L. A. Adamic and N. Glance, The political blogosphere and the 2004 us election: divided they blog, Proceedings of the 3rd international workshop on Link discovery, pp.36-43, 2005.

. Aicher, Learning latent block structure in weighted networks, Journal of Complex Networks, p.26, 2014.

[. Ajanki, Community detection in multidimensional networks, Quadratic vector equations on complex upper half-plane, pp.352-359, 2014.

. Andrzejak, Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state, Physical Review E, vol.64, issue.6, p.61907, 2001.

A. , Evolutionary formalism for products of positive random matrices, The Annals of Applied Probability, pp.859-901, 1994.

[. Avrachenkov, Spectral properties of random matrices for stochastic block model, Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), pp.537-544, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01261156

Z. Bai, Circular law, Advances In Statistics, pp.128-163, 2008.

S. Bai, Z. Bai, and J. W. Silverstein, Spectral analysis of large dimensional random matrices, vol.20, 2010.

S. Bai, Z. Bai, and J. W. Silverstein, No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices, Annals of probability, pp.316-345, 1998.

[. Bibliography and . Baik, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, Annals of Probability, pp.1643-1697, 2005.

J. Baik and J. W. Silverstein, Eigenvalues of large sample covariance matrices of spiked population models, Journal of Multivariate Analysis, vol.97, issue.6, pp.1382-1408, 2006.

. Barbillon, Stochastic block models for multiplex networks: an application to a multilevel network of researchers, Journal of the Royal Statistical Society: Series A (Statistics in Society, vol.180, issue.1, pp.295-314, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01520820

C. Georges, F. Couillet, and R. , Spectral analysis of the gram matrix of mixture models, ESAIM: Probability and Statistics, vol.20, pp.217-237, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01215342

N. Georges, F. Nadakuditi, and R. R. , The singular values and vectors of low rank perturbations of large rectangular random matrices, Journal of Multivariate Analysis, vol.111, pp.120-135, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00575203

P. Billingsley, Probability and measure. wiley series in probability and mathematical statistics, 1995.

[. Bi´nkowskibi´nkowski, , 2018.

[. Blei, Variational inference for dirichlet process mixtures, Bayesian analysis, vol.1, issue.1, pp.121-143, 2006.
DOI : 10.1214/06-ba104

URL : https://doi.org/10.1214/06-ba104

[. Boden, Mining coherent subgraphs in multi-layer graphs with edge labels, Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining, pp.1258-1266, 2012.

[. Bordenave, Nonbacktracking spectrum of random graphs: community detection and non-regular ramanujan graphs, Foundations of Computer Science (FOCS), pp.1347-1357, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01137952

. Boucheron, Concentration inequalities: A nonasymptotic theory of independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

. Boulos, Multi-scale structural community organisation of the human genome, BMC bioinformatics, vol.18, issue.1, p.209, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01507455

. Bibliography-[brandes, On finding graph clusterings with maximum modularity, In International Workshop on Graph-Theoretic Concepts in Computer Science, pp.121-132, 2007.

G. Brodka, P. Brodka, and T. Grecki, mLFR Benchamark: Testing Community Detection Algorithms in Multilayer, Multiplex and Multiple Social Networks, 2012.

[. Chapelle, Cluster kernels for semi-supervised learning, Advances in neural information processing systems, pp.601-608, 2003.

[. Chapon, The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00713811

[. Chen, Functional organization of the human 4d nucleome, Proceedings of the National Academy of Sciences, vol.112, issue.26, pp.8002-8007, 2015.

[. Chen, Spectral identification of topological domains, p.221, 2016.
DOI : 10.1093/bioinformatics/btw221

URL : https://academic.oup.com/bioinformatics/article-pdf/32/14/2151/19568527/btw221.pdf

J. Chen and B. Yuan, Detecting functional modules in the yeast protein-protein interaction network, Bioinformatics, vol.22, issue.18, pp.2283-2290, 2006.
DOI : 10.1093/bioinformatics/btl370

URL : https://academic.oup.com/bioinformatics/article-pdf/22/18/2283/16851690/btl370.pdf

[. Chen, Convexified modularity maximization for degree-corrected stochastic block models, In Artificial Intelligence and Statistics, pp.192-204, 2015.
DOI : 10.1214/17-aos1595

URL : http://arxiv.org/pdf/1512.08425

F. R. Chung-;-chung, Spectral graph theory, vol.92, 1997.

[. Clauset, Finding community structure in very large networks, Physical review E, vol.70, issue.6, p.66111, 2004.
DOI : 10.1103/physreve.70.066111

URL : http://arxiv.org/pdf/cond-mat/0408187

[. Cline, Integration of biological networks and gene expression data using cytoscape, Nature protocols, vol.2, issue.10, p.2366, 2007.

. Coja-oghlan, A. Lanka-;-coja-oghlan, and A. Lanka, Finding planted partitions in random graphs with general degree distributions, SIAM Journal on Discrete Mathematics, vol.23, issue.4, pp.1682-1714, 2009.
DOI : 10.1137/070699354

URL : http://wrap.warwick.ac.uk/43264/1/WRAP_Coja-Oghlan_fppac.pdf

. Bibliography-[comar, A framework for joint community detection across multiple related networks, Neurocomputing, vol.76, issue.1, pp.93-104, 2012.

B. Couillet, R. Couillet, and F. Benaych-georges, Kernel spectral clustering of large dimensional data, Electronic Journal of Statistics, vol.10, issue.1, pp.1393-1454, 2016.
DOI : 10.1214/16-ejs1144

URL : https://hal.archives-ouvertes.fr/hal-01215343

R. Couillet and M. Debbah, Random matrix methods for wireless communications, 2011.
DOI : 10.1017/cbo9780511994746

URL : https://hal.archives-ouvertes.fr/hal-00658725

[. Couillet, Classification asymptotics in the random matrix regime, European Signal Processing Conference, vol.18, 2018.

[. Couillet, The asymptotic performance of linear echo state neural networks, Journal of Machine Learning Research, vol.17, issue.178, pp.1-35, 2016.
DOI : 10.1109/ssp.2016.7551721

URL : https://hal.archives-ouvertes.fr/hal-01322809

[. Couillet, Training performance of echo state neural networks, Statistical Signal Processing Workshop (SSP), pp.1-4, 2016.
DOI : 10.1109/ssp.2016.7551721

URL : https://hal.archives-ouvertes.fr/hal-01633450

[. Couillet, A random matrix approach to echo-state neural networks, International Conference on Machine Learning, pp.517-525, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01812026

[. Dauphin, Identifying and attacking the saddle point problem in highdimensional non-convex optimization, Advances in neural information processing systems, pp.2933-2941, 2014.

. De-bacco, Community detection, link prediction, and layer interdependence in multilayer networks, Physical Review E, vol.95, issue.4, p.42317, 2017.

D. De, Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems, Physical Review X, vol.5, issue.1, p.11027, 2015.

D. De, Structural reducibility of multilayer networks, Nature communications, vol.6, p.6864, 2015.

[. Decelle, Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications, Physical Review E, vol.84, issue.6, p.66106, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00661643

. Bibliography-[decelle, Inference and phase transitions in the detection of modules in sparse networks, Physical Review Letters, vol.107, issue.6, p.65701, 2011.

[. Dekker, The 4d nucleome project, Nature, vol.549, issue.7671, p.219, 2017.
DOI : 10.1038/nature23884

URL : https://www.nature.com/articles/nature23884.pdf

[. Dixon, Chromatin architecture reorganization during stem cell di?erentiation, Nature, vol.518, issue.7539, p.331, 2015.
DOI : 10.1038/nature14222

URL : http://www.nature.com/nature/journal/v518/n7539/pdf/nature14222.pdf

[. Dixon, Topological domains in mammalian genomes identified by analysis of chromatin interactions, Nature, vol.485, issue.7398, pp.376-380, 2012.

J. Duch and A. Arenas, Community detection in complex networks using extremal optimization, Physical review E, vol.72, issue.2, p.27104, 2005.
DOI : 10.1103/physreve.72.027104

URL : http://arxiv.org/pdf/cond-mat/0501368

. El-karoui, The spectrum of kernel random matrices, The Annals of Statistics, vol.38, issue.1, pp.1-50, 2010.

S. Fortunato, Community detection in graphs, Physics Reports, vol.486, issue.3, pp.75-174, 2010.
DOI : 10.1016/j.physrep.2009.11.002

URL : http://arxiv.org/pdf/0906.0612v1.pdf

D. Gamerman, H. F. Lopes, . Chapman, /. Hall, and . Gao, Markov chain Monte Carlo: stochastic simulation for Bayesian inference, Community detection in degree-corrected block models, 2006.

V. L. Girko, Theory of stochastic canonical equations, vol.2, 2001.
DOI : 10.1007/978-94-010-0989-8

V. L. Girko, Theory of random determinants, vol.45, 2012.

[. Goldenberg, A survey of statistical network models, Foundations and Trends R in Machine Learning, vol.2, pp.129-233, 2010.
DOI : 10.1561/2200000005

URL : http://arxiv.org/pdf/0912.5410

[. Gretton, A kernel two-sample test, Journal of Machine Learning Research, vol.13, pp.723-773, 2012.

[. Guimera, The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles, Proceedings of the National Academy of Sciences, vol.102, issue.22, pp.7794-7799, 2005.
DOI : 10.1073/pnas.0407994102

URL : http://www.pnas.org/content/102/22/7794.full.pdf

. Bibliography-[guimera, Modularity from fluctuations in random graphs and complex networks, Physical Review E, vol.70, issue.2, p.25101, 2004.

[. Gulikers, A spectral method for community detection in moderately-sparse degree-corrected stochastic block models, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01258191

[. Gulikers, A subspace estimator for fixed rank perturbations of large random matrices, Journal of Multivariate Analysis, vol.114, pp.427-447, 2013.

[. Hachem, Deterministic equivalents for certain functionals of large random matrices, The Annals of Applied Probability, vol.17, issue.3, pp.875-930, 2007.
DOI : 10.1214/105051606000000925

URL : https://hal.archives-ouvertes.fr/hal-00621793

[. Han, Consistent estimation of dynamic and multi-layer block models, International Conference on Machine Learning, pp.1511-1520, 2015.

. Hartigan, J. A. Wong-;-hartigan, and M. A. Wong, Algorithm as 136: A k-means clustering algorithm, Journal of the Royal Statistical Society. Series C (Applied Statistics), vol.28, issue.1, pp.100-108, 1979.

A. Hero and B. Rajaratnam, Large-scale correlation screening, Journal of the American Statistical Association, vol.106, issue.496, pp.1540-1552, 2011.
DOI : 10.1198/jasa.2011.tm11015

URL : http://arxiv.org/pdf/1102.1204.pdf

. Hoydis, Iterative deterministic equivalents for the performance analysis of communication systems, 2011.

[. Jin, Fast community detection by score, The Annals of Statistics, vol.43, issue.1, pp.57-89, 2015.
DOI : 10.1214/14-aos1265

URL : http://arxiv.org/pdf/1211.5803

[. Jordan, An introduction to variational methods for graphical models, Machine learning, vol.37, issue.2, pp.183-233, 1999.
DOI : 10.1007/978-94-011-5014-9_5

URL : http://www.cis.upenn.edu/~mkearns/papers/barbados/jgjs-var.pdf

A. Kammoun, R. Couillet, B. Karrer, M. E. Newman, T. Kawamoto et al., Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors, Physical Review E, vol.83, issue.1, p.62803, 2011.

[. Kim, Di?erential flattening: A novel framework for community detection in multi-layer graphs, ACM Transactions on Intelligent Systems and Technology, vol.8, issue.2, p.27, 2017.
DOI : 10.1145/2854006.2854013

URL : http://www.sigmod.org/publications/sigmod-record/1509/pdfs/03_letter_sigmod.pdf

[. Krzakala, Spectral redemption in clustering sparse networks, Proceedings of the National Academy of Sciences, vol.110, issue.52, pp.20935-20940, 2013.
DOI : 10.1073/pnas.1312486110

URL : https://hal.archives-ouvertes.fr/cea-01223434

[. Laloux, Random matrix theory and financial correlations, International Journal of Theoretical and Applied Finance, vol.3, issue.03, pp.391-397, 2000.

[. Lancichinetti, Benchmark graphs for testing community detection algorithms, Physical review E, vol.78, issue.4, p.46110, 2008.
DOI : 10.1103/physreve.78.046110

URL : http://arxiv.org/pdf/0805.4770

Y. Lecun, The mnist database of handwritten digits, 1998.

[. Lei, Consistency of spectral clustering in stochastic block models, The Annals of Statistics, vol.43, issue.1, pp.215-237, 2015.

[. Lesieur, Mmse of probabilistic low-rank matrix estimation: Universality with respect to the output channel, Communication, Control, and Computing (Allerton), 2015 53rd Annual Allerton Conference on, pp.680-687, 2015.
URL : https://hal.archives-ouvertes.fr/cea-01222294

[. Lesieur, Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications, Journal of Statistical Mechanics: Theory and Experiment, vol.2017, issue.7, p.73403, 2017.
DOI : 10.1088/1742-5468/aa7284

URL : https://hal.archives-ouvertes.fr/cea-01447222

[. Liao, Almost global convergence to global minima for gradient descent in deep linear networks

Z. Liao and R. Couillet, A large dimensional analysis of least squares support vector machines, 2017.

C. Liao, Z. Liao, and R. Couillet, On the spectrum of random features maps of high dimensional data, 2018.

. Lieberman-aiden, Comprehensive mapping of long-range interactions reveals folding principles of the human genome, Science, vol.326, issue.5950, pp.289-293, 2009.

. Bibliography-[linden, Amazon. com recommendations: Item-to-item collaborative filtering, IEEE Internet computing, vol.7, issue.1, pp.76-80, 2003.

[. Louart, A random matrix approach to neural networks, The Annals of Applied Probability, vol.28, issue.2, pp.1190-1248, 2018.
DOI : 10.1214/17-aap1328

URL : http://arxiv.org/pdf/1702.05419

[. Lyzinski, Perfect clustering for stochastic blockmodel graphs via adjacency spectral embedding, Electronic Journal of Statistics, vol.8, issue.2, pp.2905-2922, 2014.
DOI : 10.1214/14-ejs978

URL : http://doi.org/10.1214/14-ejs978

C. Mai, X. Mai, R. Couillet, V. A. Mar?enko, and L. A. Pastur, A random matrix analysis and improvement of semi-supervised learning for large dimensional data, Mathematics of the USSR-Sbornik, vol.1, issue.4, p.457, 1967.

P. Marchenko, V. A. Marchenko, and L. A. Pastur, Distribution of eigenvalues for some sets of random matrices, Matematicheskii Sbornik, vol.114, issue.4, pp.507-536, 1967.

[. Marcotte, Detecting protein function and protein-protein interactions from genome sequences, Science, vol.285, issue.5428, pp.751-753, 1999.
DOI : 10.1126/science.285.5428.751

URL : http://www.primate.or.kr/bioinformatics/biotutorial/protein/homology/comparative_genomics/comp1.pdf

L. Massoulié, Community detection thresholds and the weak ramanujan property, Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pp.694-703, 2014.

M. L. Mehta-;-mehta and T. P. Minka, Expectation propagation for approximate bayesian inference, Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence, vol.142, pp.362-369, 2001.

. Mossel, A proof of the block model threshold conjecture, Combinatorica, pp.1-44, 2013.

. Mossel, Reconstruction and estimation in the planted partition model. Probability Theory and Related Fields, vol.162, pp.431-461, 2015.
DOI : 10.1007/s00440-014-0576-6

[. Mucha, Community structure in time-dependent, multiscale, and multiplex networks, science, vol.328, issue.5980, pp.876-878, 2010.
DOI : 10.1126/science.1184819

URL : http://arxiv.org/pdf/0911.1824.pdf

. Nadakuditi, R. R. Newman-;-nadakuditi, and M. E. Newman, Graph spectra and the detectability of community structure in networks, Physical review letters, vol.108, issue.18, p.188701, 2012.

M. Newman, M. Newman, M. Newman, and M. E. Newman, Fast algorithm for detecting community structure in networks, Community detection in networks: Modularity optimization and maximum likelihood are equivalent, vol.69, p.66133, 2004.
DOI : 10.1103/physreve.69.066133

URL : http://arxiv.org/pdf/cond-mat/0309508

M. E. Newman and M. E. Newman, Finding community structure in networks using the eigenvectors of matrices, Proceedings of the National Academy of Sciences, vol.74, issue.3, pp.8577-8582, 2006.

. Ng, On spectral clustering: Analysis and an algorithm, Advances in neural information processing systems, vol.2, pp.849-856, 2002.

. Ng, The em algorithm, Handbook of computational statistics, pp.139-172, 2012.

L. Nicosia, V. Nicosia, and V. Latora, Measuring and modeling correlations in multiplex networks, Physical Review E, vol.92, issue.3, p.32805, 2015.

. Opper, . Saad, M. Opper, and D. Saad, Advanced mean field methods: Theory and practice, 2001.

[. Oselio, Information extraction from large multi-layer social networks, Acoustics, Speech and Signal Processing, pp.5451-5455, 2015.

[. Oselio, Multi-layer graph analysis for dynamic social networks, IEEE Journal of Selected Topics in Signal Processing, vol.8, issue.4, pp.514-523, 2014.

L. A. Pastur, M. Shcherbina, S. Paul, Y. Chen, S. Paul et al., Eigenvalue distribution of large random matrices, Community detection in multirelational data with restricted multi-layer stochastic blockmodel, vol.171, 2011.

T. P. Peixoto, Inferring the mesoscale structure of layered, edgevalued, and time-varying networks, Physical Review E, vol.92, issue.4, p.42807, 2015.

J. Pennington and P. Worah, Nonlinear random matrix theory for deep learning, Advances in Neural Information Processing Systems, pp.2637-2646, 2017.

C. Pizzuti and A. Socievole, Many-objective optimization for community detection in multi-layer networks, Evolutionary Computation, pp.411-418, 2017.

T. Qin-and-rohe-;-qin and K. Rohe, Regularized spectral clustering under the degree-corrected stochastic blockmodel, Advances in Neural Information Processing Systems, pp.3120-3128, 2013.

R. , R. Reyes, P. Rodriguez, and A. , Stochastic blockmodels for exchangeable collections of networks, 2016.

[. Saade, Spectral clustering of graphs with the bethe hessian, Advances in Neural Information Processing Systems, pp.406-414, 2014.
URL : https://hal.archives-ouvertes.fr/cea-01140852

B. Schölkopf, The kernel trick for distances, Advances in neural information processing systems, pp.301-307, 2001.

S. Scholkopf, B. Scholkopf, and A. J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond, 2001.

. Silverstein, J. W. Bai-;-silverstein, and Z. Bai, On the empirical distribution of eigenvalues of a class of large dimensional random matrices, Journal of Multivariate analysis, vol.54, issue.2, pp.175-192, 1995.

[. Stanley, Clustering network layers with the strata multilayer stochastic block model, IEEE transactions on network science and engineering, vol.3, issue.2, pp.95-105, 2016.

[. Sweet, Hierarchical mixed membership stochastic blockmodels for multiple networks and experimental interventions. Handbook on mixed membership models and their applications, pp.463-488, 2014.

[. Bibliography and . Tang, Community detection via heterogeneous interaction analysis, Data Mining, 2009. ICDM'09. Ninth IEEE International Conference on, vol.25, pp.1-33, 2009.

[. Taylor, Enhanced detectability of community structure in multilayer networks through layer aggregation, vol.116, p.228301, 2016.

E. Telatar, Capacity of multi-antenna gaussian channels, Transactions on Emerging Telecommunications Technologies, vol.10, issue.6, pp.585-595, 1999.
DOI : 10.1002/ett.4460100604

URL : https://infoscience.epfl.ch/record/125918/files/On the Capacity of Multi-Antenna.pdf

[. Couillet, H. Ali, and R. Couillet, community detection in heterogeneous networks, Signals, Systems and Computers, 2016 50th Asilomar Conference on, pp.1385-1389, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01812036

[. Couillet, H. Ali, and R. Couillet, Performance analysis of spectral community detection in realistic graph models, Acoustics, Speech and Signal Processing, pp.4548-4552, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01633452

[. Couillet, H. Ali, and R. Couillet, Performance analysis of spectral community detection in realistic graph models, IEEE International Conference on Acoustics, Speech and Signal Processing, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01633452

[. , A. , C. Ali, H. Couillet, and R. , Improved spectral community detection in large heterogeneous networks, Journal of Machine Learning Research, vol.18, pp.1-49, 2018.

A. [tiomoko, Random matrix asymptotic of inner product kernel spectral clustering, International Conference on Acoustics, Speech and Signal Processing, 2018.

A. [tiomoko, Random matrix-improved kernels for large dimensional spectral clustering, Statistical Signal Processing Workshop (SSP), pp.1-4, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01812009

A. [tiomoko, , 2018.

. Valles-catala, Multilayer stochastic block models reveal the multilayer structure of complex networks, Physical Review X, vol.6, issue.1, p.11036, 2016.

[. Von-luxburg, Consistency of spectral clustering, The Annals of Statistics, pp.555-586, 2008.

[. Bibliography and . Wainwright, Graphical models, exponential families, and variational inference, Foundations and Trends R in Machine Learning, vol.1, issue.1-2, pp.1-305, 2008.

C. Wei, Y. Wei, and C. Cheng, Characteristic vectors of bordered matrices with infinite dimensions ii, The Collected Works of Eugene Paul Wigner, pp.541-545, 1989.

[. Wilson, Community extraction in multilayer networks with heterogeneous community structure, The Journal of Machine Learning Research, vol.18, issue.1, pp.5458-5506, 2017.

J. Wishart, The generalised product moment distribution in samples from a normal multivariate population, Biometrika, pp.32-52, 1928.

. Xiang, Multi-resolution modularity methods and their limitations in community detection, The European Physical Journal B, vol.85, issue.10, p.352, 2012.

[. Yedidia, Understanding belief propagation and its generalizations. Exploring artificial intelligence in the new millennium, vol.8, pp.236-239, 2003.

[. Zeng, Coherent closed quasi-clique discovery from large dense graph databases, Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp.797-802, 2006.

A. Y. Zhang and H. H. Zhou, Theoretical and computational guarantees of mean field variational inference for community detection, 2017.

[. Zhang, User community discovery from multi-relational networks, Decision Support Systems, vol.54, issue.2, pp.870-879, 2013.

[. Zhao, Consistency of community detection in networks under degree-corrected stochastic block models, The Annals of Statistics, vol.40, issue.4, pp.2266-2292, 2012.