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- Bregman centroids (closed-forms) and symmetrized Bregman centroids (usually not in closed-form).
When dealing with exponential families, Kullback-Leibler centroids amount to Bregman centroids.

Sided and Symmetrized Bregman Centroids (IEEE TIT, 2009)

- Jeffreys centroids, the symmetrized Kullback-Leibler centroids (closed-form for positive non-normalized distributions
and guaranteed approximations for probability distributions).

Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms (IEEE SPL, 2013)

- Dual pair of centroids for mixed divergences (closed-form for mixed alpha-divergences).

On Clustering Histograms with k-Means by Using Mixed alpha-Divergences (Entropy 2014)

- Jensen centroids (including Jensen-Shannon centroids), also called Burbea-Rao centroids,
and skewed Jensen centroids (with Bregman centroids in limit cases).

- The Burbea-Rao and Bhattacharyya Centroids (IEEE TIT, 2011)
- Jensen divergence based SPD matrix means and applications (ICPR 2012)

- Robust total Bregman centroids.

Shape retrieval using hierarchical total Bregman soft clustering (IEEE PAMI, 2012)

- Robust (and non-robust) total Jensen centroids.

Total Jensen divergences: Definition, properties and clustering (ICASSP 2015)

- Conformal centroids (wrt. conformal divergences).

On Conformal Divergences and Their Population Minimizers (IEEE TIT 2016)

- Symmetrized skewed centroids smoothly generalizing Jensen-Shannon centroids and Jeffreys centroids.

A family of statistical symmetric divergences based on Jensen's inequality (arxiv 2010)

- Divergences based on Shannon, Rényi, Tsallis, Sharma-Mittal entropies have closed-form formula for distributions belonging to the same exponential family.
- Entropies and cross-entropies of exponential families (ICIP 2010)
- On Rényi and Tsallis entropies and divergences for exponential families (arxiv 2011)
- A closed-form expression for the Sharma-Mittal entropy of exponential families (Journal of Physics A: Mathematical and Theoretical, 2012)

- Chernoff divergence (called Chernoff information) can be exactly characterized geometrically with closed-form for uni-order exponential famlies.

An Information-Geometric Characterization of Chernoff Information (IEEE SPL 2013)

Chernoff information of exponential families (arxiv 2011)

- Kullback-Leibler divergence of statistical mixtures is not analytic, but get deterministic lower and upper bounds
using log-sum-exp inequalities.

- Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities
- Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities(arxiv, IEEE SPL 2016)

- Model hyperbolic centroids (Fisher-Rao centroid of location-scale families).

Model centroids for the simplification of Kernel Density estimators (ICASSP 2012)

- Tailored divergences for closed-form formula on statistical mixtures: Cauchy-Schwarz divergence, Jensen-Rényi divergence.

Closed-Form Information-Theoretic Divergences for Statistical Mixtures (ICPR 2012)

- Approximations of arbitrary f-divergences for exponential families with natural affine parameter space.

On the chi square and higher-order chi distances for approximating f-divergences (IEEE SPL, 2014)

- Non-flat alpha-divergence probability centroids and flat alpha-divergence positive measure centroids.

Non-flat clustering with alpha-divergences (ICASSP 2011)

- Finsler centroids (and medians).

Medians and means in Finsler geometry (LMS Journal of Computation and Mathematics 2012)

- Optimal copula transport: Copulas can be used to either analyze the intra-dependence of
a multivariate time series or the inter-dependence between two time series.

Optimal copula transport for clustering multivariate time series (ICASSP 2016)

- Fisher-Rao geodesic distance between copulas.

Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Series (IEEE SSP 2016)

- Euclidean circumcenter.
- Bregman circumcenter.

- On the smallest enclosing information disk (IPL 2008)
- Fitting the Smallest Enclosing Bregman Ball (ECML 2005)

- Riemannian minimax center.

On approximating the Riemannian 1-center (DCG 2013)

- Hyperbolic circumcenter.

- Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry

- Hyperbolic Voronoi Diagrams Made Easy (ICCSA 2010)
- Wasserstein centroids.

Fast Computation of Wasserstein Barycenters, Marco Cuturi, Arnaud Doucet, 2013 (ICML 2014).

Tsallis Regularized Optimal Transport and Ecological Inference (arxiv 2016)

- Projective divergences and projective centroids.

Patch matching with polynomial exponential families and projective divergences (SISAP 2016)

Last updated in November 2016 by Frank Nielsen. - Wasserstein centroids.

- Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry