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Topological data analysis in information space - MaRDI portal

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Topological data analysis in information space

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Publication:5854564

DOI10.20382/JOCG.V11I2A7zbMATH Open1462.68171arXiv1903.08510OpenAlexW3135217630MaRDI QIDQ5854564

Author name not available (Why is that?)

Publication date: 17 March 2021

Abstract: 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 distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable usage of existing computational topology software in this context.


Full work available at URL: https://arxiv.org/abs/1903.08510




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