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CVV Example. DF i,j Assumption. If we assume that DF i,j = the number of documents in collection c i containing term t j : A = DF i,j / N i proportion of docs in c i containing term t j B = Sum k!=i |C| (DF k,j ) / Sum k!=i |C| (N k )

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df i j assumption
DFi,j Assumption
  • If we assume that DFi,j = the number of documents in collection ci containing term tj :
  • A = DFi,j / Ni
    • proportion of docs in ci containing term tj
  • B = Sumk!=i|C|(DFk,j) / Sumk!=i|C|(Nk)
    • proportion of docs not in ci containing term tj
    • not the same as Sumk!=i|C| (DFk,j/Nk)
  • A + B != proportion of all docs containing tj
    • see example on next page
cvv example for one term t j
CVV Example (for one term tj)
  • Given: |C| = 3, DF1..3,j={1,2,0}, N1..3={2,4,4}
  • c1: A=1/2, B = (2+0) / (4+4) = 2/8 = 1/4A+B = 1/2 + 1/4 = 3/4, CV1,j = (1/2)/(3/4) = 2/3
    • prop of all docs containing tj = (1+2) / (2+4+4) = 3/10
  • c2: A = 2/4=1/2, B = (1+0) / (2+4) = 1/6CV2,j = (1/2) / (1/2 + 1/6) = (1/2) / (4/6) = 3/4
  • c3: A = 0/4 = 0, B = (1+2) / (2+4) = 3/6 = 1/2CV3,j = 0 / (0 + 1/2) = 0
  • So, CV1..3,j = {2/3, 3/4, 0}
cvv example cont
CVV Example (cont)
  • CV1..3,j = {2/3, 3/4, 0} [from previous page]
  • avgCVj = Sumi=1|C|(CVi,j) / |C| = (2/3 + 3/4 + 0) / 3 = .472
  • CVVj = Sumi=1|C|(CVi,j - avgCVj)2 / |C| = ((.667-.472)2 + (.75-.472)2 + (0-.472)2) /3 = (.0378 + .0773 + .2228) / 3 = .113
cvv example cont1
CVV Example (cont)
  • CVVj=.113, DFi,j={1,2,0} [from previous pages]
  • Given: query q has only one term in query: tj (M=1)
  • Gi,q = Sumk=1M(CVVk * DFi,k) = CVVj * DFi,jfor our example
  • G1..3,q = {.113, .226, 0}
  • So, collection c2 is “gooder” than the others...
  • Goodness is “only an indicator as to where, among the |C| collections, the query terms are concentrated at.” <-- bad grammar!