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no code implementations • 12 Sep 2021 • Zhongyuan Zhao, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

To overcome this limitation, we propose fast heuristics based on graph convolutional networks (GCNs) that can be implemented in centralized and distributed manners.

no code implementations • 16 Aug 2021 • Gunnar Carlsson, Facundo Mémoli, Santiago Segarra

We begin by introducing three practical properties associated with the notion of robustness in hierarchical clustering: linear scale preservation, stability, and excisiveness.

no code implementations • 14 Jun 2021 • Michael T. Schaub, Jean-Baptiste Seby, Florian Frantzen, T. Mitchell Roddenberry, Yu Zhu, Santiago Segarra

Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i. e., the higher-order or multi-way relations connecting the constituent entities.

no code implementations • 31 May 2021 • David Ramírez, Antonio G. Marques, Santiago Segarra

When either the input or the filter coefficients are known, this is tantamount to assuming that the signals of interest live on a subspace defined by the supporting graph.

no code implementations • 27 May 2021 • T. Mitchell Roddenberry, Yu Zhu, Santiago Segarra

With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature.

no code implementations • 19 May 2021 • Yu Zhu, Ananthram Swami, Santiago Segarra

On the other hand, we propose a matrix factorization method based on a loss function that generalizes that of the skip-gram model with negative sampling to arbitrary similarity matrices.

1 code implementation • 20 Feb 2021 • Cameron R. Wolfe, Jingkang Yang, Arindam Chowdhury, Chen Dun, Artun Bayer, Santiago Segarra, Anastasios Kyrillidis

The graph convolutional network (GCN) is a go-to solution for machine learning on graphs, but its training is notoriously difficult to scale both in terms of graph size and the number of model parameters.

1 code implementation • 19 Feb 2021 • Yu Zhu, Boning Li, Santiago Segarra

We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs).

1 code implementation • 19 Feb 2021 • T. Mitchell Roddenberry, Nicholas Glaze, Santiago Segarra

We consider the construction of neural network architectures for data on simplicial complexes.

no code implementations • 14 Jan 2021 • Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby, T. Mitchell Roddenberry, Santiago Segarra

In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing.

no code implementations • 24 Dec 2020 • Fernando J. Iglesias Garcia, Santiago Segarra, Antonio G. Marques

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data.

no code implementations • 17 Dec 2020 • T. Mitchell Roddenberry, Santiago Segarra, Anastasios Kyrillidis

We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems.

1 code implementation • 18 Nov 2020 • Abhishek Kumar, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

We study the problem of adaptive contention window (CW) design for random-access wireless networks.

1 code implementation • 18 Nov 2020 • Gojko Cutura, Boning Li, Ananthram Swami, Santiago Segarra

We study the temporal reconstruction of epidemics evolving over networks.

1 code implementation • 18 Nov 2020 • Arindam Chowdhury, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

We study the problem of optimal power allocation in a single-hop ad hoc wireless network.

1 code implementation • 18 Nov 2020 • Zhongyuan Zhao, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

In small- to middle-sized wireless networks with tens of links, even a shallow GCN-based MWIS scheduler can leverage the topological information of the graph to reduce in half the suboptimality gap of the distributed greedy solver with good generalizability across graphs and minimal increase in complexity.

no code implementations • 21 Oct 2020 • Chiraag Kaushik, T. Mitchell Roddenberry, Santiago Segarra

We assume that signals on the nodes of the graph are regularized by the underlying graph structure via a graph filtering model, which we then leverage to distill the graph topology change-point detection problem to a subspace detection problem.

no code implementations • 16 Oct 2020 • Madeline Navarro, Yuhao Wang, Antonio G. Marques, Caroline Uhler, Santiago Segarra

Inferring graph structure from observations on the nodes is an important and popular network science task.

no code implementations • 15 Oct 2020 • T. Mitchell Roddenberry, Madeline Navarro, Santiago Segarra

In particular, we consider the case where the graph was drawn from a graphon model, and we supplement our convex optimization problem with a provably-valid regularizer on the spectrum of the graph to be recovered.

1 code implementation • 22 Sep 2020 • Arindam Chowdhury, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

We study the problem of optimal power allocation in a single-hop ad hoc wireless network.

no code implementations • 2 Aug 2020 • Antonio G. Marques, Santiago Segarra, Gonzalo Mateos

This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs).

no code implementations • 2 Aug 2019 • Samuel Rey, Antonio G. Marques, Santiago Segarra

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.

no code implementations • 22 May 2019 • Michael T. Schaub, Santiago Segarra, John N. Tsitsiklis

We consider a blind identification problem in which we aim to recover a statistical model of a network without knowledge of the network's edges, but based solely on nodal observations of a certain process.

1 code implementation • 17 May 2019 • Junteng Jia, Michael T. Schaub, Santiago Segarra, Austin R. Benson

The first strategy selects edges to minimize the reconstruction error bound and works well on flows that are approximately divergence-free.

no code implementations • 26 Apr 2019 • Michael T. Schaub, Santiago Segarra, Hoi-To Wai

We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network.

no code implementations • 5 Sep 2018 • Hoi-To Wai, Santiago Segarra, Asuman E. Ozdaglar, Anna Scaglione, Ali Jadbabaie

The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals.

no code implementations • 28 Jul 2017 • Marco Avella-Medina, Francesca Parise, Michael T. Schaub, Santiago Segarra

Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size.

no code implementations • 18 Oct 2016 • Mark Eisen, Santiago Segarra, Gabriel Egan, Alejandro Ribeiro

We first study the similarity of writing styles between Early English playwrights by comparing the profile WANs.

no code implementations • 21 Jul 2016 • Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra

This paper considers networks where relationships between nodes are represented by directed dissimilarities.

no code implementations • 21 Jul 2016 • Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation.

no code implementations • 21 Jul 2016 • Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra

We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation.

no code implementations • 17 Jun 2014 • Santiago Segarra, Mark Eisen, Alejandro Ribeiro

Attribution accuracy is observed to exceed the one achieved by methods that rely on word frequencies alone.

no code implementations • 17 Apr 2014 • Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data.

no code implementations • 31 Jan 2013 • Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra

Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less.

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