1. Motivation and Outline
Background
Definitions, etc.
The Problem
100,000+ pages
The Solution
Ranking docs
Vector space
Extensions
Relevance feedback,
clustering,
query expansion, etc.

2. Motivation
IR: representation, storage, organization of, and access to information items
Focus is on the user information need
User information need:
Find all docs containing information on college tennis teams which: (1) are maintained by a USA university and (2) participate in the NCAA tournament.
Emphasis is on the retrieval of information (not data)

3. Motivation Data retrieval Information retrieval IR system:
which docs contain a set of keywords?
Well defined semantics
a single erroneous object implies failure!
Information retrieval
information about a subject or topic
semantics is frequently loose
small errors are tolerated
IR system:
interpret contents of information items
generate a ranking which reflects relevance
notion of relevance is most important

4. Motivation IR at the center of the stage IR in the last 20 years:
classification and categorization
systems and languages
user interfaces and visualization
Still, area was seen as of narrow interest
Advent of the Web changed this perception once and for all
universal repository of knowledge
free (low cost) universal access
no central editorial board
many problems though: IR seen as key to finding the solutions!

5. Basic Concepts The User Task Retrieval Browsing information or data
purposeful
Browsing
glancing around
F1; cars, Le Mans, France, tourism
Retrieval
Browsing
Database

6. The Retrieval Process 4, 10 6, 7 5 8 2 User Interface
Text Operations (stemming, noun phrase detection etc..)
Query
Operations
(elaboration,
relevance feedback
Indexing
Searching
(hash tables etc.)
Ranking
(vector models ..)
Index
Text
query
user need
user feedback
ranked docs
retrieved docs
logical view
inverted file
DB Manager
Module
4, 10
6, 7 5 8 2
Database

7. Measuring Performancetn
Precision
Proportion of selected items that are correct
Recall
Proportion of target items that were selected
Precision-Recall curve
Shows tradeoff fp tp fn
System returned these
Actual relevant docs
Precision
Recall

8. Precision/Recall Curves
11-point recall-precision curve
Example: Suppose for a given query, 10 documents are relevant. Suppose when all documents are ranked in descending similarities, we have
d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 d21 d22 d23 d24 d25 d26 d27 d28 d29 d30 d31 …
precision .1
1.0
recall .3

9. Precision Recall Curves…
When evaluating the retrieval effectiveness of a text retrieval system or method, a large number of queries are used and their average 11-point recall-precision curve is plotted.
Methods 1 and 2 are better than method 3.
Method 1 is better than method 2 for high recalls.
precision
Method 1
Method 2
Method 3
recall

10. Query Models IR systems usually adopt index terms to process queries
a keyword or group of selected words
any word (more general)
Stemming might be used:
connect: connecting, connection, connections
An inverted file is built for the chosen index terms

11. Introduction
Docs
Index Terms
doc
match
Ranking
Information Need
query

12. Introduction Matching at index term level is quite imprecise
No surprise that users get frequently unsatisfied
Since most users have no training in query formation, problem is even worst
Frequent dissatisfaction of Web users
Issue of deciding relevance is critical for IR systems: ranking

13. Introduction
A ranking is an ordering of the documents retrieved that (hopefully) reflects the relevance of the documents to the user query
A ranking is based on fundamental premisses regarding the notion of relevance, such as:
common sets of index terms
sharing of weighted terms
likelihood of relevance
Each set of premisses leads to a distinct IR model

14. IR Models s e Adhoc r Filtering T a k Browsing Extended Boolean vector
Set Theoretic
Fuzzy
Extended Boolean
Classic Models
boolean
vector
probabilistic
Algebraic
Generalized Vector
Lat. Semantic Index
Neural Networks U s e r T a k
Retrieval:
Adhoc
Filtering
Non-Overlapping Lists
Proximal Nodes
Structured Models
Probabilistic
Inference Network
Belief Network
Browsing
Browsing
Flat
Structure Guided
Hypertext

15. IR Models
The IR model, the logical view of the docs, and the retrieval task are distinct aspects of the system

16. Retrieval: Ad Hoc x Filtering
Ad hoc retrieval: Q1 Q2 Q3
Collection
“Fixed Size” Q4 Q5

17. Retrieval: Ad Hoc x Filtering
Docs Filtered
for User 2
User 2
Profile
User 1
Profile
Docs for
User 1
Documents Stream

18. Classic IR Models - Basic Concepts
Each document represented by a set of representative keywords or index terms
An index term is a document word useful for remembering the document main themes
Usually, index terms are nouns because nouns have meaning by themselves
However, search engines assume that all words are index terms (full text representation)

19. Generating keywords Logical view of the documents
Accents
spacing
Noun
groups
Manual
indexing
Docs
stopwords
stemming
structure
structure
Full text
Index terms
Stop-word elimination
Noun phrase detection
Stemming
Generating index terms
Improving quality of terms.
Synonyms, co-occurence detection, latent semantic indexing..

20. Classic IR Models - Basic Concepts
Not all terms are equally useful for representing the document contents: less frequent terms allow identifying a narrower set of documents
The importance of the index terms is represented by weights associated to them
Let
ki be an index term
dj be a document
wij is a weight associated with (ki,dj)
The weight wij quantifies the importance of the index term for describing the document contents

21. Classic IR Models - Basic Concepts
Ki is an index term
dj is a document
t is the total number of docs
K = (k1, k2, …, kt) is the set of all index terms
wij >= 0 is a weight associated with (ki,dj)
wij = 0 indicates that term does not belong to doc
vec(dj) = (w1j, w2j, …, wtj) is a weighted vector associated with the document dj
gi(vec(dj)) = wij is a function which returns the weight associated with pair (ki,dj)

22. The Boolean Model Simple model based on set theory
Queries specified as boolean expressions
precise semantics
neat formalism
q = ka  (kb  kc)
Terms are either present or absent. Thus, wij  {0,1}
Consider
vec(qdnf) = (1,1,1)  (1,1,0)  (1,0,0)
vec(qcc) = (1,1,0) is a conjunctive component

23. The Boolean Model q = ka  (kb  kc)
(1,1,1)
(1,0,0)
(1,1,0) Ka Kb Kc
q = ka  (kb  kc)
sim(q,dj) = 1 if  vec(qcc) | (vec(qcc)  vec(qdnf))  (ki, gi(vec(dj)) = gi(vec(qcc))) otherwise

24. Drawbacks of the Boolean Model
Retrieval based on binary decision criteria with no notion of partial matching
No ranking of the documents is provided (absence of a grading scale)
Information need has to be translated into a Boolean expression which most users find awkward
The Boolean queries formulated by the users are most often too simplistic
As a consequence, the Boolean model frequently returns either too few or too many documents in response to a user query

25. The Vector Model Use of binary weights is too limiting
Non-binary weights provide consideration for partial matches
These term weights are used to compute a degree of similarity between a query and each document
Ranked set of documents provides for better matching

26. The Vector Model Define:
wij > 0 whenever ki  dj
wiq >= 0 associated with the pair (ki,q)
vec(dj) = (w1j, w2j, ..., wtj) vec(q) = (w1q, w2q, ..., wtq)
To each term ki is associated a unitary vector vec(i)
The unitary vectors vec(i) and vec(j) are assumed to be orthonormal (i.e., index terms are assumed to occur independently within the documents)
The t unitary vectors vec(i) form an orthonormal basis for a t-dimensional space
In this space, queries and documents are represented as weighted vectors

27. Document Vectors Documents are represented as “bags of words”
Represented as vectors when used computationally
A vector is like an array of floating point
Has direction and magnitude
Each vector holds a place for every term in the collection
Therefore, most vectors are sparse

28. Vector Space Example
a: System and human system engineering testing of EPS
b: A survey of user opinion of computer system response time
c: The EPS user interface management system
d: Human machine interface for ABC computer applications
e: Relation of user perceived response time to error measurement
f: The generation of random, binary, ordered trees
g: The intersection graph of paths in trees
h: Graph minors IV: Widths of trees and well-quasi-ordering
i: Graph minors: A survey

29. Document Vectors One location for each word.B C D E F G H I
nova galaxy heat h’wood film role diet fur
9 10
“Nova” occurs 10 times in text A
“Galaxy” occurs 5 times in text A
“Heat” occurs 3 times in text A
(Blank means 0 occurrences.)

30. Document Vectors One location for each word.B C D E F G H I
nova galaxy heat h’wood film role diet fur
9 10
“Hollywood” occurs 7 times in text I
“Film” occurs 5 times in text I
“Diet” occurs 1 time in text I
“Fur” occurs 3 times in text I

31. Document Vectors A B C D E F G H I
Document ids A B C D E F G H I
nova galaxy heat h’wood film role diet fur
9 10

32. We Can Plot the Vectors Star Diet Doc about movie stars
Doc about astronomy
Doc about mammal behavior
Diet

33. Illustration from Jurafsky & Martin
Documents in 3D Space
Illustration from Jurafsky & Martin

34. Similarity Function (1)
The similarity or closeness of a document d = ( w1, …, wi, …, wn ) with respect to a query q = ( q1, …, qi, …, qn ) is computed using a similarity function.
Many similarity functions exist.
Dot product function
sim(q, d) = dot(q, d) = q1  w1 + … + qn  wn
Example: Suppose d = (0.2, 0, 0.3, 1) and
q = (0.75, 0.75, 0, 1), then
sim(q, d) = = 1.15

35. Similarity Function (2)
Observations of the dot product function.
Documents having more terms in common with a query tend to have higher similarities with the query.
For terms that appear in both q and d, those with higher weights contribute more to sim(q, d) than those with lower weights.
It favors long documents over short documents.
The computed similarities have no clear upper bound.

36. A normalized similarity metricj dj  q i
Sim(q,dj) = cos() = [vec(dj)  vec(q)] / |dj| * |q| = [ wij * wiq] / |dj| * |q|
Since wij > 0 and wiq > 0, <= sim(q,dj) <=1
A document is retrieved even if it matches the query terms only partially

37. Vector Space Example cont.
interface
user c b
system a
Transition out:
We now return you to our regularly scheduled generals talk

38. Answering a Query Using Vector Space
Represent query as vector
Compute distances to all documents
Rank according to distance
Example
“computer system”

39. The Vector Model Sim(q,dj) = [ wij * wiq] / |dj| * |q|
How to compute the weights wij and wiq ?
Simple keyword frequencies tend to favor common words
E.g. Query: The Computer Tomography
A good weight must take into account two effects:
quantification of intra-document contents (similarity)
tf factor, the term frequency within a document
quantification of inter-documents separation (dissi-milarity)
idf factor, the inverse document frequency
wij = tf(i,j) * idf(i)

40. The Vector Model Let, A normalized tf factor is given by
N be the total number of docs in the collection
ni be the number of docs which contain ki
freq(i,j) raw frequency of ki within dj
A normalized tf factor is given by
f(i,j) = freq(i,j) / max(freq(l,j))
where the maximum is computed over all terms which occur within the document dj
The idf factor is computed as
idf(i) = log (N/ni)
the log is used to make the values of tf and idf comparable. It can also be interpreted as the amount of information associated with the term ki.

41. The Vector Model
The best term-weighting schemes use weights which are give by
wij = f(i,j) * log(N/ni)
the strategy is called a tf-idf weighting scheme
For the query term weights, a suggestion is
wiq = ( [0.5 * freq(i,q) / max(freq(l,q)]) * log(N/ni)
The vector model with tf-idf weights is a good ranking strategy with general collections
The vector model is usually as good as the known ranking alternatives. It is also simple and fast to compute.

42. The Vector Model Advantages: Disadvantages:
term-weighting improves quality of the answer set
partial matching allows retrieval of docs that approximate the query conditions
cosine ranking formula sorts documents according to degree of similarity to the query
Disadvantages:
assumes independence of index terms (??); not clear that this is bad though

43. The Vector Model: Example Ik1 k2 k3

44. The Vector Model: Example IIk1 k2 k3

45. The Vector Model: Example IIIk1 k2 k3