为什么我们在计算二进制数字之间的jaccard距离时不包含0个匹配项？

Question

我正在研究一个基于Jaccard距离的程序，并且我需要计算两个二进制位向量之间的Jaccard距离。我碰到下面就在网上：

If p1 = 10111 and p2 = 10011, 

The total number of each combination attributes for p1 and p2: 

M11 = total number of attributes where p1 & p2 have a value 1, 
M01 = total number of attributes where p1 has a value 0 & p2 has a value 1, 
M10 = total number of attributes where p1 has a value 1 & p2 has a value 0, 
M00 = total number of attributes where p1 & p2 have a value 0. 
Jaccard similarity coefficient = J = 
intersection/union = M11/(M01 + M10 + M11) 
= 3/(0 + 1 + 3) = 3/4, 

Jaccard distance = J' = 1 - J = 1 - 3/4 = 1/4, 
Or J' = 1 - (M11/(M01 + M10 + M11)) = (M01 + M10)/(M01 + M10 + M11) 
= (0 + 1)/(0 + 1 + 3) = 1/4 

现在，在计算系数，为什么“M00”不包括在分母？任何人都可以解释吗？

Answer 1

A和B的提花指数是|A∩B|/|A∪B| = |A∩B| /（| A | + | B | - |A∩B|）。

我们有：|A∩B| = M11，| A | = M11 + M10，| B | = M11 + M01。 （| A | + | B | - |A∩B|）= M11 /（M11 + M10 + M11 + M01-M11）= M11 /（M10 + M01 + M11）

So |A∩B| 。

这维恩图可​​以帮助：