1. VECTOR SPACE MODEL Its Applications and implementations
in Information Retrieval
Lecture -3
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

5. Cosine is a normalized dot product
Slides for Lecture 3
Cosine Similarity measure
Similarity(dvector, qvector) = cos ө
( x.y = |x |. |y | cos ө)
j=1mΣwij * qij
(j=1mΣwij2)1/2(j=1m Σ qij2)1/2
Cosine is a normalized dot product
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

9. Slides for lecture 3 How to weight terms?
Higher the weight term = higher impact on cosine
What terms are important?
>if term is present in query then its presence in
the document is relevant to the query
>Infrequent in other documents
>Frequent in document A
So the cosine needs to be modified in this respect
11/14/2019
Dr.G.Das

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)
let’s 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
11/14/2019
Dr.G.Das

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 d
d76
we can arrange the documents in a descending order of the corresponding score that is computed from tf * idf
11/14/2019
Dr.G.Das

13. Slides for lecture 3 tf * idf measure: term frequency (tf)
inverse document frequency (idf)
11/14/2019
Dr.G.Das

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 T FA and TA algorithms are used for merging of the lists
d1 d2 d FA - Fagin’s Algorithm
d2 d3 d TA –Threshold Algorithm
d3 d4 d2
d5 d2 d4 d d6 d7
11/14/2019
Dr.G.Das

15. Slides for lecture 3
After the intersected list for the multi values has been found , then take the Tf*IDF score for each and add them for the corresponding terms arrange them in decreasing order of the total
T T T3
(tf*idf + tf*idf + tf*idf)
d (this will be ranked higher) d
11/14/2019
Dr.G.Das

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
11/14/2019
Dr.G.Das

17. Slides for lecture 3 Advantages Disadvantages
>Ranked Retrieval >terms are taken
>Terms are weighted independent
according to importance >Weighting is not
very formal
11/14/2019
Dr.G.Das

18. Slides for Lecture -3 Thank you Slides Made By : Arjun Saraswat
11/14/2019
Dr.G.Das

19. Slides for lecture -3 References:
11/14/2019
Dr.G.Das