Recuperação de Informação B

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Presentation transcript:

Recuperação de Informação B Cap. 02: Modeling (Extended Boolean Model) 2.6.2 September 13, 1999

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

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

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

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

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

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

Properties 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) p 1

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

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

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)