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Advanced Information Retreival

Advanced Information Retreival. Chapter. 02: Modeling (Extended Boolean Model). Extended Boolean Model. Boolean model is simple and elegant. But, no provision for a ranking As with the fuzzy model, a ranking can be obtained by relaxing the condition on set membership

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Advanced Information Retreival

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  1. Advanced Information Retreival Chapter. 02: Modeling (Extended Boolean Model)

  2. Extended Boolean Model • Boolean model is simple and elegant. • But, no provision for a ranking • As with the fuzzy model, a ranking can be obtained by relaxing the condition on set membership • Extend the Boolean model with the notions of partial matching and term weighting • Combine characteristics of the Vector model with properties of Boolean algebra

  3. The Idea • The extended Boolean model (introduced by Salton, Fox, and Wu, 1983) is based on a critique of a basic assumption in Boolean algebra • Let, • q = kx  ky • wxj = fxj * idf(x) associated with [kx,dj] max(idf(i)) • Further, wxj = x and wyj = y

  4. The Idea: • qand = kx  ky; wxj = x and wyj = y AND 2 2 sim(qand,dj) = 1 - sqrt( (1-x) + (1-y) ) 2 (1,1) ky dj+1 y = wyj dj (0,0) x = wxj kx

  5. The Idea: • qor = kx  ky; wxj = x and wyj = y OR 2 2 sim(qor,dj) = sqrt( x + y ) 2 (1,1) ky dj+1 dj y = wyj (0,0) x = wxj kx

  6. Generalizing the Idea • We can extend the previous model to consider Euclidean distances in a t-dimensional space • This can be done using p-norms which extend the notion of distance to include p-distances, where 1  p  is a new parameter • A generalized conjunctive query is given by • qor = k1 k2 . . . kt • A generalized disjunctive query is given by • qand = k1 k2 . . . kt p p p    p p p   

  7. Generalizing the Idea 1 p p p p • sim(qor,dj) = (x1 + x2 + . . . + xm ) m 1 p • sim(qand,dj) = 1 - ((1-x1) + (1-x2) + . . . + (1-xm) ) m p p p

  8. Properties 1 p p p p • sim(qor,dj) = (x1 + x2 + . . . + xm ) m • If p = 1 then (Vector like) • sim(qor,dj) = sim(qand,dj) = x1 + . . . +xm m • If p =  then (Fuzzy like) • sim(qor,dj) = max (wxj) • sim(qand,dj) = min (wxj)

  9. Properties • By varying p, we can make the model behave as a vector, as a fuzzy, or as an intermediary model • This is quite powerful and is a good argument in favor of the extended Boolean model • (k1 k2) k3 • k1 and k2 are to be used as in a vectorial retrieval while the presence of k3 is required.  2  

  10. Properties   • q = (k1 k2) k3 • sim(q,dj) = ( (1 - ( (1-x1) + (1-x2) ) ) + x3 ) 2__________________ 2 2  1 1 p p p p p

  11. Conclusions • Model is quite powerful • Properties are interesting and might be useful • Computation is somewhat complex • However, distributivity operation does not hold for ranking computation: • q1 = (k1  k2)  k3 • q2 = (k1  k3)  (k2  k3) • sim(q1,dj)  sim(q2,dj)

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