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04/20/2023
Architectures of Topological Deep Learning: A Survey on Topological Neural Networks
The natural world is full of complex systems characterized by intricate ...
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06/01/2022
Higher-Order Attention Networks
This paper introduces higher-order attention networks (HOANs), a novel c...
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10/11/2021
Signal Processing on Cell Complexes
The processing of signals supported on non-Euclidean domains has attract...
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10/06/2021
Data-Centric AI Requires Rethinking Data Notion
The transition towards data-centric AI requires revisiting data notions ...
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03/06/2021
Simplicial Complex Representation Learning
Simplicial complexes form an important class of topological spaces that ...
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02/25/2021
Persistent Homology and Graphs Representation Learning
This article aims to study the topological invariant properties encoded ...
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02/16/2021
Topological Deep Learning: Classification Neural Networks
Topological deep learning is a formalism that is aimed at introducing to...
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01/21/2021
TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images
Topological Data Analysis (TDA) has emerged recently as a robust tool to...
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12/02/2020
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
One of the central problems in the interface of deep learning and mathem...
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10/02/2020
Cell Complex Neural Networks
Cell complexes are topological spaces constructed from simple blocks cal...
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08/31/2020
A Topological Framework for Deep Learning
We utilize classical facts from topology to show that the classification...
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05/10/2020
PageRank and The K-Means Clustering Algorithm
We introduce a graph clustering algorithm that generalizes k-means to gr...
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02/12/2020
Graph Similarity Using PageRank and Persistent Homology
The PageRank of a graph is a scalar function defined on the node set of ...
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12/20/2019
Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial
We examine the structure and dimensionality of the Jones polynomial usin...
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09/04/2019
Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs
With the popularization of Topological Data Analysis, the Reeb graph has...
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06/22/2019
TopoLines: Topological Smoothing for Line Charts
Line charts are commonly used to visualize a series of data samples. Whe...
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04/21/2019
Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions
We use persistent homology along with the eigenfunctions of the Laplacia...
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11/05/2018
Integrating Project Spatial Coordinates into Pavement Management Prioritization
To date, pavement management software products and studies on optimizing...
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10/18/2018
An Efficient Data Retrieval Parallel Reeb Graph Algorithm
The Reeb graph of a scalar function defined on a domain gives a topologi...
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07/09/2018
Inferring Quality in Point Cloud-based 3D Printed Objects using Topological Data Analysis
Assessing the quality of 3D printed models before they are printed remai...
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01/18/2018
Graph Based Analysis for Gene Segment Organization In a Scrambled Genome
DNA rearrangement processes recombine gene segments that are organized o...
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12/15/2017
Driving Interactive Graph Exploration Using 0-Dimensional Persistent Homology Features
Graphs are commonly used to encode relationships among entities, yet, th...
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12/11/2017
Distributed Mapper
The construction of Mapper has emerged in the last decade as a powerful ...
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10/24/2017
The Shape of an Image: A Study of Mapper on Images
We study the topological construction called Mapper in the context of si...
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07/20/2017
Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology
Topological data analysis is an emerging area in exploratory data analys...
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08/23/2016