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1317

answers:

7

I've had some success comparing strings using the PHP levenshtein function.

However, for two strings which contain substrings that have swapped positions, the algorithm counts those as whole new substrings.

For example:

levenshtein("The quick brown fox", "brown quick The fox"); // 10 differences

are treated as having less in common than:

levenshtein("The quick brown fox", "The quiet swine flu"); // 9 differences

I'd prefer an algorithm which saw that the first two were more similar.

How could I go about coming up with a comparison function that can identify substrings which have switched position as being distinct to edits?

One possible approach I've thought of is to put all the words in the string into alphabetical order, before the comparison. That takes the original order of the words completely out of the comparison. A downside to this, however, is that changing just the first letter of a word can create a much bigger disruption than a changing a single letter should cause.

What I'm trying to achieve is to compare two facts about people which are free text strings, and decide how likely these facts are to indicate the same fact. The facts might be the school someone attended, the name of their employer or publisher, for example. Two records may have the same school spelled differently, words in a different order, extra words, etc, so the matching has to be somewhat fuzzy if we are to make a good guess that they refer to the same school. So-far it is working very well for spelling errors (I am using a phoenetic algorithm similar to metaphone on top of this all) but very poorly if you switch the order of words around which seem common in a school: "xxx college" vs "college of xxx".

+6  A: 

Its easy. Just use the Damerau-Levenshtein distance on the words instead of letters.

Unknown
Do you mean: "for every word in A, find the levenshtein distance to every word in B, then add up your results"?
thomasrutter
No, I mean turn every word into a symbol: ie The = a, quick = b, brown = c, etc. And then run the levenshtein algorithm on that.
Unknown
No I see what you mean, you mean implement the levenshtein algorithm which compares words rather than letters. Unfortunately this still not work for me, as two words which swap position with each other would still count the same as deleting a word and creating an entirely different word.
thomasrutter
Ie levenshtein("abcd", "cbad") is still no more similar than levenshtein("abcd", "abxy")
thomasrutter
Then you might look at similar algorithms like http://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance
Unknown
I like the sound of this Damerau-Levenshtein distance (with transpositions). Only thing I'm worried about now is how much slower it's going to be implementing it in the PHP code. Thanks for the tip!
thomasrutter
+2  A: 

You can also try this. (just an extra suggestion)

$one = metaphone("The quick brown fox"); // 0KKBRNFKS
$two = metaphone("brown quick The fox"); // BRNKK0FKS
$three = metaphone("The quiet swine flu"); // 0KTSWNFL

similar_text($one, $two, $percent1); // 66.666666666667
similar_text($one, $three, $percent2); // 47.058823529412
similar_text($two, $three, $percent3); // 23.529411764706

This will show that the 1st and 2nd are more similar than one and three and two and three.

Ólafur Waage
I think this improvement in score would be more from the use of similar_text rather than from metaphone. I'm currently using a phoenetic algorithm very similar to metaphone. I haven't looked much into the algorithm similar_text uses. I was under the impression it was a lot less efficient than levenshtein, but I guess you get what you pay for. I might try it.
thomasrutter
I tried with only similar text and it gave a much lower score and a lower score between one and two, than one and three.
Ólafur Waage
A: 

Explode on spaces, sort the array, implode, then do the Levenshtein.

rooskie
+1  A: 

Take this answer and make the following change:

void match(trie t, char* w, string s, int budget){
  if (budget < 0) return;
  if (*w=='\0') print s;
  foreach (char c, subtrie t1 in t){
    /* try matching or replacing c */
    match(t1, w+1, s+c, (*w==c ? budget : budget-1));
    /* try deleting c */
    match(t1, w, s, budget-1);
  }
  /* try inserting *w */
  match(t, w+1, s + *w, budget-1);
  /* TRY SWAPPING FIRST TWO CHARACTERS */
  if (w[1]){
    swap(w[0], w[1]);
    match(t, w, s, budget-1);
    swap(w[0], w[1]);
  }
}

This is for dictionary search in a trie, but for matching to a single word, it's the same idea. You're doing branch-and-bound, and at any point, you can make any change you like, as long as you give it a cost.

Mike Dunlavey
This looks like it could be quite useful, though it will take a bit of research on my part to figure out how it works. I haven't used a Trie before, so I'll investigate.
thomasrutter
@thomas. You only need the trie if you're searching a dictionary. If you're just comparing two strings (or lists of things), the "foreach" just becomes a simple statement block. Recursive branch-and-bound is a pretty useful Swiss Army knife.
Mike Dunlavey
A: 

Eliminate duplicate words between the two strings and then use Levenshtein.

JRL
A: 

I've been implementing levenshtein in a spell checker.

What you're asking for is counting transpositions as 1 edit.

This is easy if you only wish to count transpositions of one word away. However for transposition of words 2 or more away, the addition to the algorithm is worst case scenario !(max(wordorder1.length(), wordorder2.length())). Adding a non-linear subalgorithm to an already quadratic algorithm is not a good idea.

This is how it would work.

if (wordorder1[n] == wordorder2[n-1])
{
  min(workarray[x-1, y] + 1, workarray[x, y-1] + 1, workarray[x-2, y-2]);
}
  else
{
  min(workarray[x-1, y] + 1, workarray[x, y-1] + 1);
}

JUST for touching transpositions. If you want all transpositions, you'd have to for every position work backwards from that point comparing

1[n] == 2[n-2].... 1[n] == 2[0]....

So you see why they don't include this in the standard method.

A: 

i believe this is a prime example for using a vector-space search engine.

in this technique, each document essentially becomes a vector with as many dimensions as there are different words in the entire corpus; similar documents then occupy neighboring areas in that vector space. one nice property of this model is that queries are also just documents: to answer a query, you simply calculate their position in vector space, and your results are the closest documents you can find. i am sure there are get-and-go solutions for PHP out there.

to fuzzify results from vector space, you could consider to do stemming / similar natural language processing technique, and use levenshtein to construct secondary queries for similar words that occur in your overall vocabulary.

flow