153 citations · 253 across the 21 of their papers we have counts for
24 papers
Finsler Geometry, Graph Neural Networks, and You
T. Mitchell Roddenberry, Richard G. Baraniuk
Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators. As a nonlinear al…
The Geometric Structure of Models Learning Sparse Data
Thomas Walker, T. Mitchell Roddenberry, Ahmed Imtiaz Humayun +2
The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the trainin…
Rates and architectures for learning geometrically non-trivial operators
T. Mitchell Roddenberry, Leo Tzou, Ivan Dokmanić +2
Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from v…
Implicit Neural Representations and the Algebra of Complex Wavelets
T. Mitchell Roddenberry, Vishwanath Saragadam, Maarten V. de Hoop +1
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on E…
Signal Processing on Product Spaces
T. Mitchell Roddenberry, Vincent P. Grande, Florian Frantzen +2
We establish a framework for signal processing on product spaces of simplicial and cellular complexes. For simplicity, we focus on the product of two complexes representing time an…
Windowed Fourier Analysis for Signal Processing on Graph Bundles
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. Leveraging th…
Limits of Dense Simplicial Complexes
T. Mitchell Roddenberry, Santiago Segarra
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting o…
Enhanced graph-learning schemes driven by similar distributions of motifs
Samuel Rey, T. Mitchell Roddenberry, Santiago Segarra +1
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is t…
On Local Distributions in Graph Signal Processing
T. Mitchell Roddenberry, Fernando Gama, Richard G. Baraniuk +1
Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distribut…
Signal Processing on Cell Complexes
T. Mitchell Roddenberry, Michael T. Schaub, Mustafa Hajij
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs wi…
Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes
T. Mitchell Roddenberry, Florian Frantzen, Michael T. Schaub +1
We develop wavelet representations for edge-flows on simplicial complexes, using ideas rooted in combinatorial Hodge theory and spectral graph wavelets. We first show that the Hodg…
Signal processing on simplicial complexes
Michael T. Schaub, Jean-Baptiste Seby, Florian Frantzen +3
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 th…
An Impossibility Theorem for Node Embedding
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 t…
Sparse Partial Least Squares for Coarse Noisy Graph Alignment
Michael Weylandt, George Michailidis, T. Mitchell Roddenberry
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are avai…
Principled Simplicial Neural Networks for Trajectory Prediction
T. Mitchell Roddenberry, Nicholas Glaze, Santiago Segarra
We consider the construction of neural network architectures for data on simplicial complexes. In studying maps on the chain complex of a simplicial complex, we define three desira…
Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond
Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby +2
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing,…
Rank-One Measurements of Low-Rank PSD Matrices Have Small Feasible Sets
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. The setting we consider involves rank-one sens…
Simultaneous Grouping and Denoising via Sparse Convex Wavelet Clustering
Michael Weylandt, T. Mitchell Roddenberry, Genevera I. Allen
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perh…
Network topology change-point detection from graph signals with prior spectral signatures
Chiraag Kaushik, T. Mitchell Roddenberry, Santiago Segarra
We consider the problem of sequential graph topology change-point detection from graph signals. We assume that signals on the nodes of the graph are regularized by the underlying g…
Network Topology Inference with Graphon Spectral Penalties
T. Mitchell Roddenberry, Madeline Navarro, Santiago Segarra
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering…
Blind Inference of Eigenvector Centrality Rankings
T. Mitchell Roddenberry, Santiago Segarra
We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of grap…
Blind Estimation of Eigenvector Centrality from Graph Signals: Beyond Low-pass Filtering
T. Mitchell Roddenberry, Santiago Segarra
This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. W…
HodgeNet: Graph Neural Networks for Edge Data
T. Mitchell Roddenberry, Santiago Segarra
Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational struc…
Blind Inference of Centrality Rankings from Graph Signals
T. Mitchell Roddenberry, Santiago Segarra
We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information abou…