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CVV Example

This document explores the calculation of document frequency (DF) and its implications for determining the relevance of terms in a collection of documents. We explain how to derive the proportions of documents containing specific terms in subsets of data and their impact on overall term significance. Using formulas and a detailed example with three collections, we illustrate how to compute averages and goodness metrics, leading to insights on term concentration across document subsets. The findings highlight that "goodness" is a valuable yet indicative measure in assessing document relevance.

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CVV Example

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  1. CVV Example

  2. 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

  3. 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}

  4. 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

  5. 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!

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