no code implementations • 1 Oct 2023 • T. Mitchell Roddenberry, Vishwanath Saragadam, Maarten V. de Hoop, Richard G. Baraniuk
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains.
no code implementations • 18 Mar 2023 • T. Mitchell Roddenberry, Vincent P. Grande, Florian Frantzen, Michael T. Schaub, Santiago Segarra
We establish a framework for signal processing on product spaces of simplicial and cellular complexes.
no code implementations • 11 Feb 2023 • T. Mitchell Roddenberry, Santiago Segarra
We consider the task of representing signals supported on graph bundles, which are generalizations of product graphs that allow for "twists" in the product structure.
no code implementations • 11 Jul 2022 • Samuel Rey, T. Mitchell Roddenberry, Santiago Segarra, Antonio G. Marques
Guided by this, we first assume that we have a reference graph that is related to the sought graph (in the sense of having similar motif densities) and then, we exploit this relation by incorporating a similarity constraint and a regularization term in the network topology inference optimization problem.
no code implementations • 22 Feb 2022 • T. Mitchell Roddenberry, Fernando Gama, Richard G. Baraniuk, Santiago Segarra
Leveraging this, we are able to seamlessly compare graphs of different sizes and coming from different models, yielding results on the convergence of spectral densities, transferability of filters across arbitrary graphs, and continuity of graph signal properties with respect to the distribution of local substructures.
no code implementations • 11 Oct 2021 • T. Mitchell Roddenberry, Michael T. Schaub, Mustafa Hajij
The processing of signals supported on non-Euclidean domains has attracted large interest recently.
no code implementations • 17 Sep 2021 • T. Mitchell Roddenberry, Florian Frantzen, Michael T. Schaub, Santiago Segarra
We first show that the Hodge Laplacian can be used in lieu of the graph Laplacian to construct a family of wavelets for higher-order signals on simplicial complexes.
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 • 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 • 6 Apr 2021 • Michael Weylandt, George Michailidis, T. Mitchell Roddenberry
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains.
2 code implementations • 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 • 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.
no code implementations • 8 Dec 2020 • Michael Weylandt, T. Mitchell Roddenberry, Genevera I. Allen
In contrast to common practice which denoises then clusters, our method is a unified, convex approach that performs both simultaneously.
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 • 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.