
  • Kullback S (1967) A lower bound for discrimination information in terms of variation. IEEE Trans. Inform. Theory 13(1):126–127.CrossrefGoogle Scholar
  • Le H (2001) Locating Fréchet means with application to shape spaces. Adv. Appl. Probab. 33(2):324–338.CrossrefGoogle Scholar
  • Lovasz L (2012) Large Networks and Graph Limits, Vol. 60 (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • Miclo L (1992) Recuit simulé sur Rn. Étude de l’évolution de l’énergie libre. Ann. Inst. H. Poincaré Probab. Statist. 28(2):235–266.Google Scholar
  • Miller E, Provan J, Owen M (2015) Polyhedral computational geometry for averaging metric phylogenetic trees. Adv. Appl. Math. 68(C):51–91.CrossrefGoogle Scholar
  • Monmarche P (2016) Piecewise deterministic simulated annealing. ALEA, Latin Amer. J. Probability Math. Statist. 13(1):357–398.Google Scholar
  • Munch E, Bendich P, Mukherjee S, Mattingly J, Harer J, Turner K (2015) Probabilistic Fréchet means for time varying persistence diagrams. Electronic J. Statist. 9:1173–1204.CrossrefGoogle Scholar
  • Newman M (2010) Networks, An Introduction (Oxford University Press, New York).CrossrefGoogle Scholar
  • Pardalos PM, Vavasis SA (1991) Quadratic programming with one negative eigenvalue is NP-hard. J. Global Optim. 1(1):15–22.CrossrefGoogle Scholar
  • Pennec X (2006) Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. J. Math. Imaging Vision 25:127–154.CrossrefGoogle Scholar
  • Pinsker MS (1964) Information and information stability of random variables and processes. Holden-Day, San Francisco.Google Scholar
  • Sahni S (1974) Computationally related problems. SIAM J. Comput. 3(4):262–279.CrossrefGoogle Scholar
  • Shneiderman B, Aris A (2006) Network visualization by semantic substrates. IEEE Trans. Visualization Comput. Graphics 12(5):733–740.CrossrefGoogle Scholar
  • Spoerhase J, Wirth H-C (2009) (r, p)-centroid problems on paths and trees. Theoret. Comput. Sci. 410(47–49):5128–5137.CrossrefGoogle Scholar
  • Trouvé A (1993) Parallélisation massive du recuit simulé. PhD Thesis, Université d’Orsay, Orsay, France.Google Scholar
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