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INF 2914 Information Retrieval and Web Search

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INF 2914 Information Retrieval and Web Search Lecture 7: Query Processing These s are adapted from Stanford s class CS276 / LING 286 Information Retrieval and ... – PowerPoint PPT presentation

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Title: INF 2914 Information Retrieval and Web Search


1
INF 2914 Information Retrieval and Web Search
  • Lecture 7 Query Processing
  • These slides are adapted from Stanfords class
    CS276 / LING 286
  • Information Retrieval and Web Mining

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
Brutus
Caesar
34
3
The merge
  • Walk through the two postings simultaneously, in
    time linear in the total number of postings
    entries

128
2
34
If the list lengths are x and y, the merge takes
O(xy) operations. Crucial postings sorted by
docID.
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 youre getting.

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(xy)
    or what can we achieve?

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
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
13
16
Query Brutus AND Calpurnia AND Caesar
8
Query optimization example
  • Process in order of increasing freq
  • start with smallest set, then keep cutting
    further.

This is why we kept freq in dictionary
Execute the query as (Caesar AND Brutus) AND
Calpurnia.
9
More general optimization
  • e.g., (madding OR crowd) AND (ignoble OR strife)
  • Get freqs for all terms.
  • Estimate the size of each OR by the sum of its
    freqs (conservative).
  • Process in increasing order of OR sizes.

10
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?

11
Faster postings merges Skip pointers
12
Recall basic merge
  • Walk through the two postings simultaneously, in
    time linear in the total number of postings
    entries

128
2
31
If the list lengths are m and n, the merge takes
O(mn) operations.
Can we do better? Yes,if we have pointers
13
Augment postings with skip pointers (at indexing
time)
128
16
31
8
  • Why?
  • To skip postings that will not figure in the
    search results.
  • How?
  • Where do we place skip pointers?

14
Query processing with skip pointers
128
16
31
8
Suppose weve stepped through the lists until we
process 8 on each list.
15
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.

16
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

17
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

No need to execute the query (Caesar AND Brutus)
AND Calpurnia.
18
Zig-zag example
  • Handle ORs and NOTs
  • More about Zig-zag join in the XML class

19
Phrase queries
20
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
  • ltterm docsgt entries

21
Positional indexes
  • Store, for each term, entries of the form
  • ltnumber of docs containing term
  • doc1 position1, position2
  • doc2 position1, position2
  • etc.gt

22
Positional index example
ltbe 993427 1 7, 18, 33, 72, 86, 231 2 3,
149 4 17, 191, 291, 430, 434 5 363, 367, gt
Which of docs 1,2,4,5 could contain to be or not
to be?
  • Can compress position values/offsets
  • Nevertheless, this expands postings storage
    substantially

23
Processing a phrase query
  • Extract inverted index entries for each distinct
    term to, be, or, not.
  • Merge their docposition lists to enumerate all
    positions with to be or not to be.
  • to
  • 21,17,74,222,551 48,16,190,429,433
    713,23,191 ...
  • be
  • 117,19 417,191,291,430,434 514,19,101 ...
  • Same general method for proximity searches

24
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.

25
Rules of thumb
  • A positional index is 24 as large as a
    non-positional index
  • Positional index size 3550 of volume of
    original text
  • Caveat all of this holds for English-like
    languages

26
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

27
Wild-card queries
28
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 lt moo
  • mon find words ending in mon harder
  • Maintain an additional B-tree for terms backwards

Exercise from this, how can we enumerate all
terms meeting the wild-card query procent ?
29
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
  • seate AND filer
  • This may result in the execution of many Boolean
    AND queries

30
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.

31
Permuterm index
  • For term hello index under
  • hello, elloh, llohe, lohel, ohell
  • where is a special symbol.
  • Queries
  • X lookup on X X lookup on X
  • X lookup on X X lookup on X
  • XY lookup on YX XYZ ???
  • Exercise!

32
Permuterm query processing
  • Rotate query wild-card to the right
  • Now use B-tree lookup as before.
  • Permuterm problem quadruples lexicon size

Empirical observation for English.
33
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.

a,ap,pr,ri,il,l,i,is,s,t,th,he,e,c,cr,ru, u
e,el,le,es,st,t, m,mo,on,nt,h
34
Bigram index example
m
mace
madden
mo
among
amortize
on
among
around
35
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 wed enumerate moon.
  • Must post-filter these terms against query.
  • Surviving enumerated terms are then looked up in
    the term-document inverted index.

36
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

Search
Type your search terms, use if you need
to. E.g., Alex will match Alexander.
37
Spelling correction
38
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.

39
Document correction
  • Primarily for OCRed 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).

40
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?

41
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
  • Websters 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)

42
Isolated word correction
  • Given a lexicon and a character sequence Q,
    return the words in the lexicon closest to Q
  • Whats closest?
  • Well study several alternatives
  • Edit distance
  • Weighted edit distance
  • n-gram overlap

43
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.

44
Edit distance
  • Also called Levenshtein distance
  • See http//www.merriampark.com/ld.htm for a nice
    example plus an applet to try on your own

45
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

46
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.

47
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

48
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.

49
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?

50
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 dont 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. gt 0.8, declare a match

51
Matching n-grams
  • Consider the query lord we wish to identify
    words matching 2 of its 3 bigrams (lo, or, rd)

lo
alone
lord
sloth
or
lord
morbid
border
rd
border
card
ardent
Standard postings merge will enumerate
Adapt this to using Jaccard (or another) measure.
52
Caveat
  • Even for isolated-word correction, the notion of
    an index token is critical whats the unit
    were trying to correct?
  • In Chinese/Japanese, the notions of
    spell-correction and wildcards are poorly
    formulated/understood

53
Context-sensitive spell correction
  • Text I flew from Heathrow to Narita.
  • Consider the phrase query flew form Heathrow
  • Wed like to respond
  • Did you mean flew from Heathrow?
  • because no docs matched the query phrase.

54
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?

55
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?

56
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!

57
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

58
Computational cost
  • Spell-correction is computationally expensive
  • Avoid running routinely on every query?
  • Run only on queries that matched few docs

59
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.

60
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.

61
Resources for todays 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.
  • http//www.seg.rmit.edu.au/research/research.php?a
    uthor4, D. Bahle, H. Williams, and J. Zobel.
    Efficient phrase querying with an auxiliary
    index. SIGIR 2002, pp. 215-221.

62
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. Masters
    thesis at Swedens Royal Institute of Technology.
    http//citeseer.ist.psu.edu/179155.html
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