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Table 3 Step-by-step calculation of \( RB{O}_{Z,{d}_i} \) given P Z k  = {2, 3, 1, 6, 8} and \( {P}_k^{d_i}=\left\{2,\ 1,\ 4,\ 3,\ 5\right\} \)

From: Integrating unified medical language system and association mining techniques into relevance feedback for biomedical literature search

Depth \( {P}_{depth}^Z\cap {P}_{depth}^{d_i} \) \( \frac{\left|{P}_{depth}^Z\cap {P}_{depth}^{d_i}\right|}{depth} \) \( {\varphi}^{depth-1}\frac{\left|{P}_{depth}^Z\cap {P}_{depth}^{d_i}\right|}{depth} \)
1 1 1/1 = 1 (0.9)0 × 1 = 1
2 1 1/2 = 0.5 (0.9)1 × 0.5 = 0.45
3 2 2/3 = 0.67 (0.9)2 × 0.67 = 0.54
4 3 3/4 = 0.75 (0.9)3 × 0.75 = 0.55
5 3 3/5 = 0.6 (0.9)4 × 0.6 = 0.39
\( RB{O}_{Z,{d}_i} \) (1 − 0.9) × (1 + 0.45 + 0.54 + 0.55 + 0.39) = 0.29