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Jaccard's coefficient (measure similarity) and Jaccard's distance (measure dissimilarity) are measurement of asymmetric information on binary (and non-binary) variables. Compare Jaccard's coefficient with Simple matching coefficient. For some applications, the existence of Formula Where
Jaccard's distance can be obtained from
Thus, 原文在这个地方有一个javascript小程序，演示。
Example 1:
The coordinate of Apple is (1,1,1,1) and coordinate of Banana is (0,1,0,0). Because each object is represented by 4 variables, we say that these objects has 4 dimensions. Jaccard's coefficient between Apple and Banana is 1/4 . Jaccard's distance between Apple and Banana is 3/4.
For non binary data, Jaccard's coefficient can also be computed using set relations
Example 2 Suppose we have two sets Then the union is
Of course, the set formula is also work for binary data, but we need to compute each digit using Boolean algebra. (A and B is True if both true, A or B is false if both False). Intersection set is equivalent to AND, while Union operation is equivalent to OR. Example 3 Let us use the example above
Sum of all digits can be used to compute Jaccard's coefficient
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in Simple Matching makes no sense because it represents double absence. This may happen when the value of positive and negative do not have equal information (asymmetry). For example, if the negative value is not important, counting the non-existence in both objects may have no meaningful contribution to the similarity or dissimilarity. Jaccard's coefficient remove the 
from simple matching coefficient to become 
= number of variables that positive for both objects 
= number of variables that positive for the 
th objects and negative for the 
th object 
= number of variables that negative for the 
th objects and positive for the 
th object 
= number of variables that negative for both objects 
