Blind Identification of Graph Filters

IEEE Trans. Signal Process.

et al. 2020

Self Cite

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes' labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.

Section: A Source Localizationmentioning

confidence: 99%

Invariance-Preserving Localized Activation Functions for Graph Neural Networks

Ruiz

Gama

IEEE Trans. Signal Process.

et al. 2020

Self Cite

“…3(c) assesses the reconstruction performance for different types of signals. 'Linear' signals are created following a linear diffusion process of the form xLinear = T −1 t=0 htA t s, where s is a sparse signal and T = 6 [6]. 'Median' signals are created from linear signals where the value of each node is the median of its neighbours.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Assuming complete knowledge of the graph, early GSP efforts focused on the rigorous definition and analysis of linear graph filters, This work was supported by the Spanish grants MINECO TEC2016-75361-R, Instituto de Salud Carlos III DTS17/00158, and FPU17/04520. graph Fourier representations, and their application to inverse problems such as denoising, deconvolution, or sampling and reconstruction, to name a few [3][4][5][6]. More recent efforts focus on identifying the supporting graph, developing robust GSP schemes, analyzing higher-dimensional graph signals, and developing nonlinear GSP architectures.…”

Section: Introductionmentioning

confidence: 99%

An Underparametrized Deep Decoder Architecture for Graph Signals

Rey

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

Segarra

2019

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While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform state-of-the-art methods in several tasks such as image compression and denoising. Motivated by the fact that many contemporary datasets have an irregular structure different from a 1D/2D grid, this paper generalizes untrained and underparametrized non-convolutional architectures to signals defined over irregular domains represented by graphs. The proposed architecture consists of a succession of layers, each of them implementing an upsampling operator, a linear feature combination, and a scalar nonlinearity. A novel element is the incorporation of upsampling operators accounting for the structure of the supporting graph, which is achieved by considering a systematic graph coarsening approach based on hierarchical clustering. The numerical results carried out in synthetic and real-world datasets showcase that the reconstruction performance can improve drastically if the information of the supporting graph topology is taken into account.

“…In this experiment, we consider a graph G with N nodes and generate graph diffusion processes x(t) [17] with origin at an arbitrary node c. Suppose that G has adjacency matrix W and that x(0) = x 0 , where x 0 is such that [x 0 ] i = 1 if and only if i = c and 0 everywhere else. The diffused signals x(t), t = 1, 2, .…”

Section: Source Localization On Facebook and Twittermentioning

confidence: 99%

Median Activation Functions for Graph Neural Networks

Ruiz

Gama

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

et al. 2019

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Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaningful representations of network data. However, LSI-GFs fail to encode local nonlinear graph signal behavior, and so do regular activation functions, which are nonlinear but pointwise. To address this issue, we propose median activation functions with support on graph neighborhoods instead of individual nodes. A GNN architecture with a trainable multirresolution version of this activation function is then tested on synthetic and real-word datasets, where we show that median activation functions can improve GNN capacity with marginal increase in complexity.