15-505
Internet Search Technologies
Lecture 5: Information Retrieval
Kamal Nigam
Slides adapted from Chris Manning, Prabhakar Raghavan, and Hinrich Schütze
at http://www-csli.stanford.edu/~hinrich/information-retrieval-book.html
1
Information Retrieval in 1650


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?




Slow (for large corpora)
NOT Calpurnia is non-trivial
Other operations (e.g., find the word Romans near
countrymen) not feasible
Ranked retrieval (best documents to return)
2
Term-document incidence
Antony and Cleopatra
Julius Caesar The Tempest
Hamlet
Othello
Macbeth
Antony
1
1
0
0
0
1
Brutus
1
1
0
1
0
0
Caesar
1
1
0
1
1
1
Calpurnia
0
1
0
0
0
0
Cleopatra
1
0
0
0
0
0
mercy
1
0
1
1
1
1
worser
1
0
1
1
1
0
Brutus AND Caesar but NOT
Calpurnia
1 if play contains
word, 0 otherwise
3
Incidence vectors



So we have a 0/1 vector for each term.
To answer query: take the rows for Brutus,
Caesar and Calpurnia (complemented)  bitwise
AND.
110100 AND 110111 AND 101111 = 100100.
4
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.
5
Search index construction
Documents to
be indexed.
Friends, Romans, countrymen.
Tokenizer
Token stream.
Friends Romans
Countrymen
Linguistic
modules
Modified tokens.
Inverted index.
friend
roman
countryman
Indexer friend
2
4
roman
1
2
countryman
13
6
16
Tokenization
Documents to
be indexed.
Friends, Romans, countrymen.
Tokenizer
Token stream.
Friends Romans
Countrymen
Linguistic
modules
Modified tokens.
Inverted index.
friend
roman
countryman
Indexer friend
2
4
roman
1
2
countryman
13
7
16
Tokenization




Input: “Friends, Romans and Countrymen”
Output: Tokens
 Friends
 Romans
 and
 Countrymen
Each token is candidate for an index entry, after
further processing
But what are valid tokens to emit?
8
Tokenization: tricky cases


Finland’s  Finland? Finlands? Finland’s?
Hewlett-Packard  Hewlett and Packard as one or
two tokens?

the hold-him-back-and-drag-him-away-maneuver ?

Numbers: unique token for every number?

L'ensemble  one token or two?

L ? L’ ? Le ?
German noun compounds are not segmented




Lebensversicherungsgesellschaftsangestellter
‘life insurance company employee’
Chinese and Japanese have no spaces between words:

莎拉波娃现在居住在美国东南部的佛罗里达。
9
Normalization
Documents to
be indexed.
Friends, Romans, countrymen.
Tokenizer
Token stream.
Friends Romans
Countrymen
Linguistic
modules
Modified tokens.
Inverted index.
friend
roman
countryman
Indexer friend
2
4
roman
1
2
countryman
1310 16
Normalization


Need to “normalize” terms in indexed text as well
as query terms into the same form
 We want to match U.S.A. and USA
We most commonly implicitly define equivalence
classes of terms


Alternative is to do asymmetric expansion:




e.g., by deleting periods in a term
Enter: window
Search: window, windows
Enter: windows Search: Windows, windows
Enter: Windows Search: Windows
Potentially more powerful, but less efficient
11
Case folding

Reduce all letters to lower case

exception: upper case (in mid-sentence?)





e.g., General Motors
Fed vs. fed
SAIL vs. sail
Often best to lower case everything, since users
will use lowercase regardless of ‘correct’
capitalization…
Makes some queries hard: “The Gap” – clothing
store
12
Stop words

With a stop list, you exclude from dictionary
entirely the commonest words. Intuition:



They have little semantic content: the, a, and, to, be
They take a lot of space: ~30% of postings for top 30
But the trend is away from doing this:



Good compression lets the space for stopwords be very small
Good query optimization techniques mean you pay little at
query time for including stop words.
You need them for:



Phrase queries: “King of Denmark”
Various song titles, etc.: “Let it be”, “To be or not to be”
“Relational” queries: “flights to London”
13
Stemming


Reduce terms to their “roots” before indexing
“Stemming” suggest crude affix chopping


language dependent
e.g., automate(s), automatic, automation all
reduced to automat.
for example compressed
and compression are both
accepted as equivalent to
compress.
for exampl compress and
compress ar both accept
as equival to compress
14
Porter’s algorithm

Commonest algorithm for stemming English


Conventions + 5 phases of reductions






Results suggest at least as good as other stemming options
phases applied sequentially
each phase consists of a set of commands
sample convention: Of the rules in a compound command,
select the one that applies to the longest suffix.
ies  i
ational  ate
tional  tion
15
Normalization: other languages


Accents: résumé vs. resume.
Most important criterion:



How are your users like to write their queries for
these words?
Even in languages with common accents, users
often may not type them
German: Tuebingen vs. Tübingen

Should be equivalent
16
Normalizations


Full morphological analysis – at most modest
benefits for retrieval
Do stemming and other normalizations help?

Often very mixed results: really help recall for
some queries but harm precision on others
17
Indexing
Documents to
be indexed.
Friends, Romans, countrymen.
Tokenizer
Token stream.
Friends Romans
Countrymen
Linguistic
modules
Modified tokens.
Inverted index.
friend
roman
countryman
Indexer friend
2
4
roman
1
2
countryman
1318 16
Big(ger) corpora


Consider N = 1M documents, each with about 1K
terms.
~6 bytes/term including spaces/punctuation




Say there are m = 500K distinct terms among
these.
500K x 1M matrix has half-a-trillion 0’s and 1’s.
But it has no more than one billion 1’s.


6GB of data in the documents.
matrix is extremely sparse.
Why?
What’s a better representation?

We only record the 1 positions.
19
Inverted index


For each term T, we must store a list of all
documents that contain T.
Do we use an array or a list for this?
Brutus
2
Calpurnia
1
Caesar
4
2
8
16 32 64 128
3
5
8
13 21 34
13 16
What happens if the word Caesar
is added to document 14?
20
Inverted index

Linked lists generally preferred to arrays



Dynamic space allocation
Insertion of terms into documents easy
Space overhead of pointers
Brutus
2
4
8
16
Calpurnia
1
2
3
5
Caesar
13
Dictionary
32
8
Posting
64
13
128
21
34
16
Postings lists
21
Sorted by docID (more later on why).
Indexer steps

Sequence of (Modified token, Document ID) pairs.
Doc 1
I did enact Julius
Caesar I was killed
i' the Capitol;
Brutus killed me.
Doc 2
So let it be with
Caesar. The noble
Brutus hath told you
Caesar was ambitious
Term
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
Doc #
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
caesar
2
was
ambitious
2
2
22
Indexer steps

Sort by terms.
Core indexing step.
Term
Doc #
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Term
Doc #
ambitious
2
be
2
brutus
1
brutus
2
capitol
1
caesar
1
caesar
2
caesar
2
did
1
enact
1
hath
1
I
1
I
1
i'
1
it
2
julius
1
killed
1
killed
1
let
2
me
1
noble
2
so
2
the
1
the
2
told
2
you
2
was
1
was
2
with
2
23
Indexer steps


Multiple term entries in a
single document are
merged.
Frequency information is
added.
Why frequency?
Will discuss later.
Term
Doc #
ambitious
2
be
2
brutus
1
brutus
2
capitol
1
caesar
1
caesar
2
caesar
2
did
1
enact
1
hath
1
I
1
I
1
i'
1
it
2
julius
1
killed
1
killed
1
let
2
me
1
noble
2
so
2
the
1
the
2
told
2
you
2
was
1
was
2
with
2
Term
Doc #
ambitious
be
brutus
brutus
capitol
caesar
caesar
did
enact
hath
I
i'
it
julius
killed
let
me
noble
so
the
the
told
you
was
was
with
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
2
1
2
2
Term freq
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
24

The result is split into a Dictionary file and a
Postings file.
Term
Doc #
ambitious
be
brutus
brutus
capitol
caesar
caesar
did
enact
hath
I
i'
it
julius
killed
let
me
noble
so
the
the
told
you
was
was
with
Freq
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
Doc #
Term
N docs Coll freq
ambitious
1
1
be
1
1
brutus
2
2
capitol
1
1
caesar
2
3
did
1
1
enact
1
1
hath
1
1
I
1
2
i'
1
1
it
1
1
julius
1
1
killed
1
2
let
1
1
me
1
1
noble
1
1
so
1
1
the
2
2
told
1
1
you
1
1
was
2
2
with
1
1
Freq
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
25

Where do we pay in storage?
Doc #
Terms
Freq
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
2
1
2
2
Term
N docs Coll freq
ambitious
1
1
be
1
1
brutus
2
2
capitol
1
1
caesar
2
3
did
1
1
enact
1
1
hath
1
1
I
1
2
i'
1
1
it
1
1
julius
1
1
killed
1
2
let
1
1
me
1
1
noble
1
1
so
1
1
the
2
2
told
1
1
you
1
1
was
2
2
with
1
1
Pointers
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
26
Retrieval
27
Query processing

We’ve just build something cool. How do we use
it?
28
Query processing: AND

Consider processing the query:
Brutus AND Caesar
 Locate Brutus in the Dictionary;


Locate Caesar in the Dictionary;


Retrieve its postings.
Retrieve its postings.
“Merge” the two postings:
2
4
8
16
1
2
3
5
32
8
64
13
128
21
Brutus
34 Caesar
29
The merge
Walk through the two postings simultaneously, in
time linear in the total number of postings entries

2
8
2
4
8
16
1
2
3
5
32
8
64
13
Brutus
34 Caesar
128
21
If the list lengths are x and y, the merge takes O(x+y)
operations.
Crucial: postings sorted by docID.
30
Boolean queries: Exact match

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.
31
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(x+y)
or what can we achieve?
32
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?
33
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
2
Calpurnia
1
Caesar
4
2
8
16 32 64 128
3
5
8
16 21 34
13 16
Query: Brutus AND Calpurnia AND Caesar
34
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
Brutus
2
Calpurnia
1
Caesar
4
2
8
16 32 64 128
3
5
8
13 21 34
13 16
Execute the query as (Caesar AND Brutus) AND Calpurnia.
35
Phrase queries
36
Phrase queries


Want to answer queries such as “carnegie
mellon” – as a phrase
Thus the sentence “I got money from the Mellon
bank in Carnegie” 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
37
Positional indexes

Store, for each term, entries of the form:
<number of docs containing term;
doc1: position1, position2 … ;
doc2: position1, position2 … ;
etc.>
38
Positional index example
<be: 993427;
1: 7, 18, 33, 72, 86, 231;
2: 3, 149;
4: 17, 191, 291, 430, 434;
5: 363, 367, …>


Which of docs 1,2,4,5
could contain “to be
or not to be”?
Can compress position values/offsets
Nevertheless, this expands postings storage
substantially
39
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:


be:


2:1,17,74,222,551; 4:8,16,190,429,433;
7:13,23,191; ...
1:17,19; 4:17,191,291,430,434; 5:14,19,101; ...
Same general method for proximity searches
40
Positional index size



You can compress position values/offsets
Still, a positional index expands postings storage
substantially
Standardly used because of the power and
usefulness of phrase and proximity queries …
whether used explicitly or implicitly in a ranking
retrieval system.
41
Rules of thumb



A positional index is 2–4 as large as a nonpositional index
Positional index size 35–50% of volume of
original text
Caveat: all of this holds for “English-like”
languages
42
Scoring and Ranking
43
Scoring

Thus far, our queries have all been Boolean





Docs either match or not
Good for expert users with precise understanding
of their needs and the corpus
Applications can consume 1000’s of results
Not good for (the majority of) users with poor
Boolean formulation of their needs
Most users don’t want to wade through 1000’s of
results – cf. use of web search engines
44
Scoring



We wish to return in order the documents most
likely to be useful to the searcher
How can we rank order the docs in the corpus
with respect to a query?
Assign a score – say in [0,1]


for each doc on each query
Assume no spammers

“adversarial IR” makes life complicated
45
Incidence matrices

Recall: Document is binary vector X in {0,1}v


Query is a binary vector Y
Score: Overlap measure:
X Y
Antony and Cleopatra
Julius Caesar
The Tempest
Hamlet
Othello
Macbeth
Antony
1
1
0
0
0
1
Brutus
1
1
0
1
0
0
Caesar
1
1
0
1
1
1
Calpurnia
0
1
0
0
0
0
Cleopatra
1
0
0
0
0
0
mercy
1
0
1
1
1
1
worser
1
0
1
1
1
0
46
Example



On the query ides of march, Shakespeare’s
Julius Caesar has a score of 3
All other Shakespeare plays have a score of 2
(because they contain march) or 1
Thus in a rank order, Julius Caesar would come
out tops
47
Overlap matching


What’s wrong with the overlap measure?
It doesn’t consider:


Term frequency in document
Term scarcity in collection (document
mention frequency)


of is more common than ides or march
Length of documents

(And queries: score not normalized)
48
Scoring: density-based




Thus far: overlap of terms/phrases in a doc
Next: if a document talks about a topic more,
then it is a better match
Document relevant if it has a lot of the terms
This leads to the idea of term weighting.
49
Scoring: Term weighting
50
Term-document count matrices

Consider the number of occurrences of a term in
a document:


Bag of words model
Document is a vector in ℕv: a column below
Antony and Cleopatra
Julius Caesar
The Tempest
Hamlet
Othello
Macbeth
Antony
157
73
0
0
0
0
Brutus
4
157
0
1
0
0
Caesar
232
227
0
2
1
1
Calpurnia
0
10
0
0
0
0
Cleopatra
57
0
0
0
0
0
mercy
2
0
3
5
5
1
worser
2
0
1
1
1
0
51
Bag of words view of a doc
Thus the doc
 John is quicker than Mary .
is indistinguishable from the doc
 Mary is quicker than John .

52
Term frequency tf




Idea: Score by summing all occurrences of query
words in doc
Long docs are favored because they’re more
likely to contain query terms
Can fix this to some extent by normalizing for
document length
But is raw tf the right measure?
Note: in IR frequency means unnormalized count
53
Counts vs. frequencies


Consider again the ides of march query.
 Julius Caesar has 5 occurrences of ides
 No other play has ides
 march occurs in over a dozen
 All the plays contain lots of of
By this scoring measure, the top-scoring play is
likely to be the one with the most ofs
54
Weighting term frequency: tf

What is the relative importance of




0 vs. 1 occurrence of a term in a doc
1 vs. 2 occurrences
2 vs. 3 occurrences …
Unclear: while it seems that more is better, a lot isn’t
proportionally better than a few
 Can just use raw tf

Another option commonly used in practice:
wft ,d  0 if tft ,d  0, 1  log tft ,d otherwise
Note: in IR frequency means unnormalized count
55
Score computation

Score for a query q = sum over terms t in q:
 tq tft ,d



[Note: 0 if no query terms in document]
Can use wf instead of tf in the above
Still doesn’t consider term scarcity in collection
(ides is rarer than of)
56
Weighting should depend on the
term overall


Which of these tells you more about a doc?
 10 occurrences of ides?
 10 occurrences of of?
Attenuate the weight of a common term


But what is “common”?
Consider collection frequency (cf )

The total number of occurrences of the term in the
entire collection of documents
57
Document frequency




But document frequency (df ) may be better:
df = number of docs in the corpus containing the
term
Word
cf
df
ferrari
10422
17
insurance 10440
3997
Document/collection frequency weighting is only
possible in known (static) collection.
So how do we make use of df ?
58
tf x idf term weights

tf x idf measure combines:
 term frequency (tf )


or wf, some measure of term density in a doc
inverse document frequency (idf )


measure of informativeness of a term: its rarity across
the whole corpus
The most commonly used version is:
 n 
idf i  log  
 df i 
59
Summary: tf x idf (or tf.idf)

Assign a tf.idf weight to each term i in each
document d
wi ,d  tfi ,d  log( n / df i )
What is the wt
of a term that
occurs in all
of the docs?
tfi ,d  frequency of term i in document j
n  total number of documents
df i  the number of documents that contain te rm i


Increases with the number of occurrences within a doc
Increases with the rarity of the term across the whole corpus
60
Real-valued term-document
matrices

Function (scaling) of count of a word in a
document:

Bag of words model
Each is a vector in ℝv

Here log-scaled tf.idf

Note can be >1!
Antony and Cleopatra
Julius Caesar
The Tempest
Hamlet
Othello
Macbeth
Antony
13.1
11.4
0.0
0.0
0.0
0.0
Brutus
3.0
8.3
0.0
1.0
0.0
0.0
Caesar
2.3
2.3
0.0
0.5
0.3
0.3
Calpurnia
0.0
11.2
0.0
0.0
0.0
0.0
Cleopatra
17.7
0.0
0.0
0.0
0.0
0.0
mercy
0.5
0.0
0.7
0.9
0.9
0.3
worser
1.2
0.0
0.6
0.6
0.6
0.0 61
Scoring: similarity
62
Documents as vectors


Each doc j can now be viewed as a vector of
wfidf values, one component for each term
So we have a vector space




terms are axes
docs live in this space
even with stemming, this is huge-dimensional
(The corpus of documents gives us a matrix,
which we could also view as a vector space in
which words live – transposable data)
63
Why turn docs into vectors?


You can also turn queries into (short) vectors
With q a vector, find d vectors (docs) “near” it.
64
Intuition
t3
d2
d3
q
t1
d5
t2
d4
Postulate: Text that is “close together”
in the vector space talk about similar things.
65
First cut at similarity

Idea: Distance between d1 and d2 is the length of
the vector |d1 – d2|.



Why is this not a great idea?
We still haven’t dealt with the issue of length
normalization


Euclidean distance
Short documents would be more similar to each
other by virtue of length, not topic
However, we can implicitly normalize by looking
at angles instead
66
Cosine similarity


Distance between vectors d1 and d2 captured by
the cosine of the angle x between them.
Note – this is similarity, not distance
t3
d2
d1
θ
t1
t2
67
Cosine similarity

A vector can be normalized (given a length of 1)
by dividing each of its components by its length –
here we use the L2 norm
x2
2
x
i i

This maps vectors onto the unit sphere:

Then,


Longer documents don’t get more weight

dj 
n
i 1
wi , j  1
68
Cosine similarity
 
d j  dk
sim (d j , d k )    
d j dk



n
i 1
i1 w
n
wi , j wi ,k
2
i, j
2
w
i1 i,k
n
Cosine of angle between two vectors
The denominator involves the lengths of the
vectors.
Normalization
69
Normalized vectors

For normalized vectors, the cosine is simply the
dot product:
 
 
cos( d j , d k )  d j  d k
70
Queries in the vector space model
Central idea: the query as a vector:
 We regard the query as short document
 We return the documents ranked by the
closeness of their vectors to the query, also
represented as a vector.
 
d j  dq
sim (d j , d q )    
d j dq


n
i 1
i1 w
Note that dq is very sparse!
n
wi , j wi ,q
2
i, j
2
w
i1 i,q
n
71
What did we learn today?


Length-normalized TFIDF-weighted/positional inverted
index to compute cosine similarities
 Say it three times fast
Store, for each term, entries of the form:
<number of docs containing term;
Doc1/tfidf: position1, position2 … ;
Doc2/tfidf: position1, position2 … ;
...>

Compute boolean matched documents with dot product
scores together, and present them ranked to user
72
Following up on today’s lecture

Free online textbook: http://wwwcsli.stanford.edu/~hinrich/information-retrievalbook.html

Good in-depth classes at CMU:


15-493 & 11-741
Taught by Jamie Callan and Yiming Yang
73