程序代写代做代考 scheme algorithm COMP6714: Informa2on Retrieval & Web Search

COMP6714: Informa2on Retrieval & Web Search

Introduc)on to

Informa(on Retrieval

Lecture 1: Boolean retrieval

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

Term‐document incidence

1 if play contains
word, 0 otherwise

Brutus AND Caesar BUT NOT
Calpurnia

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

The classic search model

Corpus

TASK

Info Need

Query

Verbal
form

Results

SEARCH
ENGINE

Query
Refinement

Info about removing mice
without killing them

mouse trap

Misconception?

Mistranslation?

Misformulation?

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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?

Sec. 1.1

COMP6714: Informa2on Retrieval & Web Search

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

Calpurnia

Caesar 1 2 4 5 6 16 57 132

1 2 4 11 31 45 173

2 31

What happens if the word Caesar
is added to document 14?

Sec. 1.2

174

54 101

COMP6714: Informa2on Retrieval & Web Search

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 Postings
Sorted by docID (more later on why).

Pos2ng

Sec. 1.2

Brutus

Calpurnia

Caesar 1 2 4 5 6 16 57 132

1 2 4 11 31 45 173

2 31

174

54 101

COMP6714: Informa2on Retrieval & Web Search

Tokenizer

Token stream. Friends Romans Countrymen

Inverted index construc)on

Linguistic
modules

Modified tokens. friend roman countryman

Indexer

Inverted index.

friend

roman

countryman

2 4

13 16

More on
these later.

Documents to
be indexed.

Friends, Romans, countrymen.

Sec. 1.2

COMP6714: Informa2on Retrieval & Web Search

Indexer steps: Token sequence
  Sequence of (Modified token, Document ID) pairs.

I did enact Julius
Caesar I was killed

i’ the Capitol;
Brutus killed me.

Doc 1

So let it be with
Caesar. The noble

Brutus hath told you
Caesar was ambitious

Doc 2

Sec. 1.2

COMP6714: Informa2on Retrieval & Web Search

Indexer steps: Sort

  Sort by terms
  And then docID

Core indexing step

Sec. 1.2

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 1.2

COMP6714: Informa2on Retrieval & Web Search

Where do we pay in storage?

17 Pointers

Terms
and

counts Later in the
course:
•  How do we

index
efficiently?

•  How much
storage do
we need?

Sec. 1.2

Lists of
docIDs

COMP6714: Informa2on Retrieval & Web Search

The index we just built
  How do we process a query?

  Later ‐ what kinds of queries can we process?

Today’s
focus

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

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:

128 
34 

2  4  8  16  32  64 
1  2  3  5  8  13  21 

Brutus 
Caesar 

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

The merge
  Walk through the two pos)ngs simultaneously, in
)me linear in the total number of pos)ngs entries

34 
128 2  4  8  16  32  64 

1  2  3  5  8  13  21 
128 
34 

2  4  8  16  32  64 
1  2  3  5  8  13  21 

Brutus 
Caesar 2  8 

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

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

Intersec)ng two pos)ngs lists
(a “merge” algorithm)

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 1.4

COMP6714: Informa2on Retrieval & Web Search

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….

Sec. 1.4

COMP6714: Informa2on Retrieval & Web Search

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?

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

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?

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

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.

Brutus

Caesar

Calpurnia

1 2 3 5 8 16 21 34

2 4 8 16 32 64 128

13 16

Query: Brutus AND Calpurnia AND Caesar
27 

Sec. 1.3

COMP6714: Informa2on Retrieval & Web Search

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

Execute the query as (Calpurnia AND Brutus) AND Caesar.

Sec. 1.3

Brutus

Caesar

Calpurnia

1 2 3 5 8 16 21 34

2 4 8 16 32 64 128

13 16

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 1.3

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?

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.

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

COMP6714: Informa2on Retrieval & Web Search

FASTER POSTINGS MERGES:
SKIP POINTERS/SKIP LISTS

COMP6714: Informa2on Retrieval & Web Search

Recall basic merge
  Walk through the two pos)ngs simultaneously, in
)me linear in the total number of pos)ngs entries

128

2 4 8 41 48 64

1 2 3 8 11 17 21

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 index isn’t changing too fast).

Sec. 2.3

COMP6714: Informa2on Retrieval & Web Search

Augment pos)ngs with skip pointers
(at indexing )me)

  Why?
  To skip pos)ngs that will not figure in the search
results.

  How?
  Where do we place skip pointers?

128 2 4 8 41 48 64

31 1 2 3 8 11 17 21
31 11

41 128

Sec. 2.3

COMP6714: Informa2on Retrieval & Web Search

Query processing with skip pointers

128 2 4 8 41 48 64

31 1 2 3 8 11 17 21
31 11

41 128

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.

Sec. 2.3

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 2.3

Can we skip w/o skip pointers?

COMP6714: Informa2on Retrieval & Web Search

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!

Sec. 2.3

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

skip pointers
Inverted list

CMS09::Chap5

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

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
entries

Sec. 2.4

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 2.4.1

COMP6714: Informa2on Retrieval & Web Search

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!

Sec. 2.4.1

COMP6714: Informa2on Retrieval & Web Search

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
N X X N

  Query processing: parse it into N’s and X’s
  Segment query into enhanced biwords
  Look up in index: catcher rye

Sec. 2.4.1

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 2.4.1

COMP6714: Informa2on Retrieval & Web Search

Solu)on 2: Posi)onal indexes
  In the pos)ngs, store, for each term the posi)on(s) in
which tokens of it appear:

Sec. 2.4.2

COMP6714: Informa2on Retrieval & Web Search

Posi)onal index example

  For phrase queries, we use a merge algorithm
recursively at the document level

  But we now need to deal with more than just
equality

Which of docs 1,2,4,5
could contain “to be

or not to be”?

Sec. 2.4.2

COMP6714: Informa2on Retrieval & Web Search

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

Sec. 2.4.2

COMP6714: Informa2on Retrieval & Web Search

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!

Sec. 2.4.2

COMP6714: Informa2on Retrieval & Web Search

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.

Sec. 2.4.2

COMP6714: Informa2on Retrieval & Web Search

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   SEC filings, books, even some epic poems … easily 100,000 terms   Consider a term with frequency 0.1% Why? 100 1 100,000 1 1 1000 Positional postings Postings Document size Sec. 2.4.2 COMP6714: Informa2on Retrieval & Web Search 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 Sec. 2.4.2 COMP6714: Informa2on Retrieval & Web Search 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 ¼ of the )me of using just a posi)onal index   It required 26% more space than having a posi)onal index alone Sec. 2.4.3 COMP6714: Informa2on Retrieval & Web Search Solu)on 3: Suffix Tree/Array   BANANA$   BANANA$ pos:0   ANANA$ pos:1   NANA$ pos:2   ANA$ pos:3   NA$ pos:4   A$ pos:5   A$ pos:5   ANA$ pos:3   ANANA$ pos:1   BANANA$ pos:0   NA$ pos:4   NANA$ pos:2 Sec. 2.4.3 Sort on the strings COMP6714: Informa2on Retrieval & Web Search Suffix Array   BANANA$   BANANA$ pos:0   ANANA$ pos:1   NANA$ pos:2   ANA$ pos:3   NA$ pos:4   A$ pos:5   A$ pos:5   ANA$ pos:3   ANANA$ pos:1   BANANA$ pos:0   NA$ pos:4   NANA$ pos:2 Sec. 2.4.3 Sort on the strings   If the original string is available, each suffix can be completely specified by the index of its first character 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 58 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 62 iterative proportional scaling 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 ftropical∩fish∩breeding = ftropical∩breeding ∙ ffish∩breeeding/fbreeding = 5510 ∙ 36427/81885 = 2451 vs. 1529 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   a�er processing 3,000 out of the 26,480 documents that contain “aquarium”, C = 258 ftropical∩fish∩aquarium = 258/(3000÷26480) = 2,277   A�er 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]

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