INF 2914 Information Retrieval and Web Search

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INF 2914Information Retrieval and Web Search

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

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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

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Brutus
Caesar
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The merge

• Walk through the two postings simultaneously, in
  time linear in the total number of postings
  entries

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

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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?

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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?

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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
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Query Brutus AND Calpurnia AND Caesar
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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.
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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.

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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?

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Faster postings mergesSkip pointers
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Recall basic merge

• Walk through the two postings simultaneously, in
  time linear in the total number of postings
  entries

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

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

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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

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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.
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Zig-zag example

• Handle ORs and NOTs
• More about Zig-zag join in the XML class

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Phrase queries
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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

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Positional indexes

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

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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

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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

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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.

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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

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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

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Wild-card queries
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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 ?
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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

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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.

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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!

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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.
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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
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Bigram index example
m
mace
madden
mo
among
amortize
on
among
around
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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.

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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.
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Spelling correction
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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.

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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).

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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?

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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)

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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

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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.

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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

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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

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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.

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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

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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.

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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?

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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

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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.
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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

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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.

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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?

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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?

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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!

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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

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Computational cost

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

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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.

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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.

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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.

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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