Algorithms for “fuzzy matching” strings

Question

By fuzzy matching I don\'t mean similar strings by Levenshtein distance or something similar, but the way it\'s used in TextMate/Ido/Icicles: given a list of strings, find t

Answer 1

Levenshtein 'Edit Distance' algorithms will definitely work on what you're trying to do: they will give you a measurement of how closely two words or addresses or phone numbers, psalms, monologues and scholarly articles match each other, allowing you you rank the results and choose the best match.

A more lightweight appproach is to count up the common substrings: it's not as good as Levenshtein, but it provides usable results and runs quickly in slow languages which have access to fast 'InString' functions.

I published an Excel 'Fuzzy Lookup' in Excellerando a few years ago, using 'FuzzyMatchScore' function that is, as far as I can tell, exactly what you need:

http://excellerando.blogspot.com/2010/03/vlookup-with-fuzzy-matching-to-get.html

It is, of course, in Visual Basic for Applications. Proceed with caution, crucifixes and garlic:

Public Function SumOfCommonStrings( _
                            ByVal s1 As String, _
                            ByVal s2 As String, _
                            Optional Compare As VBA.VbCompareMethod = vbTextCompare, _
                            Optional iScore As Integer = 0 _
                                ) As Integer

Application.Volatile False

' N.Heffernan 06 June 2006 
' THIS CODE IS IN THE PUBLIC DOMAIN


' Function to measure how much of String 1 is made up of substrings found in String 2

' This function uses a modified Longest Common String algorithm.
' Simple LCS algorithms are unduly sensitive to single-letter
' deletions/changes near the midpoint of the test words, eg:
' Wednesday is obviously closer to WedXesday on an edit-distance
' basis than it is to WednesXXX. So it would be better to score
' the 'Wed' as well as the 'esday' and add up the total matched

' Watch out for strings of differing lengths:
'
'    SumOfCommonStrings("Wednesday", "WednesXXXday")
'
' This scores the same as:
'
'     SumOfCommonStrings("Wednesday", "Wednesday")
'
' So make sure the calling function uses the length of the longest
' string when calculating the degree of similarity from this score.


' This is coded for clarity, not for performance.

Dim arr() As Integer    ' Scoring matrix
Dim n As Integer        ' length of s1
Dim m As Integer        ' length of s2
Dim i As Integer        ' start position in s1
Dim j As Integer        ' start position in s2
Dim subs1 As String     ' a substring of s1
Dim len1 As Integer     ' length of subs1

Dim sBefore1            ' documented in the code
Dim sBefore2
Dim sAfter1
Dim sAfter2

Dim s3 As String


SumOfCommonStrings = iScore

n = Len(s1)
m = Len(s2)

If s1 = s2 Then
    SumOfCommonStrings = n
    Exit Function
End If

If n = 0 Or m = 0 Then
    Exit Function
End If

's1 should always be the shorter of the two strings:
If n > m Then
    s3 = s2
    s2 = s1
    s1 = s3
    n = Len(s1)
    m = Len(s2)
End If

n = Len(s1)
m = Len(s2)

' Special case: s1 is n exact substring of s2
If InStr(1, s2, s1, Compare) Then
    SumOfCommonStrings = n
    Exit Function
End If

For len1 = n To 1 Step -1

    For i = 1 To n - len1 + 1

        subs1 = Mid(s1, i, len1)
        j = 0
        j = InStr(1, s2, subs1, Compare)

        If j > 0 Then

            ' We've found a matching substring...
            iScore = iScore + len1            

          ' Now clip out this substring from s1 and s2...
          ' And search the fragments before and after this excision:


            If i > 1 And j > 1 Then
                sBefore1 = left(s1, i - 1)
                sBefore2 = left(s2, j - 1)
                iScore = SumOfCommonStrings(sBefore1, _
                                            sBefore2, _
                                            Compare, _
                                            iScore)
            End If


            If i + len1 < n And j + len1 < m Then
                sAfter1 = right(s1, n + 1 - i - len1)
                sAfter2 = right(s2, m + 1 - j - len1)
                iScore = SumOfCommonStrings(sAfter1, _
                                            sAfter2, _
                                            Compare, _
                                            iScore)
            End If


            SumOfCommonStrings = iScore
            Exit Function

        End If

    Next


Next


End Function


Private Function Minimum(ByVal a As Integer, _
                         ByVal b As Integer, _
                         ByVal c As Integer) As Integer
Dim min As Integer

  min = a

  If b < min Then
        min = b
  End If

  If c < min Then
        min = c
  End If

  Minimum = min

End Function