Asynchronous Nonlinear Updates on Graphs

Teke, Oguzhan; Vaidyanathan, P.P.

doi:10.1109/acssc.2018.8645351

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…We note that U C N ¢pN-mq has orthonormal columns, i.e., U H U I and prove the upper bound in (8) first.…”

Section: Appendix a Proof Of Lemmamentioning

confidence: 85%

“…When the matrix A is considered as a local graph operator, i.e., the adjacency matrix, or the graph Laplacian, the scheme in (2) models the random asynchronous behavior of the nodes of a graph. 7,8 In this setting, the random asynchronous model (2) allows us to design polynomial graph filters that result in clustering algorithms for autonomous networks. 7,8 When extended to have a constant input signal, the model (2) is also useful for a node-asynchronous implementation of rational filters on graphs.…”

Section: Random Component-wise Power Methodsmentioning

confidence: 99%

“…7,8 In this setting, the random asynchronous model (2) allows us to design polynomial graph filters that result in clustering algorithms for autonomous networks. 7,8 When extended to have a constant input signal, the model (2) is also useful for a node-asynchronous implementation of rational filters on graphs. 9,20 When A is viewed as a data matrix, which is the case to be considered in this study, the component-wise updates of (2) allow distributed computation of the dominant eigenvector since the rows of A need not be accessed simultaneously.…”

Section: Random Component-wise Power Methodsmentioning

confidence: 99%

“…The values of the unselected indices remain unchanged. This randomized variant is first proposed in order to study the behavior of autonomous networks [7][8][9] in the context of graph signal processing. Here we will consider the randomized update scheme from a purely linear algebraic point of view.…”

Section: Introductionmentioning

confidence: 99%

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The random component-wise power method

Teke

Vaidyanathan

2019

Wavelets and Sparsity XVIII

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This paper considers a random component-wise variant of the unnormalized power method, which is similar to the regular power iteration except that only a random subset of indices is updated in each iteration. For the case of normal matrices, it was previously shown that random component-wise updates converge in the mean-squared sense to an eigenvector of eigenvalue 1 of the underlying matrix even in the case of the matrix having spectral radius larger than unity. In addition to the enlarged convergence regions, this study shows that the eigenvalue gap does not directly affect the convergence rate of the randomized updates unlike the regular power method. In particular, it is shown that the rate of convergence is affected by the phase of the eigenvalues in the case of random component-wise updates, and the randomized updates favor negative eigenvalues over positive ones. As an application, this study considers a reformulation of the component-wise updates revealing a randomized algorithm that is proven to converge to the dominant left and right singular vectors of a normalized data matrix. The algorithm is also extended to handle large-scale distributed data when computing an arbitrary rank approximation of an arbitrary data matrix. Numerical simulations verify the convergence of the proposed algorithms under different parameter settings.

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“…We note that U C N ¢pN-mq has orthonormal columns, i.e., U H U I and prove the upper bound in (8) first.…”

Section: Appendix a Proof Of Lemmamentioning

confidence: 85%