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03/14/2023
Meta-Diagrams for 2-Parameter Persistence
We first introduce the notion of meta-rank for a 2-parameter persistence...
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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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07/23/2022
The discriminating power of the generalized rank invariant
The rank invariant (RI), one of the best known invariants of persistence...
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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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11/30/2021
Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications
The notion of generalized rank invariant in the context of multiparamete...
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10/07/2021
The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation
The Gromov-Hausdorff distance (d_GH) provides a natural way of quantifyi...
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08/16/2021
Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach
We provide a complete taxonomic characterization of robust hierarchical ...
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07/04/2021
Persistent Cup-Length
Cohomological ideas have recently been injected into persistent homology...
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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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06/21/2020
The Gaussian Transform
We introduce the Gaussian transform (GT), an optimal transport inspired ...
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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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01/21/2020
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
In the applied algebraic topology community, the persistent homology ind...
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01/01/2020
Motivic clustering schemes for directed graphs
Motivated by the concept of network motifs we construct certain clusteri...
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12/28/2019
Persistent Homotopy Groups of Metric Spaces
We study notions of persistent homotopy groups of compact metric spaces ...
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10/21/2019
Sampling random graph homomorphisms and applications to network data analysis
A graph homomorphism is a map between two graphs that preserves adjacenc...
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05/31/2019
A Primer on Persistent Homology of Finite Metric Spaces
TDA (topological data analysis) is a relatively new area of research rel...
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12/03/2018
Stable Persistent Homology Features of Dynamic Metric Spaces
Characterizing the dynamics of time-evolving data within the framework o...
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10/26/2018
Generalized Persistence Diagrams for Persistence Modules over Posets
When a category C satisfies certain conditions, we define the notion of ...
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10/26/2018
Rank invariant for Zigzag Modules
The rank invariant is of great interest in studying both one-dimensional...
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10/17/2018
The Wasserstein transform
We introduce the Wasserstein transform, a method for enhancing and denoi...
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08/13/2018
The Gromov-Wasserstein distance between networks and stable network invariants
We define a metric---the Network Gromov-Wasserstein distance---on weight...
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05/28/2018
The reflection distance between zigzag persistence modules
By invoking the reflection functors introduced by Bernstein, Gelfand, an...
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04/09/2018
The Metric Space of Networks
We study the question of reconstructing a weighted, directed network up ...
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01/05/2018
The Reeb Graph Edit Distance is Universal
We consider the setting of Reeb graphs of piecewise linear functions and...
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01/02/2018
Sketching and Clustering Metric Measure Spaces
Two important optimization problems in the analysis of geometric data se...
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12/11/2017
Stable Signatures for Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence
When studying flocking/swarming behaviors in animals one is interested i...
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12/11/2017
Stable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology
When studying flocking/swarming behaviors in animals one is interested i...
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11/12/2017
Convergence of Hierarchical Clustering and Persistent Homology Methods on Directed Networks
While there has been much interest in adapting conventional clustering p...
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08/16/2017
Distances and Isomorphism between Networks and the Stability of Network Invariants
We develop the theoretical foundations of a network distance that has re...
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07/21/2016
Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks
This paper characterizes hierarchical clustering methods that abide by t...
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07/21/2016
Hierarchical Clustering of Asymmetric Networks
This paper considers networks where relationships between nodes are repr...
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09/15/2015
The Shape of Data and Probability Measures
We introduce the notion of multiscale covariance tensor fields (CTF) ass...
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04/17/2014
Hierarchical Quasi-Clustering Methods for Asymmetric Networks
This paper introduces hierarchical quasi-clustering methods, a generaliz...
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01/31/2013
Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks
This paper considers networks where relationships between nodes are repr...
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11/24/2010
Classifying Clustering Schemes
Many clustering schemes are defined by optimizing an objective function ...
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08/16/2008