Measure similarity between multi-interval sets with string labels.
Uses a client-provided definition of label similarities, where 0 is least- and 1 is most-similar.
The similarity between two multi-interval sets, where at least one is nonempty, is the ratio:
(sum of piecewise-matching between the sets) / (span of the sets)
where the span is the length of the smallest interval that contains all the intervals from both
sets, and the amount of piecewise-matching for any unit interval [i, i+1) is:
0 if neither set has a label on that interval
0 if only one set has a label on that interval
otherwise, the similarity between labels as defined by the client, explained below
Two empty sets have similarity 0.
For example, suppose you have multi-interval sets that use labels "happy", "sad", and "meh"; and
similarity between labels is defined as:
1 if both are "happy", both "sad", or both "meh"
0.5 if one is meh and the other is "happy" or "sad"
0 otherwise
Then the similarity between these two sets:
{ "happy" = [[0, 1), [2,4)], "sad" = [[1,2)] }
{ "sad" = [[1, 2)], "meh" = [[2,3)], "happy" = [[3,4)] }
... would be: (0 + 1 + 0.5 + 1) / (4 - 0) = 0.625
Label similarities are provided as an array of tuples, where the first two elements give a pair of
labels, and the third element gives the similarity between them, between 0 and 1 inclusive.
Similarity between labels is symmetric, so the order of labels in each tuple is irrelevant, and a
pair of labels may not appear more than once. The similarity between all other pairs of labels is:
1 iff they are the same string, and
0 otherwise
For example, the following gives the similarity values used above:
[ ["happy","meh",0.5], ["meh","sad",0.5] ]
When the individual piecewise-matching terms, the sum of piecewise-matching between the sets, and
the span of the sets can be represented as number values with high precision, the returned value
will have similar precision. Otherwise, it may be similarly imprecise.
PS2 instructions: this is a required function.
You may strengthen its specification, but may NOT weaken it.
Measure similarity between multi-interval sets with string labels.
Uses a client-provided definition of label similarities, where 0 is least- and 1 is most-similar.
The similarity between two multi-interval sets, where at least one is nonempty, is the ratio: (sum of piecewise-matching between the sets) / (span of the sets) where the span is the length of the smallest interval that contains all the intervals from both sets, and the amount of piecewise-matching for any unit interval [i, i+1) is:
Two empty sets have similarity 0.
For example, suppose you have multi-interval sets that use labels "happy", "sad", and "meh"; and similarity between labels is defined as:
Label similarities are provided as an array of tuples, where the first two elements give a pair of labels, and the third element gives the similarity between them, between 0 and 1 inclusive. Similarity between labels is symmetric, so the order of labels in each tuple is irrelevant, and a pair of labels may not appear more than once. The similarity between all other pairs of labels is:
For example, the following gives the similarity values used above: [ ["happy","meh",0.5], ["meh","sad",0.5] ]
When the individual piecewise-matching terms, the sum of piecewise-matching between the sets, and the span of the sets can be represented as number values with high precision, the returned value will have similar precision. Otherwise, it may be similarly imprecise.
PS2 instructions: this is a required function. You may strengthen its specification, but may NOT weaken it.