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This chapter is from the book

2.36 Calculating the Levenshtein Distance Between Two Strings

The concept of distance between strings is important in inductive learning (AI), cryptography, proteins research, and in other areas.

The Levenshtein distance is the minimum number of modifications needed to change one string into another, using three basic modification operations: del(-etion), ins(-ertion), and sub(-stitution). A substitution is also considered to be a combination of a deletion and insertion (indel).

There are various approaches to this, but we will avoid getting too technical. Suffice it to say that this Ruby implementation (shown in Listing 2.2) allows you to provide optional parameters to set the cost for the three types of modification operations and defaults to a single indel cost basis (cost of insertion = cost of deletion).

Listing 2.2 The Levenshtein distance

class String

  def levenshtein(other, ins=2, del=2, sub=1)
    # ins, del, sub are weighted costs
    return nil if self.nil?
    return nil if other.nil?
    dm = []        # distance matrix

    # Initialize first row values
    dm[0] = (0..self.length).collect { |i| i * ins }
    fill = [0] * (self.length - 1)

    # Initialize first column values
    for i in 1..other.length
      dm[i] = [i * del, fill.flatten]

    # populate matrix
    for i in 1..other.length
      for j in 1..self.length
    # critical comparison
        dm[i][j] = [
             dm[i-1][j-1] +
               (self[j-1] == other[i-1] ? 0 : sub),
                 dm[i][j-1] + ins,
             dm[i-1][j] + del

    # The last value in matrix is the
    # Levenshtein distance between the strings


s2 = "AUGGAA"
d1 = s1.levenshtein(s2)    # 9

s3 = "pennsylvania"
s4 = "pencilvaneya"
d2 = s3.levenshtein(s4)    # 7

s5 = "abcd"
s6 = "abcd"
d3 = s5.levenshtein(s6)    # 0

Now that we have the Levenshtein distance defined, it’s conceivable that we could define a similar? method, giving it a threshold for similarity. Here is an example:

class String

  def similar?(other, thresh=2)
    self.levenshtein(other) < thresh


if "polarity".similar?("hilarity")
  puts "Electricity is funny!"

Of course, it would also be possible to pass in the three weighted costs to the similar? method so that they could in turn be passed into the levenshtein method. We have omitted these for simplicity.

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