lenskit.metrics.LogRankWeight

class lenskit.metrics.LogRankWeight(*, base=2, offset=0)

Bases: RankWeight

Logarithmic weighting for result ranks, as used in NDCG.

This is the ranking model typically used for DCG and NDCG.

Since \(\operatorname{lg} 1 = 0\), simply taking the log will result in division by 0 when weights are applied. The correction for this in the original NDCG paper [JarvelinKekalainen02] is to clip the ranks, so that both of the first two positions have discount \(\operatorname{lg} 2\). A different correction somtimes seen is to compute \(\operatorname{lg} (k+1)\). This discount supports both; the default is to clip, but if the offset option is set to a positive number, it is added to the ranks instead.

Parameters:

• base (float) – The log base to use.

• offset (int) – An offset to add to ranks before computing logs.

__init__(*, base=2, offset=0)

Parameters:

• base (Annotated[float, Gt(gt=0)])

• offset (Annotated[int, Ge(ge=0)])

Methods

__init__(*[, base, offset])
log_weight(ranks)	Compute the (natural) log of the discount for the specified ranks.
series_sum()	Get the sum of the infinite series of this discount function, if known.
weight(ranks)	Compute the discount for the specified ranks.

Attributes

base
offset

weight(ranks)

Compute the discount for the specified ranks.

Ranks must start with 1.