Ochiai

Ochiai is a Japanese surname and toponym. As a surname, it is written in kanji as 落合 and is borne by many people in Japan and in Japanese-speaking communities worldwide. It also appears in the names of several districts and place names in Japan, reflecting historical geographic features or settlements.

In mathematics and statistics, the Ochiai coefficient, or Ochiai index, is a measure of similarity between two binary datasets. For two binary vectors, the coefficient is defined as a / sqrt((a+b)(a+c)), where:

- a is the number of positions where both vectors have a value of 1,

- b is the number where the first is 1 and the second is 0,

- c is the number where the first is 0 and the second is 1.

The value ranges from 0 to 1, with 1 indicating identical presence patterns. The Ochiai coefficient is equivalent to the cosine similarity for binary data and is related to the Sørensen–Dice index. It is widely used in ecology, bioinformatics, text mining, and other fields to quantify similarity between observed feature sets, gene lists, or species occurrences.

Notable people with the surname include academics, athletes, and artists in Japan and abroad. The name also appears in historical and contemporary place names and institutions across Japan.