Fuzzy regular expressions

Question

I am looking for a way to do a fuzzy match using regular expressions. I'd like to use Perl, but if someone can recommend any way to do this that would be helpful.

As an example, I want to match a string on the words "New York" preceded by a 2-digit number. The difficulty comes because the text is from OCR of a PDF, so I want to do a fuzzy match. I'd like to match:

12 New York
24 Hew York
33 New Yobk

and other "close" matches (in the sense of the Levenshtein distance), but not:

aa New York
11 Detroit

Obviously, I will need to specify the allowable distance ("fuzziness") for the match.

As I understand it, I cannot use the String::Approx Perl module to do this, because I need to include a regular expression in my match (to match the preceding digits).

Also, I should note that this is a very simplified example of what I'm really trying to match, so I'm not looking for a brute-force approach.

Edited to add:

Okay, my first example was too simple. I didn't mean for people to get hung up on the preceding digits -- sorry about the bad example. Here's a better example. Consider this string:

ASSIGNOR, BY MESHS ASSIGN1IBNTS, TO ALUSCHALME&S MANOTAC/rURINGCOMPANY, A COBPOBATlOH OF DELAY/ABE.

What this actually says is:

ASSIGNOR, BY MESNE ASSIGNMENTS, TO ALLIS-CHALMERS MANUFACTURING COMPANY, A CORPORATION OF DELAWARE

What I need to do is extract the phrase "ALUSCHALME&S MANOTAC/rURINGCOMPANY" and "DELAY/ABE". (I realize this might seem like madness. But I'm an optimist.) In general, the pattern will look something like this:

/Assignor(, by mesne assignments,)? to (company name), a corporation of (state)/i

where the matching is fuzzy.

Answer 1

If you have one pattern you want to find the best match against a text collection you can try q-gram distance. It is quite easy to implement and adopt to special needs.

Your second description actually was helpful here, because the pattern and texts should be fairly long. q-gram distance does not work well with words like "York", but if your typical pattern is a whole address, that should be fine.

Try it like this:

• transform your texts and patterns into a reduced character set, like uppercase-only, stripping, wordifying (one space between words) all symbols replaced by "#" or something.
• choose a q-gram length, to work with. Try 3 or 2. We call this q=3.
• than, build a qgram-profile of each text:
• split each text into q-words, ie. NEW_YORK becomes [NEW, EW_, W_Y, _YO, ORK], store this away with each text.
• if you search for your pattern then, you do the same with your pattern,
• loop through your text-qgram-database and
  • count for each pattern/text-pair how many qgrams are the same.
  • each hit will raise the score by 1.
• the texts with the highest score(s) are your best hits.

If you did that you can tweak this algorithm by:

• prepend all you texts (and also the pattern before search), with q-1 special chars, so even your short words will get a decent profile. For example New York becomes ^^NEW YORK$$.
• You can even play around with replacing all consonants with "x" and vowels with "o" and so on. Play around with a couple of character classes this way, or even create super symbols by replacing groups of character by one other, i.e. CK becomes K, or SCH becomes $.
• when raising the score by a qgram-hit you can adjust the value of 1 by other things, like length-difference of text vs pattern.
• store 2-grams and 3-grams both, and when counting, weigh then differently.

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Note that this algorithm in the here described basic form does not have a good running time during search, i.e. O(|T|*|P|) (with |T| and |P| the total lengths of your text and pattern). This is because I described that you loop over all your texts, and then over your pattern. Therefore this is only practical for a medium-sized texts-base. If you spend some thought, you can create an advanced index structure over the q-grams (maybe using hashtables), so this might be practical for huge texts-bases as well.