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The orthogonal group synchronization problem, which focuses on recovering orthogonal group elements from their corrupted pairwise measurements, encompasses examples such as high-dimensional Kuramoto model on general signed networks, $\mathbb{Z}_2$-synchronization, community detection under stochastic block models, and orthogonal Procrustes problem.
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A. S. Bandeira, Y. Khoo, and A. Singer · 2014
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Exact recovery in the stochastic block model
E. Abbe, A. S. Bandeira, and G. Hall · 2015
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N. Boumal · 2015
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K. N. Chaudhury, Y. Khoo, and A. Singer · 2015
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On the low-rank approach for semidefinite programs arising in synchronization and community detection
A. S. Bandeira, N. Boumal, and V. Voroninski · 2016
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Nonconvex phase synchronization
N. Boumal · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
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B. Hajek, Y. Wu, and J. Xu · 2016
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H. Maron, N. Dym, I. Kezurer, S. Kovalsky, and Y. Lipman · 2016
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A. Moitra, W. Perry, and A. S. Wein · 2016
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Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs
N. Boumal, V. Voroninski, and A. S. Bandeira · 2020
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High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally
J. Markdahl, J. Thunberg, and J. Goncalves · 2020
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Lifting sum-of-squares lower bounds: degree-2 to degree-4
S. Mohanty, P. Raghavendra, and J. Xu · 2020
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Dense networks that do not synchronize and sparse ones that do
A. Townsend, M. Stillman, and S. H. Strogatz · 2020
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Rank optimality for the Burer–Monteiro factorization
I. Waldspurger and A. Waters · 2020
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Sufficiently dense Kuramoto networks are globally synchronizing
M. Kassabov, S. H. Strogatz, and A. Townsend · 2021
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E. Abbe · 2017
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Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
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On the estimation performance and convergence rate of the generalized power method for phase synchronization
H. Liu, M.-C. Yue, and A. Man-Cho So · 2017
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Almost global consensus on the n n -sphere
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Expander graphs are globally synchronising
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A global synchronization theorem for oscillators on a random graph
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