VECTOR SPACE MODEL

1
VECTOR SPACE MODEL

• Its Applications and implementations
• in Information Retrieval
• Lecture -3

2
Slides for Lecture -3

• The Vector Space Model (VSM) is a way of
  representing documents through the words that
  they contain
• It is a standard technique in Information
  Retrieval
• The VSM allows decisions to be made about which
  documents are similar to each other and to
  keyword queries

3
Slides for Lecture 3

• The Vector Space Model
• Documents and queries both are vectors
• Di (wdi1,wdi2,.wdij)
• each wij is the weight of the term j in document
  i
• similarity metric is measured as equal to
  cosine of
• the angle between them

4
Slides for lecture 3

• Documents and Queries are represented as vectors.
• Position 1 corresponds to term 1, position 2 to
  term 2, position t to term t

5
Slides for Lecture 3

• Cosine Similarity measure
• Similarity(dvector, qvector) cos ?
• ( x.y x . y cos ?)
• j1mSwij qij
• (j1mSwij2)1/2(j1m S qij2)1/2
• Cosine is a normalized dot product

6
Slides for lecture 3

• TF-IDF Normalization
• Normalize the term weights (so longer documents
  are not unfairly given more weight)
• The longer the document, the more likely it is
  for a given term to appear in it, and the more
  often a given term is likely to appear in it. So,
  we want to reduce the importance attached to a
  term appearing in a document based on the length
  of the document

7
Slides for lecture 3

• Cosine is the normalized dot product
• Documents are ranked according to decreasing
  order of Cosine value
• sim( dvector, qvector) 1 when
• 
  dvector qvector
• sim( dvector, qvector) 0 when dvector and
  qvector share no terms

8
Slides for lecture 3

• A user enters a query
• The query is compared to all documents using a
  similarity measure
• A vector distance between the query and documents
  is used to rank the retrieved pages
• The user is shown the documents in decreasing
  order of similarity to the query term

9
Slides for lecture 3

• How to weight terms?
• Higher the weight term higher impact on cosine
• What terms are important?
• gtif term is present in query then its
  presence in
• the document is relevant to the query
• gtInfrequent in other documents
• gtFrequent in document A
• So the cosine needs to be modified in this
  respect

10
Slides for lecture 3

• Modeling and Implementation
• Example suppose a query is fired by the user
  specifying three particular terms T1, T2,T3
• Query q (T1, T2, T3)
• lets there be n documents with a total of m
  terms
• Now for implementation

11
Slides for lecture-3

• Document Ranking
• A user enters a query
• The query is compared to all documents using a
  similarity measure
• The user is shown the documents in decreasing
  order of similarity to the query term

12
Slides for lecture 3

• Example
• Term T1 T2 T3
  Tm
• Document d1 d2 d1
  .. d1
• d2 d4 d7
  d7
• d3 d8 d9
  .d10
• d9 d10 d6
  d11
• . .
  .
  .
• . .
  .
  d65
• d7 d89 .
  
  
• 
  d76
• we can arrange the documents in a descending
  order of the corresponding score that is
  computed from tf idf

13
Slides for lecture 3
tf idf measure term frequency (tf) inverse
document frequency (idf)
14
Slides for lecture 3
Slides for lecture 3

• In the case of multiple values we take the
  smallest list of documents among corresponding to
  the Query values T1, T2,T3
• T1 T2 T3 FA and TA
  algorithms are used for merging of the lists
• d1 d2 d1 FA -
  Fagins Algorithm
• d2 d3 d3 TA
  Threshold Algorithm
• d3 d4 d2
• d5 d2 d4
• . . .
• d4 . .
• . d6
• d7

15
Slides for lecture 3

• After the intersected list for the multi values
  has been found , then take the TfIDF score for
  each and add them for the corresponding terms
  arrange them in decreasing order of the total
• T1 T2 T3
• (tfidf tfidf tfidf)
• d1 106 106 0 (this
  will be ranked higher)
• d2 4 4 4

16
Slides for lecture 3

• DATBASE CONTEXT
• All distinct values are words or terms
• A tuple is taken as a Document
• Important Points
• Vector space does not force any broad conditions
• No search engine uses vector space model
• It is implemented but using some constraints

17
Slides for lecture 3

• Advantages
  Disadvantages
• gtRanked Retrieval gtterms are
  taken
• gtTerms are weighted independent
• according to importance gtWeighting is not
  
• 
  very formal

18
Slides for Lecture -3

• Thank you
• Slides Made By Arjun Saraswat

19
Slides for lecture -3

• References
• www.scit.wlv.ac.uk/jphb/cp4040/mtnotes
• http//www.cs.wisc.edu/dbbook/openAccess/thirdEdi
  tion/slides
• http//krakow.lti.cs.cmu.edu
• http//www.cs.utexas.edu/users/mooney/ir-course/sl
  ides
• http//db.uwaterloo.ca/tozsu/courses