杰卡德距离
我在计算集合（位向量）的杰卡德距离时遇到这个问题：
p1 = 10111;
p2 = 10011。
交集大小 = 3； （我们怎样才能找到它？）
并集的大小= 4，（我们怎样才能找到它？）
杰卡德相似度=（交集/并集）= 3/4。
杰卡德距离 = 1 –（杰卡德相似度）= (1-3/4) = 1/4。
但我不明白我们如何找出两个向量的“交集”和“并集”。
请帮我。
多谢。
I have this problem in calculating Jaccard Distance for Sets (Bit-Vectors):
p1 = 10111;
p2 = 10011.
Size of intersection = 3; (How could we find it out?)
Size of union = 4, (How could we find it out?)
Jaccard similarity = (intersection/union) = 3/4.
Jaccard Distance = 1 – (Jaccard similarity) = (1-3/4) = 1/4.
But I don't understand how could we find out the "intersection" and "union" of the two vectors.
Please help me.
Thanks alot.
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p1&p2 = 10011的设置位数p1|p2 = 10111的集合位数这里的向量表示二进制数组，其中第 i 位表示第 i 个元素是否存在于这一套。
Amount of set bits of
p1&p2 = 10011Amount of set bits of
p1|p2 = 10111Vector here means binary array where i-th bit means does i-th element present in this set.
如果 p1 = 10111 且 p2 = 10011，则
p1 和 p2 的每个组合属性的总数：
杰卡德相似系数 = J = 交集/并集 = M11/(M01 + M10 + M11) = 3 / (0 + 1 + 3) = 3/4，
杰卡德距离 = J' = 1 - J = 1 - 3/4 = 1/4,
或 J' = 1 - (M11/(M01 + M10 + M11)) = (M01 + M10)/(M01 + M10 + M11) = (0 + 1)/(0 + 1 + 3) = 1/4
If p1 = 10111 and p2 = 10011,
The total number of each combination attributes for p1 and p2:
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