Fetching the paper…
Reading the bibliography…
Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $\psi(A)$ for a properly chosen $\psi$.
Hermann Weyl, Das asymptotische verteilungsgesetz der eigenwerte linearer partieller differentialgleichungen (mit einer anwendung auf die theorie der hohlraumstrahlung) , Mathematische Annalen 71
1912
Earlier work this paper cites.
Daniel A. Spielman and Nikhil Srivastava, Graph sparsification by effective resistances , SIAM Journal on Computing 40
1926
Earlier work this paper cites.
Chandler Davis and William Morton Kahan, The rotation of eigenvectors by a perturbation. iii , SIAM Journal on Numerical Analysis 7
1970
Earlier work this paper cites.
A. Lubostzky, R. Phillips, and P. Sarnak, Ramanujan graphs , Combinatorica 8
1988
Earlier work this paper cites.
Kenneth Ward Church and Patrick Hanks, Word association norms, mutual information, and lexicography , Comput. Linguist. 16
1990
Earlier work this paper cites.
A. Nilli, On the second eigenvalue of a graph , Discrete Math. 91
1991
Earlier work this paper cites.
Joel Friedman, Some geometric aspects of graphs and their eigenfunctions , Duke Math. J. 69
1993
Earlier work this paper cites.
M. Penrose, Random geometric graphs , Oxford scholarship online, Oxford University Press, 2003
2003
Earlier work this paper cites.
Shlomo Hoory, Nathan Linial, and Avi Wigderson, Expander graphs and their applications , Bull. Amer. Math. Soc. (N.S.) 43
2006
Earlier work this paper cites.
Matthew D. P. Horton, Harold M. Stark, and Audrey A. Terras, What are zeta functions of graphs and what are they good for? , 2006
2006
Earlier work this paper cites.
Z. Li, J. Liu, S. Chen, and X. Tang, Noise robust spectral clustering , 2007 IEEE 11th International Conference on Computer Vision, 2007, pp. 1–8
2007
Earlier work this paper cites.
Ulrike von Luxburg, A tutorial on spectral clustering , Statistics and Computing 17
2007
Earlier work this paper cites.
B. Karrer, E. Levina, and M. E. J. Newman, Robustness of community structure in networks , (2008), no. 4, 046119
2008
Earlier work this paper cites.
A. Coja-Oghlan, Graph partitioning via adaptive spectral techniques , Comb. Probab. Comput. 19
2010
Earlier work this paper cites.
P. D. Turney and P. Pantel, From Frequency to Meaning: Vector Space Models of Semantics , ArXiv e-prints (2010)
2010
Earlier work this paper cites.
Sivaraman Balakrishnan, Min Xu, Akshay Krishnamurthy, and Aarti Singh, Noise thresholds for spectral clustering , Advances in Neural Information Processing Systems 24 (J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. Pereira, and K. Q. Weinberger, eds.), Curran Associates, Inc., 2011, pp. 954–962
2011
Earlier work this paper cites.
Chang-Long Yao, Ge Chen, and Tian-De Guo, Large deviations for the graph distance in supercritical continuum percolation , Journal of Applied Probability 48
2011
Cited alongside, same era.
A. Joseph and B. Yu, Impact of regularization on Spectral Clustering , ArXiv:1312.1733 (2013)
2013
Cited alongside, same era.
Florent Krzakala, Cristopher Moore, Elchanan Mossel, Joe Neeman, Allan Sly, Lenka Zdeborova, and Pan Zhang, Spectral redemption in clustering sparse networks , Proceedings of the National Academy of Sciences 110
2013
Cited alongside, same era.
Tsz Chiu Kwok and Lap Chi Lau, Lower Bounds on Expansions of Graph Powers , Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) (Dagstuhl, Germany) (Klaus Jansen, José D. P. Rolim, Nikhil R. Devanur, and Cristopher Moore, eds.), Leibniz International Proceedings in Informatics (LIPIcs), vol. 28, Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2014, pp. 313–324
2016
Later among the works it cites.
Ankur Moitra, William Perry, and Alexander S Wein, How robust are reconstruction thresholds for community detection? , Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, ACM, 2016, pp. 828–841
2016
Later among the works it cites.
Andrea Montanari and Subhabrata Sen, Semidefinite programs on sparse random graphs and their application to community detection , Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA), STOC 2016, ACM, 2016, pp. 814–827
2016
Later among the works it cites.
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2014
Cited alongside, same era.
L. Massoulié, Community detection thresholds and the weak Ramanujan property , STOC 2014: 46th Annual Symposium on the Theory of Computing (New York, United States), June 2014, pp. 1–10
2014
Cited alongside, same era.
2014
Cited alongside, same era.
Richard Peng and Daniel A Spielman, An efficient parallel solver for sdd linear systems , Proceedings of the forty-sixth annual ACM symposium on Theory of computing, ACM, 2014, pp. 333–342
2014
Cited alongside, same era.
2014
Cited alongside, same era.
E. Abbe and C. Sandon, Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap , ArXiv e-prints 1512.09080 (2015)
2015
Cited alongside, same era.
Charles Bordenave, Marc Lelarge, and Laurent Massoulié, Non-backtracking spectrum of random graphs: Community detection and non-regular Ramanujan graphs , Proceedings of the 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS) (Washington, DC, USA), FOCS ’15, IEEE Computer Society, 2015, pp. 1347–1357
2015
Cited alongside, same era.
D. Cheng, Y. Cheng, Y. Liu, R. Peng, and S.-H. Teng, Spectral Sparsification of Random-Walk Matrix Polynomials , ArXiv e-prints (2015)
2015
Cited alongside, same era.
2015
Cited alongside, same era.
E. Abbe, E. Boix, and C. Sandon, Graph powering and spectral gap extraction , Manuscript. Results partly presented at the Simons Institute and partly available in E. Boix PACM Thesis, Princeton University (2017)
2017
Later among the works it cites.
2017
Later among the works it cites.
Emmanuel Abbe and Colin Sandon, Proof of the achievability conjectures for the general stochastic block model , Communications on Pure and Applied Mathematics 71
2017
Later among the works it cites.
S. Galhotra, A. Mazumdar, S. Pal, and B. Saha, The Geometric Block Model , ArXiv:1709.05510 (2017)
2017
Later among the works it cites.
G. Jindal, P. Kolev, R. Peng, and S. Sawlani, Density Independent Algorithms for Sparsifying k k -Step Random Walks , ArXiv e-prints (2017)
2017
Later among the works it cites.
P. K. Kothari and D. Steurer, Outlier-robust moment-estimation via sum-of-squares , ArXiv e-prints (2017)
2017
Later among the works it cites.
J. Mu, S. Bhat, and P. Viswanath, All-but-the-Top: Simple and Effective Postprocessing for Word Representations , ArXiv e-prints (2017)
2017
Later among the works it cites.
M. Mondelli and A. Montanari, Fundamental Limits of Weak Recovery with Applications to Phase Retrieval , ArXiv e-prints (2017)
2017
Later among the works it cites.
2017
Later among the works it cites.
Emmanuel Abbe, Community detection and stochastic block models , Foundations and Trends® in Communications and Information Theory 14
2018
Closest in time.
Pravesh K. Kothari, Jacob Steinhardt, and David Steurer, Robust moment estimation and improved clustering via sum of squares , Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA), STOC 2018, ACM, 2018, pp. 1035–1046
2018
Closest in time.