10.4230/LIPICS.SOCG.2019.31
Edelsbrunner, Herbert
Herbert
Edelsbrunner0000-0002-9823-6833
Virk, Ziga
Ziga
Virk
Wagner, Hubert
Hubert
Wagner
Topological data analysis in information space
LIPIcs
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2019
2019-07-17T10:36:09Z
2020-01-21T13:21:35Z
conference
/record/6648
/record/6648.json
9783959771047
1903.08510
1355179 bytes
application/pdf
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 the usage of existing computational topology software in this context.