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Recuperação de Informação B

Recuperação de Informação B. Cap. 02: Modeling (Set Theoretic Models) 2.6 September 08, 1999. Set Theoretic Models. The Boolean model imposes a binary criterion for deciding relevance

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Recuperação de Informação B

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  1. Recuperação de Informação B Cap. 02: Modeling (Set Theoretic Models) 2.6 September 08, 1999

  2. Set Theoretic Models • The Boolean model imposes a binary criterion for deciding relevance • The question of how to extend the Boolean model to accomodate partial matching and a ranking has attracted considerable attention in the past • We discuss now two set theoretic models for this: • Fuzzy Set Model • Extended Boolean Model

  3. Fuzzy Set Model • Queries and docs represented by sets of index terms: matching is approximate from the start • This vagueness can be modeled using a fuzzy framework, as follows: • with each term is associated a fuzzy set • each doc has a degree of membership in this fuzzy set • This interpretation provides the foundation for many models for IR based on fuzzy theory • In here, we discuss the model proposed by Ogawa, Morita, and Kobayashi (1991)

  4. Fuzzy Set Theory • Framework for representing classes whose boundaries are not well defined • Key idea is to introduce the notion of a degree of membership associated with the elements of a set • This degree of membership varies from 0 to 1 and allows modeling the notion of marginal membership • Thus, membership is now a gradual notion, contrary to the crispy notion enforced by classic Boolean logic

  5. Fuzzy Set Theory • Definition • A fuzzy subset A of U is characterized by a membership function (A,u) : U  [0,1] which associates with each element u of U a number (u) in the interval [0,1] • Definition • Let A and B be two fuzzy subsets of U. Also, let ¬A be the complement of A. Then, • (¬A,u) = 1 - (A,u) • (AB,u) = max((A,u), (B,u)) • (AB,u) = min((A,u), (B,u))

  6. Fuzzy Information Retrieval • Fuzzy sets are modeled based on a thesaurus • This thesaurus is built as follows: • Let vec(c) be a term-term correlation matrix • Let c(i,l) be a normalized correlation factor for (ki,kl): c(i,l) = n(i,l) ni + nl - n(i,l) • ni: number of docs which contain ki • nl: number of docs which contain kl • n(i,l): number of docs which contain both ki and kl • We now have the notion of proximity among index terms.

  7. Fuzzy Information Retrieval • The correlation factor c(i,l) can be used to define fuzzy set membership for a document dj as follows: (i,j) = 1 -  (1 - c(i,l)) ki  dj • (i,j) : membership of doc dj in fuzzy subset associated with ki • The above expression computes an algebraic sum over all terms in the doc dj • A doc dj belongs to the fuzzy set for ki, if its own terms are associated with ki

  8. Fuzzy Information Retrieval • (i,j) = 1 -  (1 - c(i,l)) ki  dj • (i,j) : membership of doc dj in fuzzy subset associated with ki • If doc dj contains a term kl which is closely related to ki, we have • c(i,l) ~ 1 • (i,j) ~ 1 • index ki is a good fuzzy index for doc

  9. Ka Kb cc2 cc3 cc1 Kc Fuzzy IR: An Example • q = ka  (kb  kc) • vec(qdnf) = (1,1,1) + (1,1,0) + (1,0,0) = vec(cc1) + vec(cc2) + vec(cc3) • (q,dj) = (cc1+cc2+cc3,j) = 1 - (1 - (a,j) (b,j) (c,j)) * (1 - (a,j) (b,j) (1-(c,j))) * (1 - (a,j) (1-(b,j)) (1-(c,j)))

  10. Fuzzy Information Retrieval • Fuzzy IR models have been discussed mainly in the literature associated with fuzzy theory • Experiments with standard test collections are not available • Difficult to compare at this time

  11. Extended Boolean Model • Booelan retrieval is simple and elegant • But, no ranking is provided • How to extend the model? • interpret conjunctions and disjunctions in terms of Euclidean distances

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