# scoreRankings: Score the Comparison of two Rankings In OrderedList: Similarities of Ordered Gene Lists

## 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

 `1` ```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.

## 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]<n&r2[i]<n) score_i

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

## Value

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

Claudio Lottaz

## See Also

`shuffledRandomScores`,`compareLists`

OrderedList documentation built on Nov. 8, 2020, 5:41 p.m.