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LBSC 796/INFM 718R: Week 3
Boolean and Vector Space Models
Jimmy Lin
College of Information Studies
University of Maryland
Monday, February 13, 2006
Muddy Points
| Statistics, significance tests
| Precision-recall curve, interpolation
| MAP
| Math, math, and more math!
| Reading the book
The Information Retrieval Cycle
Source
Selection
Search
Query
Selection
Ranked List
Examination
Documents
Delivery
Documents
Query
Formulation
Resource
source reselection
System discovery Vocabulary discovery Concept discovery Document discovery
What is a model?
| A model is a construct designed help us understand a complex system
z A particular way of “looking at things”
| Models inevitably make simplifying assumptions
z What are the limitations of the model?
| Different types of models:
z Conceptual models
z Physical analog models
z Mathematical models
z …
The Central Problem in IR
Information Seeker Authors
Concepts Concepts
Query Terms Document Terms
Do these represent the same concepts?
The IR Black Box
Query^ Documents
Hits
Representation
Function
Representation
Function
Query Representation Document Representation
Comparison
Function Index
Today’s Topics
| Boolean model
z Based on the notion of sets
z Documents are retrieved only if they satisfy Boolean
conditions specified in the query
z Does not impose a ranking on retrieved documents
z Exact match
| Vector space model
z Based on geometry, the notion of vectors in high
dimensional space
z Documents are ranked based on their similarity to the
query (ranked retrieval)
z Best/partial match
Next Time…
| Language models
z Based on the notion of probabilities and processes for
generating text
z Documents are ranked based on the probability that
they generated the query
z Best/partial match
Representing Text
Query^ Documents
Hits
Representation
Function
Representation
Function
Query Representation Document Representation
Comparison
Function Index
How do we represent text?
| How do we represent the complexities of language?
z Keeping in mind that computers don’t “understand”
documents or queries
| Simple, yet effective approach: “bag of words”
z Treat all the words in a document as index terms for
that document
z Assign a “weight” to each term based on its
“importance”
z Disregard order, structure, meaning, etc. of the words
What’s a “word”? We’ll return to this in a few lectures…
Sample Document
McDonald's slims down spuds
Fast-food chain to reduce certain types of fat in its french fries with new cooking oil. NEW YORK (CNN/Money) - McDonald's Corp. is cutting the amount of "bad" fat in its french fries nearly in half, the fast-food chain said Tuesday as it moves to make all its fried menu items healthier. But does that mean the popular shoestring fries won't taste the same? The company says no. "It's a win-win for our customers because they are getting the same great french-fry taste along with an even healthier nutrition profile," said Mike Roberts, president of McDonald's USA. But others are not so sure. McDonald's will not specifically discuss the kind of oil it plans to use, but at least one nutrition expert says playing with the formula could mean a different taste. Shares of Oak Brook, Ill.-based McDonald's (MCD: down $0.54 to $23.22, Research, Estimates) were lower Tuesday afternoon. It was unclear Tuesday whether competitors Burger King and Wendy's International (WEN: down $0.80 to $34.91, Research, Estimates) would follow suit. Neither company could immediately be reached for comment. …
16 × said
14 × McDonalds
12 × fat
11 × fries
8 × new
6 × company french nutrition
5 × food oil percent reduce
taste Tuesday
“Bag of Words”
What’s the point?
| Retrieving relevant information is hard!
z Evolving, ambiguous user needs, context, etc.
z Complexities of language
| To operationalize information retrieval, we must vastly simplify the picture
| Bag-of-words approach:
z Information retrieval is all (and only ) about matching
words in documents with words in queries
z Obviously, not true…
z But it works pretty well!
Boolean View of a Collection
quick
brown
fox
over
lazy
dog
back
now
time
all
good
men
come
jump
aid
their
party
Term
Doc 1Doc 2 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0
Doc 3Doc 4 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0
Doc 5Doc 6 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0
Doc 7Doc 8
Each column represents the view of
a particular document: What terms
are contained in this document?
Each row represents the view of a
particular term: What documents
contain this term?
To execute a query, pick out rows
corresponding to query terms and
then apply logic table of
corresponding Boolean operator
Sample Queries
fox
dog 0 0
Term
Doc 1Doc 2Doc 3Doc 4Doc 5Doc 6Doc 7Doc 8
dog ∧ fox 0 0 1 0 1 0 0 0
dog ∨ fox 0 0 1 0 1 0 1 0
dog ¬ fox 0 0 0 0 0 0 0 0
fox ¬ dog 0 0 0 0 0 0 1 0
dog AND fox → Doc 3, Doc 5
dog OR fox → Doc 3, Doc 5, Doc 7
dog NOT fox → empty
fox NOT dog → Doc 7
good party
g ∧ p 0 0 0 0 0 1 0 1
g ∧ p ¬ o 0 0 0 0 0 1 0 0
good AND party → Doc 6, Doc 8
over 1 0 1 0 1 0 1 1
good AND party NOT over → Doc 6
Term
Doc 1Doc 2Doc 3Doc 4Doc 5Doc 6Doc 7Doc 8
Proximity Operators
| More “precise” versions of AND
z “NEAR n” allows at most n-1 intervening terms
z “WITH” requires terms to be adjacent and in order
z Other extensions: within n sentences, within n
paragraphs, etc.
| Relatively easy to implement, but less efficient
z Store position information for each word in the
document vectors
z Perform normal Boolean computations, but treat WITH
and NEAR as extra constraints
Proximity Operator Example
quick
brown
fox
over
lazy
dog
back
now
time
all
good
men
come
jump
aid
their
party
Term
Doc 1Doc 2
time AND come → Doc 2
time (NEAR 2) come → empty
quick (NEAR 2) fox → Doc 1
quick WITH fox → empty
Other Extensions
| Ability to search on fields
z Leverage document structure: title, headings, etc.
| Wildcards
z lov* = love, loving, loves, loved, etc.
| Special treatment of dates, names, companies, etc.
WESTLAW® Query Examples
| What is the statute of limitations in cases involving the federal tort claims
act?
z LIMIT! /3 STATUTE ACTION /S FEDERAL /2 TORT /3 CLAIM
| What factors are important in determining what constitutes a vessel for
purposes of determining liability of a vessel owner for injuries to a seaman
under the “Jones Act” (46 USC 688)?
z (741 +3 824) FACTOR ELEMENT STATUS FACT /P VESSEL SHIP BOAT /P (46 +3 688) “JONES ACT” /P INJUR! /S SEAMAN CREWMAN WORKER
| Are there any cases which discuss negligent maintenance or failure to
maintain aids to navigation such as lights, buoys, or channel markers?
z NOT NEGLECT! FAIL! NEGLIG! /5 MAINT! REPAIR! /P NAVIGAT! /5 AID EQUIP! LIGHT BUOY “CHANNEL MARKER”
| What cases have discussed the concept of excusable delay in the
application of statutes of limitations or the doctrine of laches involving
actions in admiralty or under the “Jones Act” or the “Death on the High
Seas Act”?
z EXCUS! /3 DELAY /P (LIMIT! /3 STATUTE ACTION) LACHES /P “JONES ACT” “DEATH ON THE HIGH SEAS ACT” (46 +3 761)
Why Boolean Retrieval Works
| Boolean operators approximate natural language
z Find documents about a good party that is not over
| AND can discover relationships between concepts
z good party
| OR can discover alternate terminology
z excellent party, wild party, etc.
| NOT can discover alternate meanings
z Democratic party
The Perfect Query Paradox
| Every information need has a perfect set of documents
z If not, there would be no sense doing retrieval
| Every document set has a perfect query
z AND every word in a document to get a query for it
z Repeat for each document in the set
z OR every document query to get the set query
| But can users realistically be expected to formulate this perfect query?
z Boolean query formulation is hard!
Why Boolean Retrieval Fails
| Natural language is way more complex
| AND “discovers” nonexistent relationships
z Terms in different sentences, paragraphs, …
| Guessing terminology for OR is hard
z good, nice, excellent, outstanding, awesome, …
| Guessing terms to exclude is even harder!
z Democratic party, party to a lawsuit, …
Strengths and Weaknesses
| Strengths
z Precise, if you know the right strategies
z Precise, if you have an idea of what you’re looking for
z Efficient for the computer
| Weaknesses
z Users must learn Boolean logic
z Boolean logic insufficient to capture the richness of
language
z No control over size of result set: either too many
documents or none
z When do you stop reading? All documents in the result
set are considered “equally good”
z What about partial matches? Documents that “don’t
quite match” the query may be useful also
Ranked Retrieval
| Order documents by how likely they are to be relevant to the information need
z Present hits one screen at a time
z At any point, users can continue browsing through
ranked list or reformulate query
| Attempts to retrieve relevant documents directly, not merely provide tools for doing so
Why Ranked Retrieval?
| Arranging documents by relevance is
z Closer to how humans think: some documents are
“better” than others
z Closer to user behavior: users can decide when to stop
reading
| Best (partial) match: documents need not have all query terms
z Although documents with more query terms should be
“better”
| Easier said than done!
How do we weight doc terms?
| Here’s the intuition:
z Terms that appear often in a document should get high
weights
z Terms that appear in many documents should get low
weights
| How do we capture this mathematically?
z Term frequency
z Inverse document frequency
The more often a document contains the term “dog”, the
more likely that the document is “about” dogs.
Words like “the”, “a”, “of” appear in (nearly) all documents.
TF.IDF Term Weighting
| Simple, yet effective!
i
i j ij n
N w (^) , =tf (^) ,⋅log
wi (^) , j
tf i , j
N
ni
weight assigned to term i in document j
number of occurrence of term i in document j
number of documents in entire collection
number of documents with term i
TF.IDF Example
nuclear
fallout
siberia
contaminated
interesting
complicated
information
retrieval
tf Wi,j
idf
Normalizing Document Vectors
| Recall our similarity function:
| Normalize document vectors in advance
z Use the “cosine normalization” method: divide each
term weight through by length of vector
∑ ∑
∑
=
⋅
n i ik
n i ij
n i ij ik
j k
j k j k w w
ww
dd
d d simd d
1
( , ) r r
r r
Normalization Example
nuclear
fallout
siberia
contaminated
interesting
complicated
information
retrieval
tf
Wi,j
idf
Length^ 1.70 0.97 2.67 0.
W'i,j
Retrieval Example
nuclear
fallout
siberia
contaminated
interesting
complicated
information
retrieval
Query: contaminated retrieval
query
W'i,j
similarity score 0.29^ 0.9^ 0.19 0.
Ranked list:
Doc 2
Doc 4
Doc 1
Doc 3
Do we need to normalize the query vector?
W'i,j
Weighted Retrieval
Query: contaminated(3) retrieval
Weight query terms by assigning different term weights to query vector
nuclear
fallout
siberia
contaminated
interesting
complicated
information
retrieval
query
W'i,j
similarity score 0.87 1.16 0.47 0.
Ranked list:
Doc 2
Doc 1
Doc 4
Doc 3
W'i,j
What’s the point?
| Information seeking behavior is incredibly complex
| In order to build actual systems, we must make many simplifications
z Absolutely unrealistic assumptions!
z But the resulting systems are nevertheless useful
| Know what these limitations are!
Summary
| Boolean retrieval is powerful in the hands of a trained searcher
| Ranked retrieval is preferred in other circumstances
| Key ideas in the vector space model
z Goal: find documents most similar to the query
z Geometric interpretation: measure similarity in terms of
angles between vectors in high dimensional space
z Documents weights are some combinations of TF, DF,
and Length
z Length normalization is critical
z Similarity is calculated via the inner product
One Minute Paper
| What was the muddiest point in today’s class?
