A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Hua, Fei; Nassif, Roula; Richard, Cédric; Wang, Haiyan; Sayed, Ali H.

doi:10.23919/eusipco.2018.8553273

Cited by 16 publications

(38 citation statements)

References 21 publications

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“…with h (m) ∈ R N . If h (m) = h m 1 for all m, model (9) reduces to the node-invariant model (1). Otherwise, each node applies different weights to the shifted signal S m x.…”

Section: A Graph Filter and Data Modelmentioning

confidence: 99%

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

Hua

Nassif

Richard

et al. 2020

IEEE Trans. on Signal and Inf. Process. over Networks

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In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graph-shift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an ill-conditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and mean-square sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results.

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“…with h (m) ∈ R N . If h (m) = h m 1 for all m, model (9) reduces to the node-invariant model (1). Otherwise, each node applies different weights to the shifted signal S m x.…”

Section: A Graph Filter and Data Modelmentioning

confidence: 99%

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

Hua

Nassif

Richard

et al. 2020

IEEE Trans. on Signal and Inf. Process. over Networks

Self Cite

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“…(2) In that sense, any matrix which satisfies condition (2) can be used as a graph shift operator. This property of locality allows a distributed implementation [14]- [16]. There are, however, other types of shift operators which do not satisfy (2); See, e.g., the isometric operator in [6].…”

Section: Parametric Modeling Via Graph Filtersmentioning

confidence: 99%

Learning Combination of Graph Filters for Graph Signal Modeling

Hua

Richard

Chen

et al. 2019

IEEE Signal Process. Lett.

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In this letter, we study the problem of parametric modeling of network-structured signals with graph filters. Unlike the popular polynomial graph filters, which are based on a single graph shift operator, we consider convex combinations of graph shift operators particularly adapted to directed graphs. As the resulting modeling problem is not convex, we reformulate it as a convex optimization problem which can be solved efficiently. Experiments on real-world data structured by undirected and directed graphs are conducted. The results show the effectiveness of this method compared to other methods reported in the literature.

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“…Recentemente, em [7]- [9] foram aplicadas estratégias de adaptação difusa [10] para propor novas ferramentas para o processamento adaptativo de sinais sobre grafos, levando a soluções baseadas no algoritmo LMS (least-mean-squares). O algoritmo distribuído de [8] foi proposto com foco na predição de sinais sobre grafos e utiliza uma estratégia distribuída eficiente para a amostragem de sinais sobre grafos baseada em uma abordagem probabilística.…”

Section: Introductionunclassified

Amostragem adaptativa aplicada a um algoritmo difuso voltado a grafos

Tiglea¹,

Candido²,

Silva³

2019

Anais De XXXVII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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Resumo-O processamento de sinais em grafos tem atraído a atenção da comunidade científica por ser uma ferramenta interessante para lidar com grandes quantidades de dados interrelacionados. Recentemente, foi proposto um algoritmo difuso para a filtragem adaptativa de sinais sobre grafos. Entretanto, esse algoritmo apresenta um custo computacional elevado, pois todos os nós do grafo são amostrados mesmo em regime permanente. Neste trabalho,é proposto um método adaptativo de amostragem para esse algoritmo que permite uma redução no custo computacional em regime permanente preservando-se o desempenho do algoritmo. Tambémé apresentada uma análise para facilitar a escolha de seus parâmetros. Palavras-Chave-Processamento de sinais em grafos, amostragem em grafos, adaptação difusa, filtragem em grafos, combinações convexas. Abstract-Graph signal processing has attracted attention in the signal processing community, since it is an effective tool to deal with large quantities of interrelated data. Recently, a diffusion algorithm for graph adaptive filtering was proposed. However, it suffers from high computational cost since all nodes in the graph are sampled even in steady state. In this paper, we propose an adaptive sampling method for this solution that reduces the computational cost in steady state, while maintaining convergence rate and steady-state performance. We also present an analysis to give insights about proper choices for its adaptation parameters.

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A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Cited by 16 publications

References 21 publications

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

Learning Combination of Graph Filters for Graph Signal Modeling

Amostragem adaptativa aplicada a um algoritmo difuso voltado a grafos

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