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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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Topological data analysis in information space
Journal of Computational Geometry, 2021 Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability
Herbert Edelsbrunner +2 more
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Topological data analysis with Bregman divergences
Journal of Computational Geometry, 2019 We show that the framework of topological data analysis can be extended from metrics to Bregman divergences, widening the scope of possible applications. Examples are the Kullback-Leibler divergence, which is commonly used for comparing text and images,
Herbert Edelsbrunner, Hubert Wagner
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Applications of Topological Data Analysis in Oncology [PDF]
Frontiers in Artificial Intelligence, 2021 The emergence of the information age in the last few decades brought with it an explosion of biomedical data. But with great power comes great responsibility: there is now a pressing need for new data analysis algorithms to be developed to make sense of ...
Anuraag Bukkuri +2 more
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Frontiers in Computational Neuroscience, 2021 Neuronal morphology is characterized by salient features such as complex axonal and dendritic arbors. In the mammalian brain, variations in dendritic morphology among cell classes, brain regions, and animal species are thought to underlie known ...
Reem Khalil +2 more
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Simplicial complex entropy for time series analysis
Scientific Reports, 2023 The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods ...
Lev Guzmán-Vargas +2 more
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Topology and Intelligent Data Analysis [PDF]
Intelligent Data Analysis, 2003 A broad range of mathematical techniques, ranging from statistics to fuzzy logic, have been used to great advantage in intelligent data analysis. Topology – the fundamental mathematics of shape – has to date been conspicuously absent from this repertoire.
Vanessa Robins +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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Towards quantum advantage via topological data analysis [PDF]
Quantum, 2022 Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce.
Casper Gyurik, Chris Cade, Vedran Dunjko
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