OrderedList (version 1.44.0)

scoreRankings: Score the Comparison of two Rankings

Description

Two rankings are accepted as input in the form of corresponding ranks in two lists. The weighted overlap score is computed efficiently without explicitly computing overlaps.

Usage

scoreRankings(r1, r2, nn, bases, two.sided=TRUE)

Arguments

r1

integer, ranks in the first list.

r2

integer, ranks in the second list. r1 and r2 must have the same length.

nn

for each alpha to be used as weighting parameter, this array of integers contains the maximal rank for which overlaps are considered.

bases

for each alpha to be used as weighting parameter, this double array contains exp(-alpha).

two.sided

if TRUE both ends of the lists are taken into account, only top ranks are considered otherwise.

Value

• An array of doubles with one score per weighting parameter to be considered is returned.

Details

The score to be computed is defined as the sum over the first ranks in two lists. The summed up measure is the weighted overlap between the two lists:

$$score := sum_(R=1)^n exp(-alpha R) * overlap(L1[1:R],L2[1:R])$$

where $n$ is the maximal rank to be considered and $L1/L2$ denote the sorted lists to be compared. In this score, each gene contributes from the first rank where it is in the overlap up to $n$. For gene i:

$$score_i = sum_(R=max(r1[i],r2[i])^n exp(-alpha R))$$

where $r1/r2$ are the ranks of genes in $L1/L2$. Since this is a finite geometric series, it can be used to speed up computation of our score:

$$score_i = (exp(-alpha min(r1[i],r2[i])) - exp(-alpha n))/(1 - exp(-alpha))$$ $$score = sum_(i|r1[i]

Analogue computations are performed by scoreRankings for list begins and list ends.

See Also

shuffledRandomScores,compareLists