Related papers: Persistent Homology Transform for Modeling Shapes …
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Data analysis that uses the output of topological data analysis as input for machine learning algorithms has been the subject of extensive research. This approach offers a means of capturing the global structure of data. Persistent homology…
We present a topology-informed approach for classifying particle jets using persistent homology, a framework that captures the structural properties of point clouds. Particle jets produced in proton-proton collisions consist of cascades of…
Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models,…
In many scientific and technological contexts we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…
The persistent homology of a stationary point process on ${\bf R}^N$ is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops,…