Cumulative overlap coefficient
cumOverlapCoefficient(list)
cumOverlapDistance(list)The cumulative overlap coefficients, a vector of values between 0 and 1, of the same length as the input list
The cumulative overlap coefficient is calculated by calculating the overlap
coefficient of element i and the union of elements between 1
and i-1. The cumulative overlap coefficient of the first element is
set as 0.0.
The cumulative overlap 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. Pratically it is calculated by 1-cumOverlapCoefficient.
Since the denominator of the overlap coefficient is the size of the smaller
set of the two, which is bound to be the size of element i, the
cumulative overlap distance can be interpreted as the proportion of new
items in each new element that are unseen in previous elements. Similarly,
the cumulative overlap coefficient can be interpreted as the proportion of
items in each new element that have been seen in previous elements. See
examples below.
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])
cumOverlapCoefficient(myList)
#> [1] 0.0 0.0 0.6 1.0
cumOverlapDistance(myList)
#> [1] 1.0 1.0 0.4 0.0