The Jaro distance is a measure of edit distance between two strings; its inverse, called the Jaro similarity, is a measure of two strings' similarity: the higher the value, the more similar the strings are. The score is normalized such that   0   equates to no similarities and   1   is an exact match.



Definition
The Jaro similarity   




d

j




{\displaystyle d_{j}}

   of two given strings   




s

1




{\displaystyle s_{1}}

   and   




s

2




{\displaystyle s_{2}}

   is

 




d

j


=

{




0



if 

m
=
0






1
3



(


m


|


s

1



|




+


m


|


s

2



|




+



m
−
t

m


)




otherwise









{\displaystyle d_{j}=\left\{{\begin{array}{l l}0&{\text{if }}m=0\\{\frac {1}{3}}\left({\frac {m}{|s_{1}|}}+{\frac {m}{|s_{2}|}}+{\frac {m-t}{m}}\right)&{\text{otherwise}}\end{array}}\right.}


Where:

 



m


{\displaystyle m}

   is the number of matching characters;
 



t


{\displaystyle t}

   is half the number of transpositions.


Two characters from   




s

1




{\displaystyle s_{1}}

   and   




s

2




{\displaystyle s_{2}}

   respectively, are considered matching only if they are the same and not farther apart than   




⌊



max
(

|


s

1



|

,

|


s

2



|

)

2


⌋

−
1


{\displaystyle \left\lfloor {\frac {\max(|s_{1}|,|s_{2}|)}{2}}\right\rfloor -1}

 characters.

Each character of   




s

1




{\displaystyle s_{1}}

   is compared with all its matching characters in   




s

2




{\displaystyle s_{2}}

. Each difference in position is half a transposition; that is, the number of transpositions is half the number of characters which are common to the two strings but occupy different positions in each one.



Example
Given the strings   




s

1




{\displaystyle s_{1}}

   DWAYNE   and   




s

2




{\displaystyle s_{2}}

   DUANE   we find:

 



m
=
4


{\displaystyle m=4}


 




|


s

1



|

=
6


{\displaystyle |s_{1}|=6}


 




|


s

2



|

=
5


{\displaystyle |s_{2}|=5}


 



t
=
0


{\displaystyle t=0}




We find a Jaro score of:

 




d

j


=


1
3



(


4
6


+


4
5


+



4
−
0

4


)

=
0.822


{\displaystyle d_{j}={\frac {1}{3}}\left({\frac {4}{6}}+{\frac {4}{5}}+{\frac {4-0}{4}}\right)=0.822}




Task
Implement the Jaro algorithm and show the similarity scores for each of the following pairs:

 ("MARTHA", "MARHTA")
 ("DIXON", "DICKSONX")
 ("JELLYFISH", "SMELLYFISH")


 See also
 Jaro–Winkler distance on Wikipedia.


 
Option Explicit
 
Function JaroWinkler(text1 As String, text2 As String, Optional p As Double = 0.1) As Double
Dim dummyChar, match1, match2 As String
Dim i, f, t, j, m, l, s1, s2, limit As Integer
 
i = 1
Do
    dummyChar = Chr(i)
    i = i + 1
Loop Until InStr(1, text1 & text2, dummyChar, vbTextCompare) = 0
 
s1 = Len(text1)
s2 = Len(text2)
limit = WorksheetFunction.Max(0, Int(WorksheetFunction.Max(s1, s2) / 2) - 1)
match1 = String(s1, dummyChar)
match2 = String(s2, dummyChar)
 
For l = 1 To WorksheetFunction.Min(4, s1, s2)
    If Mid(text1, l, 1) <> Mid(text2, l, 1) Then Exit For
Next l
l = l - 1
 
For i = 1 To s1
    f = WorksheetFunction.Min(WorksheetFunction.Max(i - limit, 1), s2)
    t = WorksheetFunction.Min(WorksheetFunction.Max(i + limit, 1), s2)
    j = InStr(1, Mid(text2, f, t - f + 1), Mid(text1, i, 1), vbTextCompare)
    If j > 0 Then
        m = m + 1
        text2 = Mid(text2, 1, f + j - 2) & dummyChar & Mid(text2, f + j)
        match1 = Mid(match1, 1, i - 1) & Mid(text1, i, 1) & Mid(match1, i + 1)
        match2 = Mid(match2, 1, f + j - 2) & Mid(text1, i, 1) & Mid(match2, f + j)
    End If
Next i
match1 = Replace(match1, dummyChar, "", 1, -1, vbTextCompare)
match2 = Replace(match2, dummyChar, "", 1, -1, vbTextCompare)
t = 0
For i = 1 To m
    If Mid(match1, i, 1) <> Mid(match2, i, 1) Then t = t + 1
Next i
 
JaroWinkler = (m / s1 + m / s2 + (m - t / 2) / m) / 3
JaroWinkler = JaroWinkler + (1 - JaroWinkler) * l * WorksheetFunction.Min(0.25, p)
End Function
 