Accelerating consensus by spectral clustering and polynomial filters

Simon Apers 1 Alain Sarlette 2
2 QUANTIC - QUANTum Information Circuits
Inria de Paris, MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - Paris, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a second-order filtering is investigated in more detail. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters and can favor symmetry breaking. A possible loss of robustness of the polynomial filter is also highlighted.
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https://hal.inria.fr/hal-01093939
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Simon Apers, Alain Sarlette. Accelerating consensus by spectral clustering and polynomial filters. IEEE Transactions on Control of Network Systems, IEEE, 2016. ⟨hal-01093939⟩

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