Impact of regularization on spectral clustering

Annals of Statistics - Tập 44 Số 4 - 2016
Antony Joseph1, Bin Yu1
1@WalmartLabs and University of California, Berkeley

Tóm tắt

Từ khóa


Tài liệu tham khảo

[6] Bickel, P. J. and Chen, A. (2009). A nonparametric view of network models and Newman–Girvan and other modularities. <i>Proc. Natl. Acad. Sci. USA</i> <b>106</b> 21068–21073.

[2] Amini, A. A., Chen, A., Bickel, P. J. and Levina, E. (2013). Pseudo-likelihood methods for community detection in large sparse networks. <i>Ann. Statist.</i> <b>41</b> 2097–2122.

[5] Bhatia, R. (1997). <i>Matrix Analysis. Graduate Texts in Mathematics</i> <b>169</b>. Springer, New York.

[3] Awasthi, P. and Sheffet, O. (2012). Improved spectral-norm bounds for clustering. In <i>Approximation</i>, <i>Randomization</i>, <i>and Combinatorial Optimization. Lecture Notes in Computer Science</i> <b>7408</b> 37–49. Springer, Heidelberg.

[4] Belkin, M. and Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. <i>Neural Comput.</i> <b>15</b> 1373–1396.

[7] Chaudhuri, K., Chung, F. and Tsiatas, A. Spectral clustering of graphs with general degrees in the extended planted partition model. <i>J. Mach. Learn. Res.</i> <b>2012</b> 1–23.

[10] 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. <i>SIAM J. Matrix Anal. Appl.</i> <b>34</b> 23–39.

[11] Hagen, L. and Kahng, A. B. (1992). New spectral methods for ratio cut partitioning and clustering. <i>IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.</i> <b>11</b> 1074–1085.

[12] Holland, P. W., Laskey, K. B. and Leinhardt, S. (1983). Stochastic blockmodels: First steps. <i>Soc. Netw.</i> <b>5</b> 109–137.

[13] Joseph, A. and Yu, B. (2016). Supplement to “Impact of regularization on spectral clustering.” <a href="DOI:10.1214/16-AOS1447SUPP">DOI:10.1214/16-AOS1447SUPP</a>.

[17] Le, C. M. and Vershynin, R. (2015). Concentration and regularization of random graphs. Available at <a href="arXiv:1506.00669">arXiv:1506.00669</a>.

[18] Mackey, L., Jordan, M. I., Chen, R. Y., Farrell, B. and Tropp, J. A. (2012). Matrix concentration inequalities via the method of exchangeable pairs. Available at <a href="arXiv:1201.6002">arXiv:1201.6002</a>.

[20] Newman, M. E. and Girvan, M. (2004). Finding and evaluating community structure in networks. <i>Phys. Rev. E</i> <b>69</b> 026113.

[21] Ng, A. Y., Jordan, M. I., Weiss, Y. et al. (2002). On spectral clustering: Analysis and an algorithm. <i>Adv. Neural Inf. Process. Syst.</i> <b>2</b> 849–856.

[22] Oliveira, R. I. (2009). Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges. Available at <a href="arXiv:0911.0600">arXiv:0911.0600</a>.

[23] Qin, T. and Rohe, K. (2013). Regularized spectral clustering under the degree-corrected stochastic blockmodel. Available at <a href="arXiv:1309.4111">arXiv:1309.4111</a>.

[24] Rohe, K., Chatterjee, S. and Yu, B. (2011). Spectral clustering and the high-dimensional stochastic blockmodel. <i>Ann. Statist.</i> <b>39</b> 1878–1915.

[25] Shi, J. and Malik, J. (2000). Normalized cuts and image segmentation. <i>IEEE Trans. Pattern Anal. Mach. Intell.</i> <b>22</b> 888–905.

[26] Sussman, D. L., Tang, M., Fishkind, D. E. and Priebe, C. E. (2012). A consistent adjacency spectral embedding for stochastic blockmodel graphs. <i>J. Amer. Statist. Assoc.</i> <b>107</b> 1119–1128.

[27] von Luxburg, U. (2007). A tutorial on spectral clustering. <i>Stat. Comput.</i> <b>17</b> 395–416.

[1] Adamic, L. A. and Glance, N. (2005). The political blogosphere and the 2004 US Election: Divided they blog. In <i>Proceedings of the</i> 3<i>rd International Workshop on Link Discovery</i> 36–43. ACM, New York.

[8] Chen, A., Amini, A., Bickel, P. and Levina, L. (2012). Fitting community models to large sparse networks. In <i>Joint Statistical Meetings</i>, <i>San Diego</i>.

[9] Dhillon, I. S. (2001). Co-clustering documents and words using bipartite spectral graph partitioning. In <i>Proc. Seventh ACM SIGKDD Inter. Conf. on Know. Disc. and Data Mining</i> 269–274. ACM, New York.

[14] Karrer, B. and Newman, M. E. J. (2011). Stochastic blockmodels and community structure in networks. <i>Phys. Rev. E</i> (3) <b>83</b> 016107.

[15] Kumar, A. and Kannan, R. (2010). Clustering with spectral norm and the $k$-means algorithm. In 2010 <i>IEEE</i> 51<i>st Annual Symposium on Foundations of Computer Science FOCS</i> 2010 299–308. IEEE Computer Soc., Los Alamitos, CA.

[16] Kwok, T. C., Lau, L. C., Lee, Y. T., Oveis Gharan, S. and Trevisan, L. (2013). Improved Cheeger’s inequality: Analysis of spectral partitioning algorithms through higher order spectral gap. In <i>STOC’</i>13<i>—Proceedings of the</i> 2013 <i>ACM Symposium on Theory of Computing</i> 11–20. ACM, New York.

[19] McSherry, F. (2001). Spectral partitioning of random graphs. In 42<i>nd IEEE Symposium on Foundations of Computer Science</i> (<i>Las Vegas</i>, <i>NV</i>, 2001) 529–537. IEEE Computer Soc., Los Alamitos, CA.