Spectral redemption in clustering sparse networks
Florent Krzakala,Cristopher Moore,Elchanan Mossel,Joe Neeman,Allan Sly,Lenka Zdeborová,Pan Zhang +6 more
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TLDR
A way of encoding sparse data using a “nonbacktracking” matrix, and it is shown that the corresponding spectral algorithm performs optimally for some popular generative models, including the stochastic block model.Abstract:
Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here, we present a class of spectral algorithms based on a nonbacktracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all of the way down to the theoretical limit. We also show the spectrum of the nonbacktracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.read more
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Machine learning and the physical sciences
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TL;DR: This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences, including conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields.
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Vital nodes identification in complex networks
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