Cumulative Jaccard Index
cumJaccardIndex(list)
cumJaccardDistance(list)A list of characters or integers
The cumulative Jaccard Index, a vector of values between 0 and 1, of the same length as the input list
The cumulative Jaccard Index is calculated by calculating the Jaccard Index
of element i and the union of elements between 1 and
i-1. The cumulative Jaccard Index of the first element is set as 0.0.
The cumulative Jaccard distance is defined in almost the same way, with the only difference the distance is returned. The value of the first element is 1.0.
An advantage of using cumulative overlap coefficient over cumulative Jaccard Index is that it is monotonic: the value is garanteed to decrease from 1 to 0, whereas the cumulative Jaccard Index may not be monotic.
myList <- list(first=LETTERS[1:5], second=LETTERS[6:10], third=LETTERS[8:12], fourth=LETTERS[1:12])
cumJaccardIndex(myList)
#> [1] 0.00 0.00 0.25 1.00
cumJaccardDistance(myList)
#> [1] 1.00 1.00 0.75 0.00