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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 for Multivariate Time Series Data [PDF]
Entropy, 2023 Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities.
Anass B. El-Yaagoubi +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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Topological data analysis in single cell biology [PDF]
Frontiers in ImmunologySingle-cell technologies have revolutionized our ability to interrogate biological systems at unprecedented resolution, revealing complex cellular heterogeneity and dynamic processes that underlie development, disease, and immune responses.
Enrique Hernández-Lemus
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A novel method for subgroup discovery in precision medicine based on topological data analysis [PDF]
BMC Medical Informatics and Decision MakingBackground The Mapper algorithm is a data mining topological tool that can help us to obtain higher level understanding of disease by visualising the structure of patient data as a similarity graph.
Ciara F. Loughrey +5 more
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A universal null-distribution for topological data analysis [PDF]
Scientific Reports, 2023 One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams arising from data. Despite much effort and its many successful applications, this is largely an open problem.
Omer Bobrowski, Primoz Skraba
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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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Statistical inference for dependence networks in topological data analysis [PDF]
Frontiers in Artificial Intelligence, 2023 Topological data analysis (TDA) provide tools that are becoming increasingly popular for analyzing multivariate time series data. One key aspect in analyzing multivariate time series is dependence between components.
Anass B. El-Yaagoubi +2 more
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