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Natali, A. (author), Isufi, E. (author), Leus, G.J.T. (author)The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To tackle this issue, we devise a new framework and...conference paper 2020
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Isufi, E. (author), Banelli, Paolo (author), Di Lorenzo, Paolo (author), Leus, G.J.T. (author)A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and...journal article 2020
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Coutino, Mario (author), Chepuri, Sundeep Prabhakar (author), Maehara, Takanori (author), Leus, G.J.T. (author)To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of...journal article 2020
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Yang, M. (author), Coutino, Mario (author), Isufi, E. (author), Leus, G.J.T. (author)While regularization on graphs has been successful for signal reconstruction, strategies for controlling the bias-variance trade-off of such methods have not been completely explored. In this work, we put forth a node varying regularizer for graph signal reconstruction and develop a minmax approach to design the vector of regularization...conference paper 2020
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Natali, A. (author), Coutino, Mario (author), Leus, G.J.T. (author)Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in...conference paper 2020
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Gama, F. (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a...journal article 2019
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Gama, Fernando (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)Convolutional neural networks (CNNs) restrict the, otherwise arbitrary, linear operation of neural networks to be a convolution with a bank of learned filters. This makes them suitable for learning tasks based on data that exhibit the regular structure of time signals and images. The use of convolutions, however, makes them unsuitable for...conference paper 2019
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Gama, F. (author), Isufi, E. (author), Ribeiro, Alejandro (author), Leus, G.J.T. (author)Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due to link failures such as changing friendships, road blocks or sensor malfunctions. Thus, it leads to...journal article 2019
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Coutino, Mario (author), Isufi, E. (author), Leus, G.J.T. (author)Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this paper generalizes state-of-the-art distributed graph filters to...journal article 2019
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Gama, F. (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)In this ongoing work, we describe several architectures that generalize convolutional neural networks (CNNs) to process signals supported on graphs. The general idea of the replace time invariant filters with graph filters to generate convolutional features and to replace pooling with sampling schemes for graph signals. The different...conference paper 2019
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Coutino, Mario (author), Isufi, E. (author), Maehara, Takanori (author), Leus, G.J.T. (author)In this work, we explore the limits of finite-time distributed consensus through the intersection of graph filters and matrix function theory. We focus on algorithms capable to compute the consensus exactly through filtering operations over a graph, and that have been proven to converge in finite time. In this context, we show that there...conference paper 2019
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Ortiz-Jimenez, Guillermo (author), Coutino, Mario (author), Chepuri, S.P. (author), Leus, G.J.T. (author)We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of...journal article 2019
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Gama, F. (author), Marques, Antonio G. (author), Ribeiro, Alejandro (author), Leus, G.J.T. (author)Graph neural networks (GNNs) regularize classical neural networks by exploiting the underlying irregular structure supporting graph data, extending its application to broader data domains. The aggregation GNN presented here is a novel GNN that exploits the fact that the data collected at a single node by means of successive local exchanges...conference paper 2019
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Gerstoft, Peter (author), Nannuru, Santosh (author), Mecklenbrauker, Christoph F. (author), Leus, G.J.T. (author)The paper considers direction of arrival (DOA) estimation from long-term observations in a very noisy environment. The concern is to derive methods obtaining reasonable DOAs at very low SNR. The noise is assumed zero-mean Gaussian and its variance varies in time and space, causing stationary data models to fit poorly over long observation...journal article 2019
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Coutino, Mario (author), Leus, G.J.T. (author)As the size of the sensor network grows, synchronization starts to become the main bottleneck for distributed computing. As a result, efforts in several areas have been focused on the convergence analysis of asynchronous computational methods. In this work, we aim to cross-pollinate distributed graph filters with results in parallel computing...conference paper 2019
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Di Lorenzo, Paolo (author), Banelli, Paolo (author), Isufi, E. (author), Barbarossa, Sergio (author), Leus, G.J.T. (author)The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly) time-varying subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS)...journal article 2018
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Liu, J. (author), Isufi, E. (author), Leus, G.J.T. (author)In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing autoregressive moving average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Prony's method, which...journal article 2018
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Coutino, Mario (author), Isufi, E. (author), Leus, G.J.T. (author)The main challenges distributed graph filters face in practice are the communication overhead and computational complexity. In this work, we extend the state-of-the-art distributed finite impulse response (FIR) graph filters to an edge-variant (EV) version, i.e., a filter where every node weights the signals from its neighbors with different...conference paper 2018
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Pribić, Radmila (author), Leus, G.J.T. (author)A stochastic approach to resolution based on information distances computed from the geometry of data models which is characterized by the Fisher information is explored. Stochastic resolution includes probability of resolution and signal-to-noise ratio (SNR). The probability of resolution is assessed from a hypothesis test by exploiting...conference paper 2018
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Liu, J. (author), Isufi, E. (author), Leus, G.J.T. (author)In graph signal processing, signals are processed by explicitly taking into account their underlying structure, which is generally characterized by a graph. In this field, graph filters play a major role to process such signals in the so-called graph frequency domain. In this paper, we focus on the design of autoregressive moving average ...conference paper 2018