So sánh phương pháp

	Khoảng cách Hellinger	Độ lệch Jensen-Shannon	Phân kỳ Kullback-Leibler
Lĩnh vực	Ra quyết định	Ra quyết định	Ra quyết định
Họ	MCDM	MCDM	MCDM
Năm ra đời	1909	1991	1951
Người khởi xướng	Ernst Hellinger	J. Lin	Solomon Kullback and Richard Leibler
Loại	Symmetric metric for probability distributions	Symmetric probability distribution dissimilarity	Asymmetric probability distribution dissimilarity
Công trình gốc	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.	Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22(1), 79-86.
Tên gọi khác	Bhattacharyya distance, Hellinger metric	JS divergence, symmetric KL divergence, JS distance	KL divergence, relative entropy, information divergence
Liên quan	2	2	2
Tóm tắt	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.	Kullback-Leibler divergence, also called relative entropy or information divergence, measures the asymmetric difference between two probability distributions. Introduced by Solomon Kullback and Richard Leibler in 1951, this information-theoretic measure quantifies how one probability distribution diverges from a reference distribution, ranging from 0 (identical distributions) to infinity. It is foundational in information theory, machine learning, and decision-making with probabilistic frameworks.