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In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. When the points are interpreted as probability distributions – notably as either values of the parameter of a parametric model or as a data set of observed values – the resulting distance is a statistical distance. The most basic Bregman divergence is the squared Euclidean distance.

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  • Bregman divergence (en)
  • Divergence de Bregman (fr)
  • Дивергенция Брэгмана (ru)
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  • En mathématiques, la divergence de Bregman est une mesure de la différence entre deux distributions dérivée d'une fonction potentiel U à valeurs réelles strictement convexe et continûment différentiable. Le concept a été introduit par (en) en 1967.Par l'intermédiaire de la transformation de Legendre, au potentiel correspond un potentiel dual et leur différentiation donne naissance à deux systèmes de coordonnées duaux. (fr)
  • In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. When the points are interpreted as probability distributions – notably as either values of the parameter of a parametric model or as a data set of observed values – the resulting distance is a statistical distance. The most basic Bregman divergence is the squared Euclidean distance. (en)
  • Дивергенция Брэгмана или расстояние Брэгмана — мера расстояния между двумя точками, определённая в терминах строго выпуклой функции. Они образуют важный класс дивергенций. Если точки интерпретировать как распределение вероятностей, либо как значения , либо как набор наблюдаемых значений, то полученное расстояние является . Самой элементарной дивергенцией Брэгмана является квадрат евклидова расстояния. Дивергенция Брэгмана названа по имени Льва Мееровича Брэгмана, предложившего концепцию в 1967 году. (ru)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Bregman_divergence_diagram_used_in_proof_of_squared_generalized_Euclidean_distances.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Bregman_divergence_Pythagorean.png
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