6 citations · 24 across the 21 of their papers we have counts for
25 papers
TopoEmbedX: A General Framework for Representation Learning on Topological Domains
Florian Frantzen, Ibrahem AlJabea, Ines Henriques-Cadby +3
Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in…
A repository for discovery and reuse of higher-order network datasets
Florian Frantzen, Michael T. Schaub
Higher-order network datasets are dispersed across publications, institutional archives, and software-specific collections, making them difficult to discover, compare, and reuse. W…
Robustness of Reinforcement Learning-Based Congestion Management in Low-Voltage Grids
Josef Hoppe, Sarra Bouchkati, Farah Nasr +7
Increases in photovoltaic generation, charging of electric vehicles and heat-pump demand challenge operating limits in low-voltage distribution grids. This requires curative curtai…
RAwR: Role-Aware Rewiring via Approximate Equitable Partition
Riccardo Porcedda, Giuseppe Squillace, Bastian Epping +4
While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of…
Faster Inference of Cell Complexes from Flows via Matrix Factorization
Til Spreuer, Josef Hoppe, Michael T. Schaub
We consider the following inference problem: Given a set of edge-flow signals observed on a graph, lift the graph to a cell complex, such that the observed edge-flow signals can be…
Global Ground Metric Learning with Applications to scRNA data
Damin Kühn, Michael T. Schaub
Optimal transport provides a robust framework for comparing probability distributions. Its effectiveness is significantly influenced by the choice of the underlying ground metric.…
Don't be Afraid of Cell Complexes! An Introduction from an Applied Perspective
Josef Hoppe, Vincent P. Grande, Michael T. Schaub
Cell complexes (CCs) are a higher-order network model deeply rooted in algebraic topology that has gained interest in signal processing and network science recently. The processing…
HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection
Florian Frantzen, Michael T. Schaub
In this paper, we propose HLSAD, a novel method for detecting anomalies in time-evolving simplicial complexes. While traditional graph anomaly detection techniques have been extens…
A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals
Lennard Rompelberg, Michael T. Schaub
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of…
Topological Trajectory Classification and Landmark Inference on Simplicial Complexes
Vincent P. Grande, Josef Hoppe, Florian Frantzen +1
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project th…
TopoBench: A Framework for Benchmarking Topological Deep Learning
Lev Telyatnikov, Guillermo Bernardez, Marco Montagna +34
This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL int…
Point-Level Topological Representation Learning on Point Clouds
Vincent P. Grande, Michael T. Schaub
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homol…
Random Abstract Cell Complexes
Josef Hoppe, Michael T. Schaub
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erdős-Rényi model for graphs and its extensions for simplicial complexes. To build a random…
Learning From Simplicial Data Based on Random Walks and 1D Convolutions
Florian Frantzen, Michael T. Schaub
Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computatio…
Ellipsoidal embeddings of graphs
Michaël Fanuel, Antoine Aspeel, Michael T. Schaub +1
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently on…
Position: Topological Deep Learning is the New Frontier for Relational Learning
Theodore Papamarkou, Tolga Birdal, Michael Bronstein +19
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new fron…
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
Mustafa Hajij, Mathilde Papillon, Florian Frantzen +40
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: h…
A Wasserstein Graph Distance Based on Distributions of Probabilistic Node Embeddings
Michael Scholkemper, Damin Kühn, Gerion Nabbefeld +3
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a d…
Faster optimal univariate microgaggregation
Felix I. Stamm, Michael T. Schaub
Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least points, thereby providing a -anonymity type disclosure guarantee…
Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou +3
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need t…
Representing Edge Flows on Graphs via Sparse Cell Complexes
Josef Hoppe, Michael T. Schaub
Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a…
Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal
Vincent P. Grande, Michael T. Schaub
The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classificat…
Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH
Vincent P. Grande, Michael T. Schaub
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtratio…
ICML 2023 Topological Deep Learning Challenge : Design and Results
Mathilde Papillon, Mustafa Hajij, Helen Jenne +53
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competi…