Normalised discounted cumulative gain at k

DCG@k = sum_{i=1..k} (2^rel_i - 1) / log2(i + 1) and NDCG@k = DCG@k / IDCG@k, where IDCG@k re-sorts the same relevances descending. An all-zero relevance list has IDCG = 0; NDCG is then undefined and is refused rather than reported as a perfect 1.

Usage

Ndcg(pred_rank, relevant, k)

Arguments

pred_rank

Items in predicted order, best first.

relevant

Either a named numeric vector of graded relevances (absent items score 0) or a plain vector of relevant items, in which case membership is used as binary relevance.

k

Cut-off.

Value

List with estimate (NDCG@k), dcg, idcg, k, n.

References

Jarvelin and Kekalainen (2002), ACM TOIS 20(4), 422-446, doi:10.1145/582415.582418 .

Examples

Ndcg(pred_rank = c(1, 2, 3, 4, 5, 6, 7, 8), relevant = c(1, 2, 3, 4, 5, 6, 7, 8), k = 5L)
#> $estimate
#> [1] 1
#> 
#> $dcg
#> [1] 2.948459
#> 
#> $idcg
#> [1] 2.948459
#> 
#> $k
#> [1] 5
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "NDCG@k (Jarvelin and Kekalainen 2002)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"