Controllability of Bandlimited Graph Processes Over Random Time Varying Graphs

Gama, Fernando; Isufi, Elvin; Ribeiro, Alejandro; Leus, Geert

doi:10.1109/tsp.2019.2952053

Cited by 25 publications

(13 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a finite small constant , the first constraint upper bound the quantization MSE in the cases of both fixed and decreasing quantization stepsizes [cf. (52)]. The second constraint aims to further reduce the quantization MSE where decreasing quantization stepsize is used through φ 1 .…”

Section: Filter Designmentioning

confidence: 99%

See 1 more Smart Citation

Quantization Analysis and Robust Design for Distributed Graph Filters

Saad

Beferull-Lozano

Isufi

2022

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

Distributed graph filters have recently found applications in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and reconstruction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities. Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the two most common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive analysis, we devise theoretical performance guarantees on the filter performance when the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more reduction of the quantization noise than in the fixed-stepsize quantization. For ARMA graph filters, we show that decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both timeinvariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.

show abstract

Section: Filter Designmentioning

confidence: 99%

“…Let also S, S t , and S denote, respectively, the shift operator of the underlying graph G, the graph realization G t at iteration t, and the expected graph Ḡ. Since graph G has an upper bounded shift operator S 2 ≤ ρ, all its realizations G t have also an upper bounded shift operator S t 2 ≤ S 2 ≤ ρ [52], [53].…”

Section: Graphsmentioning

confidence: 99%

Quantization Analysis and Robust Design for Distributed Graph Filters

Saad

Beferull-Lozano

Isufi

2022

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…We would like to note that the mean and mean-squared behavior of random graph processes have been of interest in recent years. For example, the study [49] considers the case of time varying graphs and considers the mean controllability of graph processes while providing mean-squared error analysis. Similarly, the study [50] studies graph processes from tracking viewpoint and provides mean and meansquared analysis of Kalman filtering over graphs.…”

Section: Second Order Stability Of the State Variablesmentioning

confidence: 99%

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Teke

Vaidyanathan

2021

IEEE Access

View full text Add to dashboard Cite

In graph signal processing signals are defined over a graph, and filters are designed to manipulate the variation of signals over the graph. On the other hand, time domain signal processing treats signals as time series, and digital filters are designed to manipulate the variation of signals in time. This study focuses on the notion of vertex-time filters, which manipulates the variation of a time-dependent graph signal both in the time domain and graph domain simultaneously. The key aspects of the proposed filtering operations are due to the random and asynchronous behavior of the nodes, in which they follow a collectcompute-broadcast scheme. For the analysis of the randomized vertex-time filtering operations, this study first considers the random asynchronous variant of linear discrete-time state-space models, in which each state variable gets updated randomly and independently (and asynchronously) in every iteration. Unlike previous studies that analyzed similar models under certain assumptions on the input signal, this study considers the model in the most general setting with arbitrary time-dependent input signals, which lay the foundations for the vertex-time graph filtering operations. This analysis shows that exponentials continue to be eigenfunctions in a statistical sense in spite of the random asynchronous nature of the model. This study also presents the necessary and sufficient condition for the mean-squared stability and shows that stability of the underlying state transition matrix is neither necessary nor sufficient for the mean-squared stability of the randomized asynchronous recursions. Then, the proposed filtering operations are proven to be mean-square stable if and only if the filter, the graph operator and the update probabilities satisfy a certain condition. The results show that some unstable vertex-time graph filters (in the synchronous case) can be implemented in a stable manner in the presence of randomized asynchronicity, which is also demonstrated by numerical examples.INDEX TERMS Autonomous networks, asynchronous updates, randomized iterations, vertex-time filters.

show abstract

“…Examples include path planning in multi-agent robotics [1], optimal power allocation in smart grids [2], or traffic coordination in smart cities [3]. The ability to control network dynamical systems thus becomes a technological problem of paramount importance [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Graph Neural Networks for Decentralized Controllers

Gama

Tolstaya

Ribeiro

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

View full text Add to dashboard Cite

Dynamical systems comprised of autonomous agents arise in many relevant problems such as multi-agent robotics, smart grids, or smart cities. Controlling these systems is of paramount importance to guarantee a successful deployment. Optimal centralized controllers are readily available but face limitations in terms of scalability and practical implementation. Optimal decentralized controllers, on the other hand, are difficult to find. In this paper, we propose a framework using graph neural networks (GNNs) to learn decentralized controllers from data. While GNNs are naturally distributed architectures, making them perfectly suited for the task, we adapt them to handle delayed communications as well. Furthermore, they are equivariant and stable, leading to good scalability and transferability properties. The problem of flocking is explored to illustrate the potential of GNNs in learning decentralized controllers.

show abstract

Controllability of Bandlimited Graph Processes Over Random Time Varying Graphs

Cited by 25 publications

References 43 publications

Quantization Analysis and Robust Design for Distributed Graph Filters

Quantization Analysis and Robust Design for Distributed Graph Filters

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Graph Neural Networks for Decentralized Controllers

Contact Info

Product

Resources

About