Vector Space Model in Information Retrieval and related problems

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Vector Space Model in Information Retrieval and
related problems

• 614 Fall/2004
• YooJin Ha

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What is Vector space model?

• The possibility of viewing index terms as
• corresponding to various dimensions of space
  and the documents as vectors in such a space
  (Salton, 1975)
• The various information retrieval objects are
  modelled as elements of a vector space.
• (terms, documents, queries, concepts) (Wong
  Raghvan)

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Vector space of terms
(x, y)

• Assumption1. There is no relation between terms
  (Orthogonality)
• To give a document value in a vector space
• which is composed of terms

document1
term1
term2
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Presentation of documents in the vector space
d t a b c d e f
d1 1 1 0 0 0 1
d2 0 0 1 1 0 1
d3 1 0 1 0 1 0
If a document has a term such a (or others) it
can have a value 1 otherwise 0.
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Measurement of similarity between documents

• Assumption2 Nearer document to query is likely
  to satisfy the users information need
• To calculate the distance (similarity
  coefficient) between documents in a vector space
  composed by n numbers of terms.
• As applied this model to IR, we can get
• ranking models for documents and queries.

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Measurement of similarity between documents
(Cont)
document1
Document 2

• Cosine, dice etc

term1
term2
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Relate problems1 Orthogonal

• OrthogonalThere are some terms are related not
  orthogonal
• Latent Semantic Indexing
• As applying eigen (egns) analysis, bound
• some related terms together (age, weight)
• L1 L2

a b c d e f g
d 0 0 1 1 1 0 0
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Related problem2 Unit of analysis Word vs.
phrase

• What can be the unit of analysis?
• Whether word or phrase?
• How define the word, term, phrase?
• Frequency

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Related Problem3 Polysemy Synonymy

• Polysemy one word has many different meanings
• Synonymy many other words have similar meanings
• - Latent Semantic Indexing can be applied to
  reduce this problem

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References

• Salton. (1975). A Theory of Indexing.
  Philadelphia, PA Society for Industrial and
  Applied Mathematics.
• Salton, Wong, Yang. (1975). A vector space
  model for automatic indexing. Communication of
  the ACM, 18. 613-620. (p.273).
• Raghavan Wong. (1986). A critical analysis of
  the vector space model for information retrieval.
  JASIS, 37. 279-287.