COMP6714: Informa2on Retrieval & Web Search
Introduc)on to
Informa(on Retrieval
Lecture 1: Boolean retrieval
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Unstructured data in 1680
Which plays of Shakespeare contain the words Brutus
AND Caesar but NOT Calpurnia?
One could grep all of Shakespeare’s plays for Brutus
and Caesar, then strip out lines containing Calpurnia?
Why is that not the answer?
Slow (for large corpora)
NOT Calpurnia is non‐trivial
Other opera)ons (e.g., find the word Romans near countrymen) not feasible
Ranked retrieval (best documents to return) Later lectures
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Term‐document incidence
1 if play contains word, 0 otherwise
Brutus AND Caesar BUT NOT Calpurnia
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Incidence vectors
So we have a 0/1 vector for each term.
To answer query: take the vectors for Brutus, Caesar and Calpurnia (complemented) bitwise AND.
110100 AND 110111 AND 101111 = 100100.
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Answers to query
Antony and Cleopatra, Act III, Scene ii
Agrippa [Aside to DOMITIUS ENOBARBUS]: Why, Enobarbus, When Antony found Julius Caesar dead,
He cried almost to roaring; and he wept When at Philippi he found Brutus slain.
Hamlet, Act III, Scene ii
Lord Polonius: I did enact Julius Caesar I was killed i’ the Capitol; Brutus killed me.
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Basic assump)ons of Informa)on Retrieval Collec)on: Fixed set of documents
Goal: Retrieve documents with informa)on that is relevant to the user’s informa)on need and helps the user complete a task
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COMP6714: Informa2on Retrieval & Web Search
The classic search model
TASK
Info Need
Verbal form
Query
mouse trap
Misconception?
Info about removing mice without killing them
Mistranslation?
Misformulation?
SEARCH ENGINE
Query Refinement
Results
Corpus
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
How good are the retrieved docs?
Precision : Frac)on of retrieved docs that are relevant to user’s informa)on need
Recall : Frac)on of relevant docs in collec)on that are retrieved
More precise defini)ons and measurements to follow in later lectures
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Bigger collec)ons
Consider N = 1 million documents, each with about 1000 words.
Avg 6 bytes/word including spaces/punctua)on 6GB of data in the documents.
Say there are M = 500K dis2nct terms among these.
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Can’t build the matrix
500K x 1M matrix has half‐a‐trillion 0’s and 1’s.
But it has no more than one billion 1’s. matrix is extremely sparse.
What’s a be^er representa)on? We only record the 1 posi)ons.
Why?
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Inverted index
For each term t, we must store a list of all documents that contain t.
Iden)fy each by a docID, a document serial number Can we used fixed‐size arrays for this?
Brutus
1
2
4
11
31
45
173
174
Caesar
1
2
4
5
6
16
57
132
Calpurnia
2
31
54
101
What happens if the word Caesar is added to document 14?
11
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Inverted index
We need variable‐size pos)ngs lists
On disk, a con)nuous run of pos)ngs is normal and best
In memory, can use linked lists or variable length arrays
Some tradeoffs in size/ease of inser)on
Dictionary
Pos2ng
Brutus
1
2
4
11
31
45
173
174
Caesar
1
2
4
5
6
16
57
132
Calpurnia
2
31
54
101
Postings
Sorted by docID (more later on why).
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COMP6714: Informa2on Retrieval & Web Search
Inverted index construc)on
Sec. 1.2
Documents to be indexed.
Token stream.
Modified tokens.
Inverted index.
Tokenizer
Linguistic modules
Indexer
More on these later.
Friends, Romans, countrymen.
Friends
Romans
Countrymen
friend
roman
countryman
friend
roman
1
13
4
2
16
countryman
2
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Indexer steps: Token sequence Sequence of (Modified token, Document ID) pairs.
Doc 1 Doc 2
I did enact Julius Caesar I was killed
i’ the Capitol; Brutus killed me.
So let it be with Caesar. The noble
Brutus hath told you Caesar was ambitious
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Indexer steps: Sort Sort by terms
And then docID
Core indexing step
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Indexer steps: Dic)onary & Pos)ngs
Mul)ple term entries in a single document are merged.
Split into Dic)onary and Pos)ngs
Doc. frequency informa)on is added.
Why frequency? Will discuss later.
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Where do we pay in storage?
Lists of docIDs
Terms and counts
Pointers
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Later in the course:
• How do we index
efficiently?
• How much storage do we need?
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
The index we just built
How do we process a query?
Later ‐ what kinds of queries can we process?
Today’s focus
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query processing: AND
Consider processing the query:
Brutus AND Caesar
Locate Brutus in the Dic)onary; Retrieve its pos)ngs.
Locate Caesar in the Dic)onary; Retrieve its pos)ngs.
“Merge” the two pos)ngs:
2
4
8
16
32
64
128
Brutus
Caesar
1
2
3
5
8
13
21
34
19
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
The merge
Walk through the two pos)ngs simultaneously, in )me linear in the total number of pos)ngs entries
Brutus
Caesar
If the list lengths are x and y, the merge takes O(x+y) operations.
Crucial: postings sorted by docID.
2
4
8
16
32
64
128
2
8
1
2
3
5
8
13
21
34
20
COMP6714: Informa2on Retrieval & Web Search
Intersec)ng two pos)ngs lists (a “merge” algorithm)
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
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 condi)on or not.
Perhaps the simplest model to build an IR system on
Primary commercial retrieval tool for 3 decades.
Many search systems you s)ll use are Boolean: Email, library catalog, Mac OS X Spotlight
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.4
Example: WestLaw http://www.westlaw.com/
Largest commercial (paying subscribers) legal search service (started 1975; ranking added 1992)
Tens of terabytes of data; 700,000 users
Majority of users still use boolean queries
Example query:
What is the statute of limitations in cases involving
the federal tort claims act?
LIMIT! /3 STATUTE ACTION /S FEDERAL /2 TORT /3 CLAIM
foo! = foo*, /3 = within 3 words, /S = in same sentence
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.4
Example: WestLaw http://www.westlaw.com/
Another example query:
Requirements for disabled people to be able to access a workplace
disabl! /p access! /s work‐site work‐place (employment /3 place
Note that SPACE is disjunc)on, not conjunc)on!
Long, precise queries; proximity operators;
incrementally developed; not like web search
Many professional searchers s)ll like Boolean search
You know exactly what you are geqng
But that doesn’t mean it actually works be^er….
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Boolean queries: More general merges
Exercise: Adapt the merge for the queries: Brutus AND NOT Caesar
Brutus OR NOT Caesar
Can we s)ll run through the merge in )me O(x+y)? What can we achieve?
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Merging
What about an arbitrary Boolean formula?
(Brutus OR Caesar) AND NOT
(Antony OR Cleopatra)
Can we always merge in “linear” )me? Linear in what?
Can we do be^er?
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query op)miza)on
What is the best order for query processing?
Consider a query that is an AND of n terms.
For each of the n terms, get its pos)ngs, then AND them together.
21 34
27
Brutus
2
4
8
16
32
64
128
Caesar
1
2
3
5
8
16
Calpurnia
13
16
Query: Brutus AND Calpurnia AND Caesar
COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query op)miza)on example Process in order of increasing freq:
start with the smallest set, then keep cuNng further. This is why we kept
document freq. in dictionary
Brutus
2
4
8
16
32
64
128
Caesar
21 34
1
2
3
5
8
16
Calpurnia
13
16
Execute the query as (Calpurnia AND Brutus) AND Caesar.
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
More general op)miza)on
e.g., (madding OR crowd) AND (ignoble OR
strife) AND (light OR lord)
Get doc. freq.’s for all terms.
Es)mate the size of each OR by the sum of its doc. freq.’s (conserva)ve).
Process in increasing order of OR sizes.
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COMP6714: Informa2on Retrieval & Web Search
Exercise
Recommend a query processing order for
(tangerine OR trees) AND (marmalade OR skies) AND (kaleidoscope OR eyes)
Q: Any more accurate way to es)mate the cardinality of intermediate results? Q: Can we merge mul)ple lists (>2) simultaneously?
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COMP6714: Informa2on Retrieval & Web Search
Problema)c Cases
COMP6714: Informa2on Retrieval & Web Search
Query processing exercises
Exercise: 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 execu)on in )me linear in the total pos)ngs size?
Hint: Begin with the case of a Boolean formula query: in this, each query term appears only once in the query.
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COMP6714: Informa2on Retrieval & Web Search
Exercise
Try the search feature at
h^p://www.rhymezone.com/shakespeare/
Write down five search features you think it could do be^er
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COMP6714: Informa2on Retrieval & Web Search
FASTER POSTINGS MERGES: SKIP POINTERS/SKIP LISTS
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Recall basic merge
Walk through the two pos)ngs simultaneously, in )me linear in the total number of pos)ngs entries
Brutus Caesar
If the list lengths are m and n, the merge takes O(m+n) operations.
Can we do better?
Yes (if index isn’t changing too fast).
2
4
8
41
48
64
128
2
8
1
2
3
8
11
17
21
31
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Augment pos)ngs with skip pointers (at indexing )me)
41
11
128
31
2
4
8
41
48
64
128
1
2
3
8
11
17
21
31
Why?
To skip pos)ngs that will not figure in the search
results.
How?
Where do we place skip pointers?
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Query processing with skip pointers
41
11
128
31
2
4
8
41
48
64
128
1
2
3
8
11
17 21 31
Suppose we’ve stepped through the lists until we process 8 on each list. We match it and advance.
We then have 41 and 11 on the lower. 11 is smaller.
But the skip successor of 11 on the lower list is 31, so we can skip ahead past the intervening postings.
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
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.
Can we skip w/o skip pointers?
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Placing skips
Simple heuris)c: for pos)ngs of length L, use L1/2 evenly‐spaced skip pointers.
This ignores the distribu)on of query terms.
Easy if the index is rela)vely sta)c; harder if L keeps
changing because of updates.
This definitely used to help; with modern hardware it may not (Bahle et al. 2002) unless you’re memory‐ based
The I/O cost of loading a bigger pos)ngs list can outweigh the gains from quicker in memory merging!
COMP6714: Informa2on Retrieval & Web Search
Skip Pointers
A skip pointer (d, p) contains a document number d and a byte (or bit) posi)on p
Means there is an inverted list pos)ng that starts at posi)on p, and the pos)ng before it was for document d
CMS09::Chap5
skip pointers
Inverted list
COMP6714: Informa2on Retrieval & Web Search
Skip Pointers Example
Inverted list D‐gaps
Skip pointers
COMP6714: Informa2on Retrieval & Web Search
PHRASE QUERIES AND POSITIONAL INDEXES
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4
Phrase queries
Want to be able 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; one of the few “advanced search” ideas that works
Many more queries are implicit phrase queries For this, it no longer suffices to store only
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Solu)on 1: Biword indexes
Index every consecu)ve pair of terms in the text as a
phrase
For example the text “Friends, Romans, Countrymen” would generate the biwords
friends romans
romans countrymen
Each of these biwords is now a dic)onary term
Two‐word phrase query‐processing is now immediate.
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Longer phrase queries
Longer phrases are processed as we did with wild‐ cards:
stanford university palo alto can be broken into the Boolean query on biwords:
stanford university AND university palo AND palo alto
Without the docs, we cannot verify that the docs matching the above Boolean query do contain the phrase.
Can have false positives!
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Extended biwords
Parse the indexed text and perform part‐of‐speech‐tagging (POST).
Bucket the terms into (say) Nouns (N) and ar)cles/ preposi)ons (X).
Call any string of terms of the form NX*N an extended biword.
Each such extended biword is now made a term in the dic)onary.
Example: catcher in the rye NXXN
Query processing: parse it into N’s and X’s Segment query into enhanced biwords Look up in index: catcher rye
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Issues for biword indexes False posi)ves, as noted before
Index blowup due to bigger dic)onary
Infeasible for more than biwords, big even for them
Biword indexes are not the standard solu)on (for all biwords) but can be part of a compound strategy
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Solu)on 2: Posi)onal indexes
In the pos)ngs, store, for each term the posi)on(s) in
which tokens of it appear:
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index example
Which of docs 1,2,4,5 could contain “to be
or not to be”? For phrase queries, we use a merge algorithm
recursively at the document level
But we now need to deal with more than just equality
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Processing a phrase query
Extract inverted index entries for each dis)nct term:
to, be, or, not.
Merge their doc:posi2on lists to enumerate all posi)ons 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
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Proximity queries
LIMIT! /3 STATUTE /3 FEDERAL /2 TORT Again, here, /k means “within k words of”.
Clearly, posi)onal indexes can be used for such queries; biword indexes cannot.
Exercise: Adapt the linear merge of pos)ngs to handle proximity queries. Can you make it work for any value of k?
This is a li^le tricky to do correctly and efficiently See Figure 2.12 of IIR (Page 39)
There’s likely to be a problem on it!
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index size
You can compress posi)on values/offsets: we’ll talk about that in lecture 5
Nevertheless, a posi)onal index expands pos)ngs storage substan2ally
Nevertheless, a posi)onal index is now standardly used because of the power and usefulness of phrase and proximity queries … whether used explicitly or implicitly in a ranking retrieval system.
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index size
Need an entry for each occurrence, not just once per document
Index size depends on average document size Average web page has <1000 terms
Why?
SEC filings, books, even some epic poems ... easily 100,000 terms
Consider a term with frequency 0.1%
Document size
Postings
Positional postings
1000
1
1
100,000
1
100
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Rules of thumb
A posi)onal index is 2–4 as large as a non‐posi)onal index
Posi)onal index size 35–50% of volume of original text
Caveat: all of this holds for “English‐like” languages
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.3
Combina)on schemes
These two approaches can be profitably combined
For par)cular phrases (“Michael Jackson”, “Britney Spears”) it is inefficient to keep on merging posi)onal pos)ngs lists
Even more so for phrases like “The Who”
Williams et al. (2004) evaluate a more
sophis)cated mixed indexing scheme
A typical web query mixture was executed in 1⁄4 of the )me of using just a posi)onal index
It required 26% more space than having a posi)onal index alone
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.3
Solu)on 3: Suffix Tree/Array BANANA$
BANANA$
ANANA$
NANA$
ANA$
NA$
A$
A$
ANA$
ANANA$
BANANA$
NA$
NANA$
pos:0
pos:1
pos:2
pos:3
pos:4
pos:5
pos:5
pos:3
pos:1
pos:0
pos:4
pos:2
Sort on the strings
COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.3
Suffix Array BANANA$
If the original string is available, each suffix can be completely specified by the index of its first character
BANANA$
ANANA$
NANA$
ANA$
NA$
A$
A$
ANA$
ANANA$
BANANA$
NA$
NANA$
pos:0
pos:1
pos:2
pos:3
pos:4
pos:5
pos:5
pos:3
pos:1
pos:0
pos:4
pos:2
Sort on the strings
B
A
N
A
N
A
$
4
3
6
2
5
1
7
COMP6714: Informa2on Retrieval & Web Search
Resources for today’s lecture
Introduc2on to Informa2on Retrieval, chapter 1
Shakespeare:
h^p://www.rhymezone.com/shakespeare/
Try the neat browse by keyword sequence feature!
Managing Gigabytes, chapter 3.2
Modern Informa2on Retrieval, chapter 8.2
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COMP6714: Informa2on Retrieval & Web Search
Resources for today’s lecture
Skip Lists theory: Pugh (1990)
Mul)level 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^p://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.
COMP6714: Informa2on Retrieval & Web Search
Es)ma)ng Result Set Size
How many pages contain all of the query terms?
For the query “a b c”:
fabc = N ∙ fa/N ∙ fb/N ∙ fc/N = (fa ∙ fb ∙ fc)/N2
Assuming that terms occur independently
fabc is the es)mated size of the result set
fa, fb, fc are the number of documents that terms a, b, and c occur in
N is the number of documents in the collec)on
CMS09::Chap4
COMP6714: Informa2on Retrieval & Web Search
GOV2 Example
Collection size (N) is 25,205,179
COMP6714: Informa2on Retrieval & Web Search
Inconsistent Es)mate by Google circa 2007
iterative proportional scaling
62
COMP6714: Informa2on Retrieval & Web Search
Result Set Size Es)ma)on
Poor es)mates because words are not independent
Be^er es)mates possible if co‐occurrence informa)on available
P(a ∩ b ∩ c) = P(a ∩ c) ∙ P(b|(a ∩ c)) ≈ P(a ∩ c) ∙ P(b|c)
= P(a ∩ c) ∙ P(b ∩ c) / P(c) ftropical∩fish∩aquarium = ftropical∩aquarium ∙ ffish∩aquarium/faquarium
= 1921 ∙ 9722/26480 = 705
vs. 1529
ftropical∩fish∩breeding = ftropical∩breeding ∙ ffish∩breeeding/fbreeding = 5510 ∙ 36427/81885 = 2451
vs. 3629
COMP6714: Informa2on Retrieval & Web Search
Result Set Es)ma)on
Even be^er es)mates using ini)al result set
Es)mate is simply C/s
where s is the propor)on of the total documents that have been ranked, and C is the number of documents found that contain all the query words
E.g., “tropical fish aquarium” in GOV2
aÄer processing 3,000 out of the 26,480 documents that contain
“aquarium”, C = 258
ftropical∩fish∩aquarium = 258/(3000÷26480) = 2,277
AÄer processing 20% of the documents, ftropical∩fish∩aquarium = 1,778 (1,529 is real value)
COMP6714: Informa2on Retrieval & Web Search
Mo)va)on into a Be^er Es)mator
Example
1. N = 100, fA = 10, fB = 20
2. 1 sec into the intersec)on query processing, the current cursors points to docID = 20 and 30 on A and B’s inverted lists, respec)vely; and there are 1 documents in the
intersec)on. (Assuming docIDs are randomly assigned)
Es)ma)on
1. Based on independence: fAB = (10/100)*(20/100)*100 = 2 2. Based on “sampling”: fAB = 1 * (100/min(20, 30)) = 5
Can we combine the “strength” of both es)mators? Condi)onal random sampling [Li & Church, A Sketch Algorithm for
Es)ma)ng Two‐Way and Mul)‐Way Associa)ons]