str_similarity_ranker

Given an array of strings as FIRST, and N_ARRAYS arrays of strings, rank N_ARRAYS by similarity to FIRST.

Check out the tests to get a feel for how it works in practice.

High-level algorithm overview

Exclusive combinations

A Sentence is described as an array of strings, where each word is a string in the array.

In order to rank N Sentences against a Reference Sentence based on similarity, pairs made up of [Reference Sentence, Other Sentence] are tried in such a way that each exclusive combination is tried. "Exclusive combination" is designated that way because every word can only be compared once for a given run. As an illustration, consider

A. ["Foo", "Bar"]

B. ["Feo", "Bor"]

The following exclusive combinations across those sets can be made:

1. {A0, B0} = ["Foo", "Feo"], {A1, B1} = ["Bar", "Bor"]

2. {A0, B1} = ["Foo", "Bor"], {A1, B0} = ["Bar", "Feo"]

Exclusive combinations are considered because a different score might be achieved depending on the order in which the pairs are picked.

Edit Distance Sum

After creating the pairs, each combination is compared by Levenshtein distance. The first combination is always decided iteratively (in the sense that every index combination should always be tried); however, after making the first exclusive combination, successive combinations try to find the pair with lowest distance between each other.

Aside from recording the distances, a history with the indexes of each pair tried is also stored, which will be used as a tie-breaker in case two combinations have the same distance sum.

Having ran all the distances across all different starting points between the two Sentences, pairs are first ranked by their distance sum. For instance, between

A. ["Foo", "Bar"]

B. ["Foo", "Bor"]

The lowest possible Edit Distance Sum is 1, given the following combination

{A0, B0} = ["Foo", "Foo"], {A1, B1} = ["Bar", "Bor"]

"Foo" and "Foo" have 0 edit distance because they're the same, where as "Bar" and "Bor" have 1 edit distance due to the middle character being different.

Tie-breaker: Relative Index Variance

If two distinct pairs have the same Edit Distance Sum, as briefly mentioned previously, the Relative Index Variance is chosen as a tie-break. Consider

A (Reference). ["Foo", "Bar", "Biz"]

B. ["Foo", "Bor", "Biz"]

C. ["Foo", "Biz", "Bor"]

Although the pairs {A, B} and {A, C} have the same Edit Distance Sum of 1, B better matches the order in relation to A - notice how "Foo" is at index 0 on both and "Biz" is at index A on both; therefore, B will be sorted before C due to the tie-breaker rules.