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Morency, M.W. (author), Leus, G.J.T. (author)Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the graph shift operator. Our approach is to investigate the question of graph filtering on a graph about...journal article 2021
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Leus, G.J.T. (author), Segarra, Santiago (author), Ribeiro, Alejandro (author), Marques, Antonio G. (author)Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph shift operator (GSO), which is a sparse matrix accounting...journal article 2021
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Leus, G.J.T. (author), Yang, Maosheng (author), Coutino, Mario (author), Isufi, E. (author)To deal with high-dimensional data, graph filters have shown their power in both graph signal processing and data science. However, graph filters process signals exploiting only pairwise interactions between the nodes, and they are not able to exploit more complicated topological structures. Graph Volterra models, on the other hand, are also...conference paper 2021
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Coutino, Mario (author), Isufi, E. (author), Maehara, T. (author), Leus, G.J.T. (author)In this work, we explore the state-space formulation of network processes to recover the underlying network structure (local connections). To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology inference problem. This approach provides a unified view of the traditional...conference paper 2020
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Li, Qiongxiu (author), Coutino, Mario (author), Leus, G.J.T. (author), Christensen, M. Graesboll (author)With an increasingly interconnected and digitized world, distributed signal processing and graph signal processing have been proposed to process its big amount of data. However, privacy has become one of the biggest challenges holding back the widespread adoption of these tools for processing sensitive data. As a step towards a solution, we...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), 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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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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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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Coutino, Mario (author), Chepuri, S.P. (author), Leus, G.J.T. (author)In this work, we address the problem of identifying the underlying network structure of data. Different from other approaches, which are mainly based on convex relaxations of an integer problem, here we take a distinct route relying on algebraic properties of a matrix representation of the network. By describing what we call possible...conference paper 2018
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Isufi, E. (author), Di Lorenzo, Paolo (author), Banelli, Paolo (author), Leus, G.J.T. (author)This paper proposes strategies for distributed Wiener-based reconstruction of graph signals from subsampled measurements. Given a stationary signal on a graph, we fit a distributed autoregressive moving average graph filter to a Wiener graph frequency response and propose two reconstruction strategies: i) reconstruction from a single temporal...conference paper 2018
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Chepuri, S.P. (author), Eldar, Yonina C. (author), Leus, G.J.T. (author)In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior...conference paper 2018
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Chepuri, S.P. (author), Coutino, Mario (author), Marques, Antonio G. (author), Leus, G.J.T. (author)An analytical algebraic approach for distributed network identification is presented in this paper. The information propagation in the network is modeled using a state-space representation. Using the observations recorded at a single node and a known excitation signal, we present algorithms to compute the eigenfrequencies and eigenmodes of...conference paper 2018
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Gama, F. (author), Isufi, E. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)In this work, we jointly exploit tools from graph signal processing and control theory to drive a bandlimited graph signal that is being diffused on a random time-varying graph from a subset of nodes. As our main contribution, we rely only on the statistics of the graph to introduce the concept of controllability in the mean, and therefore...conference paper 2018
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Ortiz-Jimenez, Guillermo (author), Coutino, Mario (author), Chepuri, S.P. (author), Leus, G.J.T. (author)In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The...conference paper 2018
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Segarra, Santiago (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)A novel scheme for sampling graph signals is proposed. Space-shift sampling can be understood as a hybrid scheme that combines selection sampling -- observing the signal values on a subset of nodes - and aggregation sampling - observing the signal values at a single node after successive aggregation of local data. Under the assumption of...conference paper 2016