NDCG.md (952B)
1 # Normalized Discounted Cumulative Gain (NDCG) 2 3 **Source:** Where to fuzz paper 4 5 **Definition:** Normalized discounted cumulative gain is a metric used for the evaluation of information retrieval systems. 6 7 ## Cumulative Gain 8 9 $CG_p = \Sigma_{i=1}^{p} \text{rel}_i$ 10 11 This metric is a simpler variant of DCG which doesn't take into account rank (position / ordering). 12 13 ## Discounted Cumulative Gain 14 15 $DCG_p = \Sigma_{i=1}^{p} \frac{\text{rel}_i}{\text{log}_2(i+1)} + \Sigma_{i=2}^{p} \frac{\text{rel}_i}{\text{log}_2(i+1)}$ 16 17 The idea with DCG is that the appearance of relevant items lower in results should be pentalized. 18 19 ## Normalized Discounted Cumulative Gain 20 21 $nDCG_p = \frac{DCG_p}{IDCG_p}$ 22 23 Where $IDCG_p$ is the ideal discounted cumulative gain. 24 25 Basically, the NDCG is the DCG of the ordering divided by the optimal document ordering wrt DCG. 26 27 The value of NDCG is its comparative abilities across evaluations as results are between 0 and 1.