Project Euclid

References

• Aloise, D., Deshpande, A., Hansen, P. and Popat, P. (2009). NP-hardness of Euclidean sum-of-squares clustering. Machine Learning 75 245–248.
• Alon, N. and Spencer, J. H. (2004). The Probabilistic Method, 2nd ed. Wiley, Hoboken.
• Amini, A. A., Chen, A., Bickel, P. J. and Levina, E. (2012). Pseudo-likelihood methods for community detection in large sparse networks. Preprint. Available at arXiv:1207.2340.
• Anandkumar, A., Ge, R., Hsu, D. and Kakade, S. M. (2013). A tensor spectral approach to learning mixed membership community models. Preprint. Available at arXiv:1302.2684.
• Awasthi, P. and Sheffet, O. (2012). Improved spectral-norm bounds for clustering. In Approximation, Randomization, and Combinatorial Optimization. Lecture Notes in Computer Science 7408 37–49. Springer, Heidelberg.
  Mathematical Reviews (MathSciNet): MR3003539
  Digital Object Identifier: doi:10.1007/978-3-642-32512-0_4
  
• Balakrishnan, S., Xu, M., Krishnamurthy, A. and Singh, A. (2011). Noise thresholds for spectral clustering. In Advances in Neural Information Processing Systems 24 (J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. Pereira and K. Q. Weinberger, eds.) 954–962. Curran Associates, Red Hook, NY.
• Bhatia, R. (1997). Matrix Analysis. Graduate Texts in Mathematics 169. Springer, New York.
  Mathematical Reviews (MathSciNet): MR1477662
  
• Bickel, P. J. and Chen, A. (2009). A nonparametric view of network models and Newman–Girvan and other modularities. Proc. Natl. Acad. Sci. USA 106 21068–21073.
• Celisse, A., Daudin, J.-J. and Pierre, L. (2012). Consistency of maximum-likelihood and variational estimators in the stochastic block model. Electron. J. Stat. 6 1847–1899.
  Mathematical Reviews (MathSciNet): MR2988467
  Digital Object Identifier: doi:10.1214/12-EJS729
  Project Euclid: euclid.ejs/1349355605
  
• Channarond, A., Daudin, J.-J. and Robin, S. (2012). Classification and estimation in the stochastic blockmodel based on the empirical degrees. Electron. J. Stat. 6 2574–2601.
  Mathematical Reviews (MathSciNet): MR3020277
  Digital Object Identifier: doi:10.1214/12-EJS753
  Project Euclid: euclid.ejs/1357913089
  
• Charikar, M., Guha, S., Tardos, É. and Shmoys, D. B. (1999). A constant-factor approximation algorithm for the $k$-median problem. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing 1–10. ACM, New York, NY.
• Chaudhuri, K., Chung, F. and Tsiatas, A. (2012). Spectral clustering of graphs with general degrees in the extended planted partition model. JMLR: Workshop and Conference Proceedings 2012 35.1–35.23.
• Chen, Y., Sanghavi, S. and Xu, H. (2012). Clustering sparse graphs. In Advances in Neural Information Processing Systems 25 (F. Pereira, C. J. C. Burges, L. Bottou and K. Q. Weinberger, eds.) 2204–2212. Curran Associates, Red Hook, NY.
• Choi, D. S., Wolfe, P. J. and Airoldi, E. M. (2012). Stochastic blockmodels with a growing number of classes. Biometrika 99 273–284.
  Mathematical Reviews (MathSciNet): MR2931253
  Digital Object Identifier: doi:10.1093/biomet/asr053
  
• Chung, F. and Radcliffe, M. (2011). On the spectra of general random graphs. Electron. J. Combin. 18 Paper 215, 14.
  Mathematical Reviews (MathSciNet): MR2853072
  
• Coja-Oghlan, A. (2010). Graph partitioning via adaptive spectral techniques. Combin. Probab. Comput. 19 227–284.
  Mathematical Reviews (MathSciNet): MR2593622
  Digital Object Identifier: doi:10.1017/S0963548309990514
  
• Decelle, A., Krzakala, F., Moore, C. and Zdeborová, L. (2011). Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Phys. Rev. E (3) 84 066106.
• Deshpande, Y. and Montanari, A. (2013). Finding hidden cliques of size $\sqrt{N/e}$ in nearly linear time. Preprint. Available at arXiv:1304.7047.
• Feige, U. and Ofek, E. (2005). Spectral techniques applied to sparse random graphs. Random Structures Algorithms 27 251–275.
  Mathematical Reviews (MathSciNet): MR2155709
  
• Fishkind, D. E., Sussman, D. L., Tang, M., Vogelstein, J. T. and Priebe, C. E. (2013). Consistent adjacency-spectral partitioning for the stochastic block model when the model parameters are unknown. SIAM J. Matrix Anal. Appl. 34 23–39.
  Mathematical Reviews (MathSciNet): MR3032990
  Digital Object Identifier: doi:10.1137/120875600
  
• Goldenberg, A., Zheng, A. X., Fienberg, S. E. and Airoldi, E. M. (2010). A survey of statistical network models. Foundations and Trends® in Machine Learning 2 129–233.
• Holland, P. W., Laskey, K. B. and Leinhardt, S. (1983). Stochastic blockmodels: First steps. Social Networks 5 109–137.
  Mathematical Reviews (MathSciNet): MR718088
  Digital Object Identifier: doi:10.1016/0378-8733(83)90021-7
  
• Jin, J. (2012). Fast community detection by SCORE. Available at arXiv:1211.5803.
  Mathematical Reviews (MathSciNet): MR3285600
  Digital Object Identifier: doi:10.1214/14-AOS1265
  Project Euclid: euclid.aos/1416322036
  
• Karrer, B. and Newman, M. E. J. (2011). Stochastic blockmodels and community structure in networks. Phys. Rev. E (3) 83 016107, 10.
  Mathematical Reviews (MathSciNet): MR2788206
  Digital Object Identifier: doi:10.1103/PhysRevE.83.016107
  
• Kolaczyk, E. D. (2009). Statistical Analysis of Network Data: Methods and Models. Springer, New York.
  Mathematical Reviews (MathSciNet): MR2724362
  
• Krzakala, F., Moore, C., Mossel, E., Neeman, J., Sly, A., Zdeborová, L. and Zhang, P. (2013). Spectral redemption in clustering sparse networks. Proc. Natl. Acad. Sci. USA 110 20935–20940.
  Mathematical Reviews (MathSciNet): MR3174850
  Digital Object Identifier: doi:10.1073/pnas.1312486110
  
• Kumar, A. and Kannan, R. (2010). Clustering with spectral norm and the $k$-means algorithm. In Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science FOCS 299–308. IEEE, Los Alamitos, CA.
  Mathematical Reviews (MathSciNet): MR3025203
  
• Kumar, A., Sabharwal, Y. and Sen, S. (2004). A simple linear time $(1+\varepsilon)$-approximation algorithm for $k$-means clustering in any dimensions. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science 454–462. IEEE Computer Society, Washington, DC.
• Lei, J. and Rinaldo, A. (2014). Supplement to “Consistency of spectral clustering in stochastic block models.” DOI:10.1214/14-AOS1274SUPP.
  Mathematical Reviews (MathSciNet): MR3285605
  Digital Object Identifier: doi:10.1214/14-AOS1274
  Project Euclid: euclid.aos/1418135620
  
• Li, S. and Svensson, O. (2013). Approximating k-median via pseudo-approximation. In Proceedings of the 45th Annual ACM Symposium on Symposium on Theory of Computing 901–910. ACM, New York.
  Mathematical Reviews (MathSciNet): MR3210852
  
• Lu, L. and Peng, X. (2012). Spectra of edge-independent random graphs. Preprint. Available at arXiv:1204.6207.
  Mathematical Reviews (MathSciNet): MR3158266
  
• Lyzinski, V., Sussman, D., Tang, M., Athreya, A. and Priebe, C. (2013). Perfect clustering for stochastic blockmodel graphs via adjacency spectral embedding. Preprint. Available at arXiv:1310.0532.
  Mathematical Reviews (MathSciNet): MR3299126
  Digital Object Identifier: doi:10.1214/14-EJS978
  Project Euclid: euclid.ejs/1420815881
  
• Massoulie, L. (2013). Community detection thresholds and the weak Ramanujan property. Preprint. Available at arXiv:1311.3085.
• McSherry, F. (2001). Spectral partitioning of random graphs. In 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001) 529–537. IEEE, Los Alamitos, CA.
  Mathematical Reviews (MathSciNet): MR1948742
  
• Mossel, E., Neeman, J. and Sly, A. (2012). Stochastic block models and reconstruction. Preprint. Available at arXiv:1202.1499.
• Mossel, E., Neeman, J. and Sly, A. (2013). A proof of the block model threshold conjecture. Preprint. Available at arXiv:1311.4115.
• Newman, M. E. J. (2010). Networks: An Introduction. Oxford Univ. Press, Oxford.
  Mathematical Reviews (MathSciNet): MR2676073
  
• Newman, M. E. J. and Girvan, M. (2004). Finding and evaluating community structure in networks. Phys. Rev. E (3) 69 026113.
• Ng, A. Y., Jordan, M. I., Weiss, Y. et al. (2002). On spectral clustering: Analysis and an algorithm. Adv. Neural Inf. Process. Syst. 2 849–856.
• Qin, T. and Rohe, K. (2013). Regularized spectral clustering under the degree-corrected stochastic blockmodel. Preprint. Available at arXiv:1309.4111.
• Rohe, K., Chatterjee, S. and Yu, B. (2011). Spectral clustering and the high-dimensional stochastic blockmodel. Ann. Statist. 39 1878–1915.
  Mathematical Reviews (MathSciNet): MR2893856
  Digital Object Identifier: doi:10.1214/11-AOS887
  Project Euclid: euclid.aos/1314190618
  
• Sarkar, P. and Bickel, P. (2013). Role of normalization in spectral clustering for stochastic blockmodels. Preprint. Available at arXiv:1310.1495.
• Sussman, D. L., Tang, M., Fishkind, D. E. and Priebe, C. E. (2012). A consistent adjacency spectral embedding for stochastic blockmodel graphs. J. Amer. Statist. Assoc. 107 1119–1128.
  Mathematical Reviews (MathSciNet): MR3010899
  Digital Object Identifier: doi:10.1080/01621459.2012.699795
  
• Tropp, J. A. (2012). User-friendly tail bounds for sums of random matrices. Found. Comput. Math. 12 389–434.
  Mathematical Reviews (MathSciNet): MR2946459
  Digital Object Identifier: doi:10.1007/s10208-011-9099-z
  
• von Luxburg, U. (2007). A tutorial on spectral clustering. Stat. Comput. 17 395–416.
  Mathematical Reviews (MathSciNet): MR2409803
  Digital Object Identifier: doi:10.1007/s11222-007-9033-z
  
• Vu, V. Q. and Lei, J. (2013). Minimax sparse principal subspace estimation in high dimensions. Ann. Statist. 41 2905–2947.
  Mathematical Reviews (MathSciNet): MR3161452
  Digital Object Identifier: doi:10.1214/13-AOS1151
  Project Euclid: euclid.aos/1388545673
  
• Zhao, Y., Levina, E. and Zhu, J. (2012). Consistency of community detection in networks under degree-corrected stochastic block models. Ann. Statist. 40 2266–2292.
  Mathematical Reviews (MathSciNet): MR3059083
  Digital Object Identifier: doi:10.1214/12-AOS1036
  Project Euclid: euclid.aos/1358951382