1. 1 INF 2914 Information Retrieval and Web Search Lecture 9: Query Processing These slides are adapted from Stanford’s class CS276 / LING 286 Information Retrieval and Web Mining

2. 2 Query processing: AND Consider processing the query: Brutus AND Caesar Locate Brutus in the Dictionary; Retrieve its postings. Locate Caesar in the Dictionary; Retrieve its postings. “Merge” the two postings: 128 34 248163264123581321 Brutus Caesar

3. 3 34 12824816 3264 12 3 581321 The merge Walk through the two postings simultaneously, in time linear in the total number of postings entries 128 34 248163264123581321 Brutus Caesar 2 8 If the list lengths are x and y, the merge takes O(x+y) operations. Crucial: postings sorted by docID.

4. 4 Boolean queries: Exact match The Boolean Retrieval model is being able to ask a query that is a Boolean expression: Boolean Queries are queries using AND, OR and NOT to join query terms Views each document as a set of words Is precise: document matches condition or not. Primary commercial retrieval tool for 3 decades. Professional searchers (e.g., lawyers) still like Boolean queries: You know exactly what you’re getting.

5. 5 Boolean queries: More general merges Exercise: Adapt the merge for the queries: Brutus AND NOT Caesar Brutus OR NOT Caesar Can we still run through the merge in time O(x+y) or what can we achieve?

6. 6 Merging What about an arbitrary Boolean formula? (Brutus OR Caesar) AND NOT (Antony OR Cleopatra) Can we always merge in “linear” time? Linear in what? Can we do better?

7. 7 Query optimization What is the best order for query processing? Consider a query that is an AND of t terms. For each of the t terms, get its postings, then AND them together. Brutus Calpurnia Caesar 12358162134 248163264128 1316 Query: Brutus AND Calpurnia AND Caesar

8. 8 Query optimization example Process in order of increasing freq: start with smallest set, then keep cutting further. Brutus Calpurnia Caesar 12358132134 248163264128 1316 This is why we kept freq in dictionary Execute the query as (Caesar AND Brutus) AND Calpurnia.

9. 9 More general optimization e.g., (madding OR crowd) AND (ignoble OR strife) Get freq’s for all terms. Estimate the size of each OR by the sum of its freq’s (conservative). Process in increasing order of OR sizes.

10. 10 Exercise Recommend a query processing order for (tangerine OR trees) AND (marmalade OR skies) AND (kaleidoscope OR eyes)

11. 11 Query processing exercises If the query is friends AND romans AND (NOT countrymen), how could we use the freq of countrymen? Exercise: Extend the merge to an arbitrary Boolean query. Can we always guarantee execution in time linear in the total postings size?

12. 12 Faster postings merges: Skip pointers

13. 13 Recall basic merge Walk through the two postings simultaneously, in time linear in the total number of postings entries 128 31 248163264123581721 Brutus Caesar 2 8 If the list lengths are m and n, the merge takes O(m+n) operations. Can we do better? Yes,if we have pointers…

14. 14 Augment postings with skip pointers (at indexing time) Why? To skip postings that will not figure in the search results. How? Where do we place skip pointers? 12824816326431123581721 31 8 16 128

15. 15 Query processing with skip pointers 12824816326431123581721 31 8 16 128 Suppose we’ve stepped through the lists until we process 8 on each list. When we get to 16 on the top list, we see that its successor is 32. But the skip successor of 8 on the lower list is 31, so we can skip ahead past the intervening postings.

16. 16 Where do we place skips? Tradeoff: More skips  shorter skip spans  more likely to skip. But lots of comparisons to skip pointers. Fewer skips  few pointer comparison, but then long skip spans  few successful skips.

17. 17 B-Trees Use B-Trees, instead of skip pointers Handle large posting lists Top levels of the B-Tree always in memory for most used posting lists Better caching performance Read-only B-Trees Simple implementation No internal fragmentation

18. 18 Zig-zag join Join all lists at the same time Self-optimized Heuristic: when a result is found, move list with the smallest residual term frequency Want to move the list which will skip the most number of entries Brutus Calpurnia Caesar 12358132134 248163264128 1316 No need to execute the query (Caesar AND Brutus) AND Calpurnia.

19. 19 Zig-zag example Brutus Calpurnia Caesar 12358132134 248163264128 1316 Handle OR’s and NOT’s More about Zig-zag join in the XML class

20. 20 Phrase queries

21. 21 Phrase queries Want to answer queries such as “stanford university” – as a phrase Thus the sentence “I went to university at Stanford” is not a match. The concept of phrase queries has proven easily understood by users; about 10% of web queries are phrase queries No longer suffices to store only entries

22. 22 Positional indexes Store, for each term, entries of the form: <number of docs containing term; doc1: position1, position2 … ; doc2: position1, position2 … ; etc.>

23. 23 Positional index example Can compress position values/offsets Nevertheless, this expands postings storage substantially <be: 993427; 1: 7, 18, 33, 72, 86, 231; 2: 3, 149; 4: 17, 191, 291, 430, 434; 5: 363, 367, …> Which of docs 1,2,4,5 could contain “to be or not to be”?

24. 24 Processing a phrase query Extract inverted index entries for each distinct term: to, be, or, not. Merge their doc:position lists to enumerate all positions with “to be or not to be”. to: 2:1,17,74,222,551; 4:8,16,190,429,433; 7:13,23,191;... be: 1:17,19; 4:17,191,291,430,434; 5:14,19,101;... Same general method for proximity searches

25. 25 Proximity queries LIMIT! /3 STATUTE /3 FEDERAL /2 TORT Here, /k means “within k words of”. Clearly, positional indexes can be used for such queries; biword indexes cannot. Exercise: Adapt the linear merge of postings to handle proximity queries. Can you make it work for any value of k?

26. 26 Positional index size You can compress position values/offsets Nevertheless, a positional index expands postings storage substantially It is now vastly used because of the power and usefulness of phrase and proximity queries … whether used explicitly or implicitly in a ranking retrieval system.

27. 27 Rules of thumb A positional index is 2 – 4 as large as a non- positional index Positional index size 35 – 50% of volume of original text Caveat: all of this holds for “English-like” languages

28. 28 Combination schemes Biword an positional indexes can be profitably combined For particular phrases (“Michael Jackson”, “Britney Spears”) it is inefficient to keep on merging positional postings lists Even more so for phrases like “The Who” Williams et al. (2004) evaluate a more sophisticated mixed indexing scheme A typical web query mixture was executed in ¼ of the time of using just a positional index It required 26% more space than having a positional index alone

29. 29 Wild-card queries

30. 30 Exercise: from this, how can we enumerate all terms meeting the wild-card query pro*cent ? Wild-card queries: * mon*: find all docs containing any word beginning “mon”. Easy with binary tree (or B-tree) lexicon: retrieve all words in range: mon ≤ w < moo *mon: find words ending in “mon”: harder Maintain an additional B-tree for terms backwards

31. 31 Query processing At this point, we have an enumeration of all terms in the dictionary that match the wild-card query We still have to look up the postings for each enumerated term E.g., consider the query: se*ate AND fil*er This may result in the execution of many Boolean AND queries

32. 32 B-trees handle *’s at the end of a query term How can we handle *’s in the middle of query term? (Especially multiple *’s) The solution: transform every wild-card query so that the *’s occur at the end This gives rise to the Permuterm Index.

33. 33 Query = hel*o X=hel, Y=o Lookup o$hel* Permuterm index For term hello index under: hello$, ello$h, llo$he, lo$hel, o$hell where $ is a special symbol. Queries: X lookup on X$X* lookup on X*$ *X lookup on X$**X* lookup on X* X*Y lookup on Y$X*X*Y*Z ??? Exercise!

34. 34 Empirical observation for English. Permuterm query processing Rotate query wild-card to the right Now use B-tree lookup as before. Permuterm problem: ≈ quadruples lexicon size

35. 35 $a,ap,pr,ri,il,l$,$i,is,s$,$t,th,he,e$,$c,cr,ru, ue,el,le,es,st,t$, $m,mo,on,nt,h$ Bigram indexes Enumerate all k-grams (sequence of k chars) occurring in any term e.g., from text “April is the cruelest month” we get the 2-grams (bigrams) $ is a special word boundary symbol Maintain an “inverted” index from bigrams to dictionary terms that match each bigram.

36. 36 mo on among $mmace among amortize madden around Bigram index example

37. 37 Processing n-gram wild-cards Query mon* can now be run as $m AND mo AND on Fast, space efficient. Gets terms that match AND version of our wildcard query. But we’d enumerate moon. Must post-filter these terms against query. Surviving enumerated terms are then looked up in the term-document inverted index.

38. 38 Search Type your search terms, use ‘*’ if you need to. E.g., Alex* will match Alexander. Processing wild-card queries As before, we must execute a Boolean query for each enumerated, filtered term. Wild-cards can result in expensive query execution

39. 39 Spelling correction

40. 40 Spell correction Two principal uses Correcting document(s) being indexed Retrieve matching documents when query contains a spelling error Two main flavors: Isolated word Check each word on its own for misspelling Will not catch typos resulting in correctly spelled words e.g., from  form Context-sensitive Look at surrounding words, e.g., I flew form Heathrow to Narita.

41. 41 Document correction Primarily for OCR’ed documents Correction algorithms tuned for this Goal: the index (dictionary) contains fewer OCR- induced misspellings Can use domain-specific knowledge E.g., OCR can confuse O and D more often than it would confuse O and I (adjacent on the keyboard, so more likely interchanged in typing).

42. 42 Query mis-spellings Our principal focus here E.g., the query Alanis Morisett We can either Retrieve documents indexed by the correct spelling, OR Return several suggested alternative queries with the correct spelling Did you mean Alanis Morissette?

43. 43 Isolated word correction Fundamental premise – there is a lexicon from which the correct spellings come Two basic choices for this A standard lexicon such as Webster’s English Dictionary An “industry-specific” lexicon – hand-maintained The lexicon of the indexed corpus E.g., all words on the web All names, acronyms etc. (Including the mis-spellings)

44. 44 Isolated word correction Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q What’s “closest”? We’ll study several alternatives Edit distance Weighted edit distance n-gram overlap

45. 45 Edit distance Given two strings S1 and S2, the minimum number of basic operations to covert one to the other Basic operations are typically character-level Insert Delete Replace E.g., the edit distance from cat to dog is 3. Generally found by dynamic programming.

46. 46 Edit distance Also called “Levenshtein distance” See http://www.merriampark.com/ld.htm for a nice example plus an applet to try on your ownhttp://www.merriampark.com/ld.htm

47. 47 Weighted edit distance As above, but the weight of an operation depends on the character(s) involved Meant to capture keyboard errors, e.g. m more likely to be mis-typed as n than as q Therefore, replacing m by n is a smaller edit distance than by q (Same ideas usable for OCR, but with different weights) Require weight matrix as input Modify dynamic programming to handle weights

48. 48 Using edit distances Given query, first enumerate all dictionary terms within a preset (weighted) edit distance (Some literature formulates weighted edit distance as a probability of the error) Then look up enumerated dictionary terms in the term-document inverted index Slow but no real fix Tries help Better implementations – see Kukich, Zobel/Dart references.

49. 49 Edit distance to all dictionary terms? Given a (mis-spelled) query – do we compute its edit distance to every dictionary term? Expensive and slow How do we cut the set of candidate dictionary terms? Here we use n-gram overlap for this

50. 50 n-gram overlap Enumerate all the n-grams in the query string as well as in the lexicon Use the n-gram index to retrieve all lexicon terms matching any of the query n-grams Threshold by number of matching n-grams Variants – weight by keyboard layout, etc.

51. 51 Example with trigrams Suppose the text is november Trigrams are nov, ove, vem, emb, mbe, ber. The query is december Trigrams are dec, ece, cem, emb, mbe, ber. So 3 trigrams overlap (of 6 in each term) How can we turn this into a normalized measure of overlap?

52. 52 One option – Jaccard coefficient A commonly-used measure of overlap (remember dup detection) Let X and Y be two sets; then the J.C. is Equals 1 when X and Y have the same elements and zero when they are disjoint X and Y don’t have to be of the same size Always assigns a number between 0 and 1 Now threshold to decide if you have a match E.g., if J.C. > 0.8, declare a match

53. 53 lo or rd alonelordsloth lordmorbid bordercard border ardent Standard postings “merge” will enumerate … Adapt this to using Jaccard (or another) measure. Matching n-grams Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd)

54. 54 Caveat Even for isolated-word correction, the notion of an index token is critical – what’s the unit we’re trying to correct? In Chinese/Japanese, the notions of spell- correction and wildcards are poorly formulated/understood

55. 55 Context-sensitive spell correction Text: I flew from Heathrow to Narita. Consider the phrase query “flew form Heathrow” We’d like to respond Did you mean “flew from Heathrow”? because no docs matched the query phrase.

56. 56 Context-sensitive correction Need surrounding context to catch this NLP too heavyweight for this. First idea: retrieve dictionary terms close (in weighted edit distance) to each query term Now try all possible resulting phrases with one word “fixed” at a time flew from heathrow fled form heathrow flea form heathrow etc. Suggest the alternative that has lots of hits?

57. 57 Exercise Suppose that for “flew form Heathrow” we have 7 alternatives for flew, 19 for form and 3 for heathrow. How many “corrected” phrases will we enumerate in this scheme?

58. 58 Another approach Break phrase query into a conjunction of biwords Look for biwords that need only one term corrected. Enumerate phrase matches and … rank them!

59. 59 General issue in spell correction Will enumerate multiple alternatives for “Did you mean” Need to figure out which one (or small number) to present to the user Use heuristics The alternative hitting most docs Query log analysis + tweaking For especially popular, topical queries

60. 60 Computational cost Spell-correction is computationally expensive Avoid running routinely on every query? Run only on queries that matched few docs

61. 61 Thesauri Thesaurus: language-specific list of synonyms for terms likely to be queried car  automobile, etc. Machine learning methods can assist Can be viewed as hand-made alternative to edit- distance, etc.

62. 62 Query expansion Usually do query expansion rather than index expansion No index blowup Query processing slowed down Docs frequently contain equivalences May retrieve more junk puma  jaguar retrieves documents on cars instead of on sneakers.

63. 63 Resources for today’s lecture IIR 2 MG 3.6, 4.3; MIR 7.2 Skip Lists theory: Pugh (1990) Multilevel skip lists give same O(log n) efficiency as trees H.E. Williams, J. Zobel, and D. Bahle. 2004. “Fast Phrase Querying with Combined Indexes”, ACM Transactions on Information Systems. H.E. WilliamsJ. ZobelD. Bahle http://www.seg.rmit.edu.au/research/research.ph p?author=4, D. Bahle, H. Williams, and J. Zobel. Efficient phrase querying with an auxiliary index. SIGIR 2002, pp. 215-221. http://www.seg.rmit.edu.au/research/research.ph p?author=4,

64. 64 Resources MG 4.2 Efficient spell retrieval: K. Kukich. Techniques for automatically correcting words in text. ACM Computing Surveys 24(4), Dec 1992. J. Zobel and P. Dart. Finding approximate matches in large lexicons. Software - practice and experience 25(3), March 1995. http://citeseer.ist.psu.edu/zobel95finding.html Nice, easy reading on spell correction: Mikael Tillenius: Efficient Generation and Ranking of Spelling Error Corrections. Master’s thesis at Sweden’s Royal Institute of Technology. http://citeseer.ist.psu.edu/179155.html http://citeseer.ist.psu.edu/179155.html