Results 11 to 20 of about 426,517 (268)
Topological analysis of data [PDF]
EPJ Data Science, 2017 Propelled by a fast evolving landscape of techniques and datasets, data science is growing rapidly. Against this background, topological data analysis (TDA) has carved itself a niche for the analysis of datasets that present complex interactions and rich
Alice Patania +2 more
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Topological Information Data Analysis [PDF]
Entropy, 2019 This paper presents methods that quantify the structure of statistical interactions within a given data set, and were applied in a previous article.
Pierre Baudot +3 more
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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists
Frontiers in Artificial Intelligence, 2021 With the recent explosion in the amount, the variety, and the dimensionality of available data, identifying, extracting, and exploiting their underlying structure has become a problem of fundamental importance for data analysis and statistical learning ...
Frédéric Chazal, Bertrand Michel
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Topological Data Analysis with Bregman Divergences [PDF]
, 2016 Given a finite set in a metric space, the topological analysis generalizes hierarchical clustering using a 1-parameter family of homology groups to quantify connectivity in all dimensions.
Edelsbrunner, Herbert, Wagner, Hubert
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Topological Data Analysis for Particulate Gels
ACS NanoSoft gels, formed via the self-assembly of particulate organic materials, exhibit intricate multi-scale structures that provides them with flexibility and resilience when subjected to external stresses. This work combines molecular simulations and topological data analysis (TDA) to characterize the complex multi-scale structure of soft gels.
Alexander D. Smith +3 more
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Scientific Reports, 2022 The roughness of material surfaces is of greatest relevance for applications. These include wear, friction, fatigue, cytocompatibility, or corrosion resistance.
Jan F. Senge +4 more
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Topological data analysis and machine learning
Advances in Physics: X, 2023 Topological data analysis refers to approaches for systematically and reliably computing abstract ‘shapes’ of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest among physicists.
Daniel Leykam, Dimitris G. Angelakis
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, 2022 It has been observed since a long time that data are often carrying interesting topological and geometric structures. Characterizing such structures and providing efficient tools to infer and exploit them is a challenging problem that asks for new mathematics and that is motivated by a real need from applications.
Boissonnat, Jean-Daniel +2 more
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Topological data analysis [PDF]
Nature Photonics, 2018 Topological data analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. These methods include clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.
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Cluster Persistence for Weighted Graphs
Entropy, 2023 Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology.
Omer Bobrowski, Primoz Skraba
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