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08/18/2023
Random Walks, Conductance, and Resistance for the Connection Graph Laplacian
We investigate the concept of effective resistance in connection graphs,...
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08/01/2023
Neural approximation of Wasserstein distance via a universal architecture for symmetric and factorwise group invariant functions
Learning distance functions between complex objects, such as the Wassers...
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02/16/2023
Distances for Markov Chains, and Their Differentiation
(Directed) graphs with node attributes are a common type of data in vari...
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02/14/2023
Understanding Oversquashing in GNNs through the Lens of Effective Resistance
Message passing graph neural networks are popular learning architectures...
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02/07/2023
A generalization of the persistent Laplacian to simplicial maps
The graph Laplacian is a fundamental object in the analysis of and optim...
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02/01/2023
The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs
In this paper, we present a novel interpretation of the so-called Weisfe...
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01/27/2023
On the Connection Between MPNN and Graph Transformer
Graph Transformer (GT) recently has emerged as a new paradigm of graph l...
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01/06/2023
Principal Component Analysis in Space Forms
Principal component analysis (PCA) is a workhorse of modern data science...
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11/07/2022
Implicit Graphon Neural Representation
Graphons are general and powerful models for generating graphs of varyin...
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10/31/2022
The Numerical Stability of Hyperbolic Representation Learning
Given the exponential growth of the volume of the ball w.r.t. its radius...
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10/21/2022
Learning Ultrametric Trees for Optimal Transport Regression
Optimal transport provides a metric which quantifies the dissimilarity b...
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06/06/2022
On the Convergence of Optimizing Persistent-Homology-Based Losses
Topological loss based on persistent homology has shown promise in vario...
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02/05/2022
Weisfeiler-Lehman meets Gromov-Wasserstein
The Weisfeiler-Lehman (WL) test is a classical procedure for graph isomo...
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01/28/2022
Neural Approximation of Extended Persistent Homology on Graphs
Persistent homology is a widely used theory in topological data analysis...
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01/25/2022
Convergence of Invariant Graph Networks
Although theoretical properties such as expressive power and over-smooth...
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09/15/2021
Graph skeletonization of high-dimensional point cloud data via topological method
Geometric graphs form an important family of hidden structures behind da...
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04/15/2021
Approximation algorithms for 1-Wasserstein distance between persistence diagrams
Recent years have witnessed a tremendous growth using topological summar...
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04/12/2021
Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph
We present a SE(3)-equivariant graph neural network (GNN) approach that ...
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03/18/2021
Topology-Aware Segmentation Using Discrete Morse Theory
In the segmentation of fine-scale structures from natural and biomedical...
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02/02/2021
Graph Coarsening with Neural Networks
As large-scale graphs become increasingly more prevalent, it poses signi...
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12/04/2020
Persistent Laplacians: properties, algorithms and implications
The combinatorial graph Laplacian has been a fundamental object in the a...
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11/11/2020
Ordinally Consensus Subset over Multiple Metrics
In this paper, we propose to study the following maximum ordinal consens...
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06/23/2020
A Note on Over-Smoothing for Graph Neural Networks
Graph Neural Networks (GNNs) have achieved a lot of success on graph-str...
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03/20/2020
Detection and skeletonization of single neurons and tracer injections using topological methods
Neuroscientific data analysis has traditionally relied on linear algebra...
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03/10/2020
Elder-Rule-Staircodes for Augmented Metric Spaces
An augmented metric space is a metric space (X, d_X) equipped with a fun...
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01/27/2020
An efficient algorithm for 1-dimensional (persistent) path homology
This paper focuses on developing an efficient algorithm for analyzing a ...
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01/16/2020
Understanding the Power of Persistence Pairing via Permutation Test
Recently many efforts have been made to incorporate persistence diagrams...
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11/01/2019
A limit theorem for the 1st Betti number of layer-1 subgraphs in random graphs
We initiate the study of local topology of random graphs. The high level...
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09/15/2019
Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methods
Automatic Extraction of road network from satellite images is a goal tha...
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07/31/2019
A Structural Average of Labeled Merge Trees for Uncertainty Visualization
Physical phenomena in science and engineering are frequently modeled usi...
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07/31/2019
Intrinsic Interleaving Distance for Merge Trees
Merge trees are a type of graph-based topological summary that tracks th...
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04/27/2019
Learning metrics for persistence-based summaries and applications for graph classification
Recently a new feature representation and data analysis methodology base...
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03/20/2019
Local Versus Global Distances for Zigzag Persistence Modules
This short note establishes explicit and broadly applicable relationship...
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12/13/2018
The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs
Metric graphs are meaningful objects for modeling complex structures tha...
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12/06/2018
An Improved Cost Function for Hierarchical Cluster Trees
Hierarchical clustering has been a popular method in various data analys...
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12/06/2018
A New Cost Function for Hierarchical Cluster Trees
Hierarchical clustering has been a popular method in various data analys...
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11/08/2018
A simple yet effective baseline for non-attribute graph classification
Graphs are complex objects that do not lend themselves easily to typical...
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11/06/2018
FPT-algorithms for computing Gromov-Hausdorff and interleaving distances between trees
Gromov-Hausdorff (GH) distance is a natural way to measure the distortio...
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10/19/2018
Local cliques in ER-perturbed random geometric graphs
Random graphs are mathematical models that have applications in a wide r...
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06/27/2018
A Topological Regularizer for Classifiers via Persistent Homology
Regularization plays a crucial role in supervised learning. Most existin...
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06/27/2018
TopoReg: A Topological Regularizer for Classifiers
Regularization plays a crucial role in supervised learning. A successful...
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05/14/2018
Topological Skeletonization and Tree-Summarization of Neurons Using Discrete Morse Theory
Neuroscientific data analysis has classically involved methods for stati...
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03/14/2018
Graph Reconstruction by Discrete Morse Theory
Recovering hidden graph-like structures from potentially noisy data is a...
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01/21/2018
Efficient algorithms for computing a minimal homology basis
Efficient computation of shortest cycles which form a homology basis und...
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12/18/2017
Vietoris-Rips and Cech Complexes of Metric Gluings
We study Vietoris-Rips and Cech complexes of metric wedge sums and metri...
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06/20/2017
Unperturbed: spectral analysis beyond Davis-Kahan
Classical matrix perturbation results, such as Weyl's theorem for eigenv...
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07/06/2016
Graphons, mergeons, and so on!
In this work we develop a theory of hierarchical clustering for graphs. ...
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06/21/2015
Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering
Hierarchical clustering is a popular method for analyzing data which ass...
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11/28/2012