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robust graph Filter Identification and graph Denoising From signal Observations

IEEE TRANSACTIONS ON signal processing 2023年 71卷 3651-3666页

作者： Rey, Samuel Tenorio, Victor M. Marques, Antonio G. King Juan Carlos Univ Dept Signal Theory & Commun Madrid 28933 Spain

When facing graph signal processing tasks, it is typically assumed that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observational errors and perturbations. As a result, any method that relies on the graph topology and ignores the presence of perturbations may yield suboptimal results. Motivated by this, we propose a novel approach for handling perturbations on the links of the graph and apply it to the problem of robust graph filter (GF) identification from input-output observations. Different from existing works, we formulate a non-convex optimization problem that operates in the vertex domain and jointly performs GF identification and graph denoising. As a result, on top of learning the desired GF, an estimate of the graph is obtained as a byproduct. To handle the resulting bi-convex problem, we design an algorithm that blends techniques from alternating optimization and majorization minimization, showing its convergence to a stationary point. The second part of the paper i) generalizes the design to a robust setup where several GFs are jointly estimated, and ii) introduces an alternative algorithmic implementation that reduces the computational complexity. Finally, the detrimental influence of the perturbations and the benefits resulting from the robust approach are numerically analyzed over synthetic and real-world datasets, comparing them with other state-of-the-art alternatives.

关键词： graph filter identification graph denoising robust graph signal processing graph perturbations

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BLIND DECONVOLUTION OF SPARSE graph signalS IN THE PRESENCE OF PERTURBATIONS 49

BLIND DECONVOLUTION OF SPARSE GRAPH SIGNALS IN THE PRESENCE ...

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49th IEEE International Conference on Acoustics, Speech, and signal processing (ICASSP)

作者： Tenorio, Victor M. Rey, Samuel Marques, Antonio G. King Juan Carlos Univ Dept Signal Theory & Commun Madrid Spain

ISBN: (纸本)9798350344868;9798350344851

Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional assumptions, such as the sources being sparse, to be solvable. This paper addresses the blind deconvolution problem in the presence of imperfect graph information, where the observed graph is a perturbed version of the (unknown) true graph. While not having perfect knowledge of the graph is arguably more the norm than the exception, the body of literature on this topic is relatively small. This is partly due to the fact that translating the uncertainty about the graph topology to standard graph signal processing tools (e.g. eigenvectors or polynomials of the graph) is a challenging endeavor. To address this limitation, we propose an optimization-based estimator that solves the blind identification in the vertex domain, aims at estimating the inverse of the generating filter, and accounts explicitly for additive graph perturbations. Preliminary numerical experiments showcase the effectiveness and potential of the proposed algorithm.

关键词： graph Filter Identification Sparse recovery graph Denoising robust graph signal processing

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robust graph Neural Network based on graph Denoising 57

Robust Graph Neural Network based on Graph Denoising

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57th Asilomar Conference on signals, Systems and Computers

作者： Tenorio, Victor M. Rey, Samuel Marques, Antonio G. King Juan Carlos Univ Dept Signal Theory & Commun Madrid Spain

ISBN: (纸本)9798350325744

graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to errors stemming from observational noise, graph-learning limitations, or adversarial attacks. If ignored, these perturbations may drastically hinder the performance of GNNs. To address this limitation, this work proposes a robust implementation of GNNs that explicitly accounts for the presence of perturbations in the observed topology. For any task involving GNNs, our core idea is to i) solve an optimization problem not only over the learnable parameters of the GNN but also over the true graph, and ii) augment the fitting cost with a term accounting for discrepancies on the graph. Specifically, we consider a convolutional GNN based on graph filters and follow an alternating optimization approach to handle the (non-differentiable and constrained) optimization problem by combining gradient descent and projected proximal updates. The resulting algorithm is not limited to a particular type of graph and is amenable to incorporating prior information about the perturbations. Finally, we assess the performance of the proposed method through several numerical experiments.

关键词： graph Neural Networks Non-Euclidean Data robust graph signal processing graph Perturbations

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robust graph-FILTER IDENTIFICATION WITH graph DENOISING REGULARIZATION

ROBUST GRAPH-FILTER IDENTIFICATION WITH GRAPH DENOISING REGU...

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IEEE International Conference on Acoustics, Speech and signal processing (ICASSP)

作者： Rey, Samuel Marques, Antonio G. King Juan Carlos Univ Dept Signal Theory & Commun Madrid Spain

ISBN: (纸本)9781728176055

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance. Tailored to those setups, this paper presents a robust formulation for the problem of graph-filter identification from input-output observations. Different from existing works, our approach consists in addressing the robust identification by formulating a joint graph denoising and graph-filter identification problem. Such a problem is formulated as a nonconvex optimization, suitable relaxations are proposed, and graph-stationarity assumptions are incorporated to enhance performance. Finally, numerical experiments with synthetic and real-world graphs are used to assess the proposed schemes and compare them with existing (robust) alternatives.

关键词： robust graph signal processing graph denoising robust filter identification

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graph signal processing in the Presence of Topology Uncertainties

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IEEE TRANSACTIONS ON signal processing 2020年第0期68卷 1558-1573页

作者： Ceci, Elena Barbarossa, Sergio Sapienza Univ Rome Dept Informat Engn Elect & Telecommun I-00184 Rome Italy

The goal of this paper is to expand graph signal processing tools to deal with cases where the graph topology is not perfectly known. Assuming that the uncertainty affects only a limited number of edges, we make use of small perturbation analysis to derive closed form expressions instrumental to formulate signal processing algorithms that are resilient to imperfect knowledge of the graph topology. Then, we formulate a Bayesian approach to estimate the presence/absence of uncertain edges based only on the observed data and on the statistics of the data. Finally, we exploit our perturbation analysis to analyze clustering and semi-supervised learning algorithms. Numerical tests confirm the benefits of our perturbation-aware methods.

关键词： Perturbation methods Topology Laplace equations Uncertainty signal processing Network topology robustness graph topologies random networks robust graph signal processing small perturbation analysis

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