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On the low-rank approach for semidefinite programs arising in synchronization and community detection [article]

Afonso S. Bandeira, Nicolas Boumal, Vladislav Voroninski
2016 arXiv   pre-print
We focus on Synchronization and Community Detection problems and provide theoretical guarantees shedding light on the remarkable efficiency of this heuristic.  ...  Over a decade ago, exploiting the fact that in many applications of interest the desired solutions are low rank, Burer and Monteiro proposed a heuristic to solve such semidefinite programs by restricting  ...  ASB acknowledges Wotao Yin for pointing the author to the relevant reference (Wen and Yin, 2013) which helped motivate the start of the investigation in this paper.  ... 
arXiv:1602.04426v2 fatcat:fvae5k6wdvdklapftrwudnx2ku

Inference on graphs via semidefinite programming

Afonso S. Bandeira
2016 Proceedings of the National Academy of Sciences of the United States of America  
[DKMZ11] used tools from statistical physics to make remarkably precise predictions of the performance of belief propagation in Community Detection and, based on those, conjectured the exact location of  ...  In a nutshell, the idea is to have each node record its confidence of belonging to one of the communities and, in each iteration, have each node observe the confidences of all its neighbors and update  ...  Bandeira was supported by NSF grant DMS-1317308 and acknowledges insightful discussions with Emmanuel Abbe, Gérard Ben Arous, Florent  ... 
doi:10.1073/pnas.1603405113 pmid:27071125 pmcid:PMC4843415 fatcat:jvi7aknjffhjfa6vwkx3mqjusu

Multiuser Detection in CDMA—A Comparison of Relaxations, Exact, and Heuristic Search Methods

P.H. Tan, L.K. Rasmussen
2004 IEEE Transactions on Wireless Communications  
In this paper, we compare several optimization methods for solving the optimal multiuser detection problem exactly or approximately.  ...  When the number of users increases, the tabu search method is more effective and efficient than the semidefinite relaxation approach.  ...  Dropping the rank one constraint yields the basic semidefinite relaxation [31] of (9) (10) This is known as a semidefinite program in the matrix variable , because it is a linear problem in with the  ... 
doi:10.1109/twc.2004.834699 fatcat:apk2fy3ihnbufmmwbf5bmuvqnu

Block-Coordinate Minimization for Large SDPs with Block-Diagonal Constraints [article]

Yulun Tian, Kasra Khosoussi, Jonathan P. How
2019 arXiv   pre-print
The so-called Burer-Monteiro method is a well-studied technique for solving large-scale semidefinite programs (SDPs) via low-rank factorization.  ...  Hence, in such problems, the Burer-Monteiro approach can provide a scalable and reliable alternative to interior-point methods that scale poorly.  ...  Bandeira, Nicolas Boumal, and Vladislav Voroninski. On the low-rank approach for semidefinite programs arising in synchronization and community de- tection.  ... 
arXiv:1903.00597v4 fatcat:s2hkbwcuabgq3g2lspvrrjyotm

Solving Orthogonal Group Synchronization via Convex and Low-Rank Optimization: Tightness and Landscape Analysis [article]

Shuyang Ling
2020 arXiv   pre-print
It has found many applications in community detection, clock synchronization, and joint alignment problem.  ...  In this work, we first study the semidefinite programming (SDP) relaxation of the orthogonal group synchronization and its tightness, i.e., the SDP estimator is exactly equal to the least squares estimator  ...  In [8] , the authors prove that the optimization landscape is benign for Z 2 -synchronization as well as community detection under the stochastic block model if p = 2.  ... 
arXiv:2006.00902v1 fatcat:pkgajpzbabactdojwnfubgpos4

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics [article]

Anirudha Majumdar, Georgina Hall, Amir Ali Ahmadi
2019 arXiv   pre-print
In this paper, we survey recent approaches for addressing this challenge including (i) approaches for exploiting structure (e.g., sparsity and symmetry) in a problem, (ii) approaches that produce low-rank  ...  Our hope is that this paper will serve as a gateway to the rich and exciting literature on scalable semidefinite programming for both theorists and practitioners.  ...  ACKNOWLEDGMENTS We thank Cemil Dibek for his constructive feedback on the first draft of this manuscript.  ... 
arXiv:1908.05209v3 fatcat:g2vqfhv27vgddbv7l4xciywf4u

A near-optimal multiuser detector for ds-cdma systems using semidefinite programming relaxation

X.M. Wang, W.-S. Lu, A. Antoniou
2003 IEEE Transactions on Signal Processing  
A multiuser detector for direct-sequence code-division multiple-access systems based on semidefinite programming (SDP) is proposed.  ...  Index Terms-Duality theory, maximum likelihood detection, multiuser detection, semidefinite programming.  ...  The use of semidefinite programming was also explored recently in [5] and [6] .  ... 
doi:10.1109/tsp.2003.815382 fatcat:j3u6ac37arhnnjd57p42ow4qxy

On the simplicity and conditioning of low rank semidefinite programs [article]

Lijun Ding, Madeleine Udell
2021 arXiv   pre-print
Low rank matrix recovery problems appear widely in statistics, combinatorics, and imaging. One celebrated method for solving these problems is to formulate and solve a semidefinite program (SDP).  ...  Moreover, we show that simplicity holds generically, and also for many structured low rank matrix recovery problems, including the stochastic block model, ℤ_2 synchronization, and matrix completion.  ...  We would also like to thank the editor and anonymous reviewers for their feedback.  ... 
arXiv:2002.10673v2 fatcat:4kwvof5yvzb7jofhgs455kpiza

Sync-Rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and Semidefinite Programming Synchronization [article]

Mihai Cucuringu
2015 arXiv   pre-print
Finally, synchronization-based ranking, combined with a spectral technique for the densest subgraph problem, allows one to extract locally-consistent partial rankings, in other words, to identify the rank  ...  We propose a similar synchronization-based algorithm for the rank-aggregation problem, which integrates in a globally consistent ranking pairwise comparisons given by different rating systems on the same  ...  He would like to thank Andrea Bertozzi for her support via AFOSR MURI grant FA9550-10-1-0569, Alex d'Aspremont and Fajwel Fogel for useful discussions on their Serial-Rank algorithm and pointers to the  ... 
arXiv:1504.01070v1 fatcat:tmm36aduofcrdpxj3jqvpjm7gq

Sync-Rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and SDP Synchronization

Mihai Cucuringu
2016 IEEE Transactions on Network Science and Engineering  
Existing theoretical guarantees on the group synchronization problem imply lower bounds on the largest amount of noise permissible in the data while still achieving exact recovery of the ground truth ranking  ...  We propose a similar synchronization-based algorithm for the rank-aggregation problem, which integrates in a globally consistent ranking many pairwise rank-offsets or partial rankings, given by different  ...  He would like to thank Andrea Bertozzi for her support via AFOSR MURI grant FA9550-10-1-0569, Alex d'Aspremont and Fajwel Fogel for useful discussions on their Serial-Rank algorithm and pointers to the  ... 
doi:10.1109/tnse.2016.2523761 fatcat:q4rro2hnnncylghhqkem4xfgai

Random Laplacian matrices and convex relaxations [article]

Afonso S. Bandeira
2015 arXiv   pre-print
It easily implies the optimality of the semidefinite relaxation approaches to problems such as Z_2 Synchronization and Stochastic Block Model recovery.  ...  The main tool is a recent estimate on the spectral norm of matrices with independent entries by van Handel and the author.  ...  The author acknowledges Amit Singer, Emmanuel Abbe, Ramon van Handel, and Georgina Hall for many insightful discussions on the topic of this paper and, specialy, for motivating the author to write this  ... 
arXiv:1504.03987v2 fatcat:kpyyp5uccbf77ghhopai5z5hqq

Synchronization overZ2and community detection in signed multiplex networks with constraints

Mihai Cucuringu
2015 Journal of Complex Networks  
When one has the additional information that certain subsets of nodes represent the same unknown group element, we consider and compare several algorithms based on spectral, semidefinite programming (SDP  ...  Here, we focus on synchronization over Z_2, and consider the problem of identifying communities in a multiplex network when the interaction between the nodes is described by a signed (possibly weighted  ...  We gratefully acknowledge the SAMSI Institute for hosting the year-long program in Complex Networks, providing support, and facilitating discussions via workshops and research meetings.  ... 
doi:10.1093/comnet/cnu050 fatcat:c3exykkusnhrtkc7gpf34lfibe

Compressed sensing applied to weather radar

Kumar Vijay Mishra, Anton Kruger, Witold F. Krajewski
2014 2014 IEEE Geoscience and Remote Sensing Symposium  
Ground clutter is sparse and the weather signal is low-rank. The addition of two is a corrupted low-rank matrix. XPOL-5 data as observed on 25 May, 2013.  ...  SDPT3 (Tütüncü et al. 2003 ) solver for the semidefinite programs.  ... 
doi:10.1109/igarss.2014.6946811 dblp:conf/igarss/MishraKK14 fatcat:mc6kcyx4engrpcdldpaabl5gsi

Linear inverse problems on Erdős-Rényi graphs: Information-theoretic limits and efficient recovery

Emmanuel Abbe, Afonso S. Bandeira, Annina Bracher, Amit Singer
2014 2014 IEEE International Symposium on Information Theory  
In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate.  ...  All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems.  ...  We also thank Yuxin Chen, Andrea Goldsmith, Peter Huang, and Leo Guibas for making their related then unpublished work [8] , [9] available to us following the announcement of this paper's results by  ... 
doi:10.1109/isit.2014.6875033 dblp:conf/isit/AbbeBBS14 fatcat:yeiecgwhcvd6dgoap2zkf6vcn4

Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix Estimation [article]

Yudong Chen, Yuejie Chi
2018 arXiv   pre-print
On one side, convex relaxations such as nuclear norm minimization often lead to statistically optimal procedures for estimating low-rank matrices, where first-order methods are developed to address the  ...  Attention is paid to rigorous characterization of the performance of these algorithms, and to problems where the low-rank matrix have additional structural properties that require new algorithmic designs  ...  Chen is supported in part by NSF under the CRII award 1657420 and grant CCF-1704828. The work  ... 
arXiv:1802.08397v3 fatcat:36g2hujdirdq3cjymurxslllhm
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