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Distance functions and IE

Distance functions and IE. William W. Cohen CALD. Announcements. March 25 Thus – talk from Carlos Guestrin (Assistant Prof in Cald as of fall 2004) on max-margin Markov nets time constraints? Writeups: nothing today “distance metrics for text” – three papers due next Monday, 3/22.

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Distance functions and IE

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  1. Distance functions and IE William W. Cohen CALD

  2. Announcements • March 25 Thus – talk from Carlos Guestrin (Assistant Prof in Cald as of fall 2004) on max-margin Markov nets • time constraints? • Writeups: • nothing today • “distance metrics for text” – three papers due next Monday, 3/22

  3. Record linkage: definition • Record linkage: determine if pairs of data records describe the same entity • I.e., find record pairs that are co-referent • Entities: usually people (or organizations or…) • Data records: names, addresses, job titles, birth dates, … • Main applications: • Joining two heterogeneous relations • Removing duplicates from a single relation

  4. Record linkage: terminology • The term “record linkage” is possibly co-referent with: • For DB people:data matching, merge/purge, duplicate detection, data cleansing, ETL (extraction, transfer, and loading), de-duping • For AI/ML people: reference matching, database hardening, object consolidation, • In NLP: co-reference/anaphora resolution • Statistical matching, clustering, language modeling, …

  5. Motivation • Q: What does this have to do with IE? • A: Quite a lot, actually... Webfind (Monge & Elkan, 1995)

  6. Finding a technical paper c. 1995 • Start with citation: " Experience With a Learning Personal Assistant", T.M. Mitchell, R. Caruana, D. Freitag, J. McDermott, and D. Zabowski, Communications of the ACM, Vol. 37, No. 7, pp. 81-91, July 1994. • Find author’s institution (w/ INSPEC) • Find web host (w/ NETFIND) • Find author’s home page and (hopefully) the paper by browsing

  7. Automatically finding a technical paper c. 1995 with WebFind • Start with citation: " Experience With a Learning Personal Assistant", T.M. Mitchell, R. Caruana, D. Freitag, J. McDermott, and D. Zabowski, Communications of the ACM, Vol. 37, No. 7, pp. 81-91, July 1994. • Find author’s institution (w/ automated search against INSPEC) • Find web host (w/ auto search on NETFIND) • Find author’s home page and (hopefully) the paper by heuristic spidering

  8. The data integration problem

  9. The data integration problem • Control flow (modulo details about querying • Extract (author, department) pairs from DB1 • Extract (department ,www server) pairs from DB2 • Execute the two-step plan to get paper: • author -> department -> wwwServer • two steps means matching (linking, integrating, deduping, ....) department names in DB1/DB2 • issues are completely different if user is executing a one-step plan: • one-step plan is retrieval

  10. String distance metrics: Levenshtein • Edit-distance metrics • Distance is shortest sequence of edit commands that transform s to t. • Simplest set of operations: • Copy character from s over to t • Delete a character in s (cost 1) • Insert a character in t (cost 1) • Substitute one character for another (cost 1) • This is “Levenshtein distance”

  11. Levenshtein distance - example • distance(“William Cohen”, “Willliam Cohon”) s alignment t op cost

  12. Levenshtein distance - example • distance(“William Cohen”, “Willliam Cohon”) s gap alignment t op cost

  13. D(i-1,j-1), if si=tj //copy D(i-1,j-1)+1, if si!=tj //substitute D(i-1,j)+1 //insert D(i,j-1)+1 //delete = min Computing Levenshtein distance - 1 D(i,j) = score of best alignment from s1..si to t1..tj

  14. Computing Levenshtein distance - 2 D(i,j) = score of best alignment from s1..si to t1..tj D(i-1,j-1) + d(si,tj) //subst/copy D(i-1,j)+1 //insert D(i,j-1)+1 //delete = min (simplify by letting d(c,d)=0 if c=d, 1 else) also let D(i,0)=i (for i inserts) and D(0,j)=j

  15. = D(s,t) Computing Levenshtein distance - 3 D(i-1,j-1) + d(si,tj) //subst/copy D(i-1,j)+1 //insert D(i,j-1)+1 //delete D(i,j)= min

  16. Computing Levenshtein distance – 4 D(i-1,j-1) + d(si,tj) //subst/copy D(i-1,j)+1 //insert D(i,j-1)+1 //delete D(i,j) = min A trace indicates where the min value came from, and can be used to find edit operations and/or a best alignment (may be more than 1)

  17. d(c,d) is an arbitrary distance function on characters (e.g. related to typo frequencies, amino acid substitutibility, etc) William Cohen Wukkuan Cigeb Needleman-Wunch distance D(i-1,j-1) + d(si,tj) //subst/copy D(i-1,j) +G//insert D(i,j-1) + G//delete D(i,j) = min G = “gap cost”

  18. Smith-Waterman distance - 1 0 //start over D(i-1,j-1) - d(si,tj) //subst/copy D(i-1,j) - G //insert D(i,j-1) - G //delete D(i,j) = max Distance is maximum over all i,j in table of D(i,j)

  19. Smith-Waterman distance - 2 0 //start over D(i-1,j-1) - d(si,tj) //subst/copy D(i-1,j) - G //insert D(i,j-1) - G //delete D(i,j) = max G = 1 d(c,c) = -2 d(c,d) = +1

  20. Smith-Waterman distance - 3 0 //start over D(i-1,j-1) - d(si,tj) //subst/copy D(i-1,j) - G //insert D(i,j-1) - G //delete D(i,j) = max G = 1 d(c,c) = -2 d(c,d) = +1

  21. Smith-Waterman distance: Monge & Elkan’s WEBFIND (1996)

  22. Smith-Waterman distance in Monge & Elkan’s WEBFIND (1996) Used a standard version of Smith-Waterman with hand-tuned weights for inserts and character substitutions. Split large text fields by separators like commas, etc, and explore different pairings (since S-W assigns a large cost to large transpositions) Result competitive with plausible competitors.

  23. Smith-Waterman distance in Monge & Elkan’s WEBFIND (1996) • String s=A1 A2 ... AK, string t=B1 B2 ... BL • sim’ is editDistance scaled to [0,1] • Monge-Elkan’s “recursive matching scheme” is average maximal similarity of Aito Bj:

  24. Smith-Waterman distance: Monge & Elkan’s WEBFIND (1996) 0.51 0.92 0.5 1.0

  25. Results: S-W from Monge & Elkan

  26. Affine gap distances • Smith-Waterman fails on some pairs that seem quite similar: William W. Cohen William W. ‘Don’t call me Dubya’ Cohen Intuitively, a single long insertion is “cheaper” than a lot of short insertions Intuitively, are springlest hulongru poinstertimon extisn’t “cheaper” than a lot of short insertions

  27. Affine gap distances - 2 • Idea: • Current cost of a “gap” of n characters: nG • Make this cost: A + (n-1)B, where A is cost of “opening” a gap, and B is cost of “continuing” a gap.

  28. D(i-1,j) - A IS(i-1,j) - B Best score in which si is aligned with a ‘gap’ IS(i,j) = max Best score in which tj is aligned with a ‘gap’ D(i,j-1) - A IT(i,j-1) - B IT(i,j) = max Affine gap distances - 3 D(i-1,j-1) + d(si,tj) IS(I-1,j-1) + d(si,tj) IT(I-1,j-1) + d(si,tj) D(i-1,j-1) + d(si,tj) //subst/copy D(i-1,j)-1 //insert D(i,j-1)-1 //delete D(i,j) = max

  29. Affine gap distances - 4 -B IS -d(si,tj) -A D -d(si,tj) -A -d(si,tj) -B IT

  30. Affine gap distances – experiments (from McCallum,Nigam,Ungar KDD2000) • Goal is to match data like this:

  31. Affine gap distances – experiments (from McCallum,Nigam,Ungar KDD2000) • Hand-tuned edit distance • Lower costs for affine gaps • Even lower cost for affine gaps near a “.” • HMM-based normalization to group title, author, booktitle, etc into fields

  32. Affine gap distances – experiments

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