手法を比較

	ブレイ・カーティス距離（Bray-Curtis Dissimilarity）	キャンベラ距離	ヘリンガー距離
分野	意思決定	意思決定	意思決定
系統	MCDM	MCDM	MCDM
提唱年	1957	1967	1909
提唱者	John Bray and John T. Curtis	Geoffrey Lance and William Williams	Ernst Hellinger
種類	Ecological community similarity measure	Normalized city-block distance	Symmetric metric for probability distributions
原典	Bray, J. R., & Curtis, J. T. (1957). An ordination of the upland forest communities of southern Wisconsin. Ecological Monographs, 27(4), 325-349.	Lance, G. N., & Williams, W. T. (1967). A general theory of classificatory sorting strategies. Computer Journal, 10(3), 271-277.	Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die Reine und Angewandte Mathematik, 136, 210-271.
別名	Bray-Curtis index, Sorensen-Bray-Curtis, percentage difference	Canberra metric, normalized Manhattan distance	Bhattacharyya distance, Hellinger metric
関連	3	1	2
概要	Bray-Curtis dissimilarity is a quantitative measure of compositional difference between two samples, widely used in ecology and community analysis. Introduced by John Bray and John T. Curtis in 1957 for comparing forest communities, this index ranges from 0 (identical composition) to 1 (completely different). It is sensitive to abundance differences and is particularly effective for abundance data such as species counts, microbial populations, or preference intensities.	Canberra distance is a weighted version of the Manhattan distance that normalizes differences by the sum of absolute values. Introduced by Geoffrey Lance and William Williams in 1967 as part of their work on clustering classification methods, this metric emphasizes differences in small values and is sensitive to changes in relative proportions. It is commonly used in taxonomy, ecology, decision-making, and any application where normalized relative differences matter.	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.