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Found 27 papers, 7 papers with code
Position Paper: Challenges and Opportunities in Topological Deep Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
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: hypergraphs, simplicial, cellular, path and combinatorial complexes.
Topo-MLP : A Simplicial Network Without Message Passing
To overcome such limitations, we propose Topo-MLP, a purely MLP-based simplicial neural network algorithm to learn the representation of elements in a simplicial complex without explicitly relying on message passing.
Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs
In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e. g., to develop a spectral theory.
ICML 2023 Topological Deep Learning Challenge : Design and Results
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.
Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks
The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.
Topological Deep Learning: Going Beyond Graph Data
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations.
Signal Processing on Cell Complexes
The processing of signals supported on non-Euclidean domains has attracted large interest recently.
Data-Centric AI Requires Rethinking Data Notion
The transition towards data-centric AI requires revisiting data notions from mathematical and implementational standpoints to obtain unified data-centric machine learning packages.
Singquandles, Psyquandles and Singular Knots: A Survey
These enhancements include a singquandle cocycle invariant and several polynomial invariants of singular knots obtained from the singquandle structure.
Geometric Topology
Simplicial Complex Representation Learning
In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved.
Persistent Homology and Graphs Representation Learning
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology.
Topological Deep Learning: Classification Neural Networks
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning problem.
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 extract and compare the structure of datasets.
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
The deep networks obtained via \textbf{AIDN} are \textit{algebraically-informed} in the sense that they satisfy the algebraic relations of the presentation of the algebraic structure that serves as the input to the algorithm.
Cell Complex Neural Networks
Cell complexes are topological spaces constructed from simple blocks called cells.
A Topological Framework for Deep Learning
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions.
PageRank and The K-Means Clustering Algorithm
We utilize the PageRank vector to generalize the $k$-means clustering algorithm to directed and undirected graphs.
Fast and Scalable Complex Network Descriptor Using PageRank and Persistent Homology
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph.
Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial
We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques.
Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions
We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds.
Integrating Project Spatial Coordinates into Pavement Management Prioritization
To date, pavement management software products and studies on optimizing the prioritization of pavement maintenance and rehabilitation (M&R) have been mainly focused on three parameters; the pre-treatment pavement condition, the rehabilitation cost, and the available budget.
An Efficient Data Retrieval Parallel Reeb Graph Algorithm
That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure.
Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs
Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints.
Graph Based Analysis for Gene Segment Organization In a Scrambled Genome
The analysis shows some emerging star-like graph structures indicating that segments of a single gene can interleave, or even contain all of the segments from fifteen or more other genes in between its segments.
Parallel Mapper
The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees.
The Shape of an Image: A Study of Mapper on Images
We study the topological construction called Mapper in the context of simply connected domains, in particular on images.
