Methoden vergleichen

	Hellinger-Distanz	Jensen-Shannon-Divergenz
Fachgebiet	Entscheidungsfindung	Entscheidungsfindung
Familie	MCDM	MCDM
Entstehungsjahr	1909	1991
Urheber	Ernst Hellinger	J. Lin
Typ	Symmetric metric for probability distributions	Symmetric probability distribution dissimilarity
Wegweisende Quelle	Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die Reine und Angewandte Mathematik, 136, 210-271.	Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37(1), 145-151.
Aliasnamen	Bhattacharyya distance, Hellinger metric	JS divergence, symmetric KL divergence, JS distance
Verwandt	2	2
Zusammenfassung	Hellinger distance is a symmetric, bounded metric that measures the difference between two probability distributions. Rooted in the work of Ernst Hellinger (1909) and later formalized in statistical divergence by Anil Bhattacharyya (1946), this distance ranges from 0 (identical distributions) to 1. It is a true metric satisfying all mathematical distance properties and is particularly well-suited for comparing probability distributions in a symmetric, numerically stable manner.	Jensen-Shannon divergence is a symmetric information-theoretic measure of the difference between two probability distributions. Developed by Jian Lin in 1991 as a refinement to the asymmetric Kullback-Leibler divergence, it overcomes KL's directional limitation by averaging the divergences in both directions. The result is a true metric (satisfying triangle inequality) that ranges from 0 (identical distributions) to 1, making it suitable for symmetric comparison tasks.