介绍

骰子系数（Dice coefficient），也称索伦森 - 骰子系数（Sørensen–Dice coefficient），是一种集合相似度度量函数，通常用于计算两个样本的相似度（也可以度量字符串的相似性）。

Dice 系数可以计算两个字符串的相似度： Dice（s1,s2）=2*comm(s1,s2)/(leng(s1)+leng(s2)) 。其中， comm (s1,s2) 是 s1、s2 中相同字符的个数 leng(s1)，leng(s2) 是字符串 s1、s2 的长度。

实现

JavaScript

Dice 系数是通过比较两个字符串的 bigrams 来计算的， 一个 bigrams 是长度为 2 的字符串的一个子串。

/* The Sørensen–Dice coefficient（系数） is a statistic used to （估计） the similarity of two samples.
 * Applied to strings, it can give you a value between 0 and 1 (included) which tells you how similar they are.
 * Dice coefficient is calculated by comparing the bigrams of both strings,
 * a bigram is a substring of the string of length 2.
 * read more: https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient
 */

// Time complexity: O(m + n), m and n being the sizes of string A and string B

// Find the bistrings of a string and return a hashmap (key => bistring, value => count)
function mapBigrams(string) {
 const bigrams = new Map();
 for (let i = 0; i < string.length - 1; i++) {
  const bigram = string.substring(i, i + 2);
  const count = bigrams.get(bigram);
  bigrams.set(bigram, (count || 0) + 1);
 }
 return bigrams;
}

// Calculate the number of common bigrams between a map of bigrams and a string

function countCommonBigrams(bigrams, string) {
 let count = 0;
 for (let i = 0; i < string.length - 1; i++) {
  const bigram = string.substring(i, i + 2);
  if (bigrams.has(bigram)) count++;
 }
 return count;
}

// Calculate Dice coeff of 2 strings
function diceCoefficient(stringA, stringB) {
 if (stringA === stringB) return 1;
 else if (stringA.length < 2 || stringB.length < 2) return 0;

 const bigramsA = mapBigrams(stringA);

 const lengthA = stringA.length - 1;
 const lengthB = stringB.length - 1;

 let dice = (2 * countCommonBigrams(bigramsA, stringB)) / (lengthA + lengthB);

 // cut 0.xxxxxx to 0.xx for simplicity
 dice = Math.floor(dice * 100) / 100;

 return dice;
}

• substring() (opens new window) 方法返回一个字符串在开始索引到结束索引之间的一个子集，或从开始索引直到字符串的末尾的一个子集。

扩展

• 医学影像分割 ---Dice Loss - 知乎 (opens new window)

参考

• Sørensen–Dice coefficient - Wikiwand (opens new window)
• Dice 系数 - Wikiwand (opens new window)