2020
DOI: 10.48550/arxiv.2009.01983
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Density estimation and modeling on symmetric spaces

Abstract: In many applications, data and/or parameters are supported on non-Euclidean manifolds. It is important to take into account the geometric structure of manifolds in statistical analysis to avoid misleading results. Although there has been a considerable focus on simple and specific manifolds, there is a lack of general and easy-to-implement statistical methods for density estimation and modeling on manifolds. In this article, we consider a very broad class of manifolds: non-compact Riemannian symmetric spaces. … Show more

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“…Our current technique focuses on but is not limited to the spherical dataset. Similar designs of loss functions can be generalized to a wider variety of spaces like symmetric spaces (Li et al, 2020) using multivariate decomposition technique like ICA, and a wider range of datasets like binary datasets (Landgraf and Lee, 2020). DR methods that do not incorporate the information of the global geometry or topology well enough would lead to the problematic results (Figure 1.1).…”
Section: Discussion and Future Workmentioning
confidence: 99%
“…Our current technique focuses on but is not limited to the spherical dataset. Similar designs of loss functions can be generalized to a wider variety of spaces like symmetric spaces (Li et al, 2020) using multivariate decomposition technique like ICA, and a wider range of datasets like binary datasets (Landgraf and Lee, 2020). DR methods that do not incorporate the information of the global geometry or topology well enough would lead to the problematic results (Figure 1.1).…”
Section: Discussion and Future Workmentioning
confidence: 99%