DISTANCE BETWEEN SETS
DISTANCE BETWEEN SETS
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DOI：
10.1038/234034a0
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发表时间：
1971-01-01
期刊：
影响因子：
64.8
通讯作者：
WINTER, D
中科院分区：
文献类型：
--
作者：
LEVANDOWSKY, M;WINTER, D
表示集合的不同程度的距离函数在物理人类学、心理学、数字分类学、生态学和其他领域都有应用。在一次生态学研究中，我们注意到生态学中使用的Jaccard6的相似系数产生了一个满足三角不等式的度量函数。对于两个非空有限集合X， Y，雅卡德系数是X与Y的交集X∩Y中的元素数量。这个系数（我们使用绝对值符号来表示元素数量）有一个启发式解释。它测量两个集合中至少一个集合的元素同时是两个集合的元素的概率，因此是两个集合之间相似性或“重叠”的合理度量。然后，单补可以被认为是两个集合不相似度的度量。
DISTANCE functions expressing the degree of dissimilarity of sets have found use in physical anthropology1, psychology2, numerical taxonomy3, ecology3 and elsewhere. During an ecological study by one of us, it was noticed that the similarity coefficient of Jaccard6, used in ecology, gives rise to a metric function satisfying the triangle inequality. For two non-empty finite sets X, Y, the Jaccard coefficient is the number of elements in the intersection X∩ Y of X and Y. This coefficient (we use absolute value signs to indicate number of elements) has a heuristic interpretation. It measures the probability that an element of at least one of two sets is an element of both, and thus is a reasonable measure of similarity or “overlap” between the two. The one-complement may then be considered a measure of the dissimilarity of the two sets.