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INF 2914Information Retrieval and Web

Search

Lecture 7: Query ProcessingThese slides are adapted from

Stanford’s class CS276 / LING 286Information 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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2 4 8 16 32 64

1 2 3 5 8 13

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Brutus

Caesar

3

34

1282 4 8 16 32 64

1 2 3 5 8 13 21

The merge

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

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2 4 8 16 32 64

1 2 3 5 8 13 21

Brutus

Caesar2 8

If the list lengths are x and y, the merge takes O(x+y)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 you’re getting.

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Boolean queries: More general merges

Exercise: Adapt the merge for the queries:Brutus AND NOT CaesarBrutus OR NOT Caesar

Can we still run through the merge in time O(x+y) 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

1 2 3 5 8 16 21 34

2 4 8 16 32 64 128

13 16

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.

Brutus

Calpurnia

Caesar

1 2 3 5 8 13 21 34

2 4 8 16 32 64 128

13 16

This is why we keptfreq 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 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.

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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 merges:Skip 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 4 8 16 32 64

1 2 3 5 8 17 21

Brutus

Caesar2 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…

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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?

1282 4 8 16 32 64

311 2 3 5 8 17 21318

16 128

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Query processing with skip pointers

1282 4 8 16 32 64

311 2 3 5 8 17 21318

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 itssuccessor is 32.

But the skip successor of 8 on the lower list is 31, sowe can skip ahead past the intervening postings.

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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 entriesBrutus

Calpurnia

Caesar

1 2 3 5 8 13 21 34

2 4 8 16 32 64 128

13 16

No need to execute the query (Caesar AND Brutus) AND Calpurnia.

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Zig-zag example

Brutus

Calpurnia

Caesar

1 2 3 5 8 13 21 34

2 4 8 16 32 64 128

13 16

Handle OR’s and NOT’s 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 <term : docs> entries

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Positional indexes

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

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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 1,2,4,5could contain “to be

or not to be”?

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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

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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 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

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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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Exercise: from this, how can we enumerate all termsmeeting 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

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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: se*ate AND fil*er 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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Query = hel*oX=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!

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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

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$a,ap,pr,ri,il,l$,$i,is,s$,$t,th,he,e$,$c,cr,ru,ue,el,le,es,st,t$, $m,mo,on,nt,h$

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.

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mo

on

among

$m mace

among

amortize

madden

around

Bigram index example

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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 we’d 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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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

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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 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).

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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

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)

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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

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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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YXYX /

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

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lo

or

rd

alone lord

sloth

lord

morbid

border card

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)

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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

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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.

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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 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.

http://www.seg.rmit.edu.au/research/research.php?author=4, 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. Master’s thesis at Sweden’s Royal Institute of Technology. http://citeseer.ist.psu.edu/179155.html