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.
Journal of Computational Geometry
This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7
Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.
Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.
Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
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