GetStabilityDistance: Stability measures for gene rankings
In GeneSelector: Stability and Aggregation of ranked gene lists

Description Usage Arguments Value Author(s) References See Also Examples

The similarity of two rankings is assessed by computing a weighted distance measure. This function implements weighted absolute- and squared distance, a weighted versions of Spearman's rank correlation coefficient and Kendall's tau. Note that Spearman's rank correlation coefficient is not a distance measure in the classical sense, but can be obtained as transformation of the squared distance.

1 2	GetStabilityDistance(RR, scheme = c("original", "pairwise"), measure = c("l1", "l2", "spearman", "kendall"), decay = c("linear", "quadratic", "exponential"), alpha = 1, ...)

`RR`	An object of class `RepeatedRanking`
`scheme`	If `scheme = "original"`, a reference ranking is compared with alternative rankings. If `scheme = "pairwise"`, all possible pairs of rankings are compared. The latter is normally used in the absence of a reference ranking, e.g. if the agreement of different ranking procedures is of interest.
`measure`	The measure to be used. `measure = "l1"` computes a weighted absolute distance, `measure = "l2"` a weighted squared distance. `measure = "spearman"` computes a weighted version of Spearman's rank correlation coefficient. `measure = "kendall"` computes a weighted version of Kendall's tau. Note that, unlike in the function `cor` in `R base`, Kendall's tau ranges from `0` to `1`, and not from `-1` to `1`, which is the case when `measure = "spearman"`. Absolute- and squared distance are suitably normalized to fall into the unit interval for the sake of better interpretability, with zero corresponding to maximal instability.
`decay`	Argument controlling the weight decay of the weights of the summands contributing to the stability measure. If `decay="linear"`, then we have weight `1/r` for rank `r`, if `decay="quadratic"`, then the weight is `1/r^2` and if `decay="exponential"`, then the weight is `exp(-alpha*r)` where `alpha` is a tuning parameter, specified via the argument `alpha`.
`alpha`	s. `decay`.
`...`	Currently unused argument.

An object of class StabilityDistance

Martin Slawski
Anne-Laure Boulesteix

Jurman, G., Merler, S., Barla, A., Paoli, S., Galea, A., Furlanello, C. (2008).
Algebraic stability indicators for ranked lists in molecular profiling. Bioinformatics 24, 258-264

DeConde, R. P., Hawley, S., Falcon, S., Clegg, N., Knudsen, B., Etzioni, R. (2006).
Combining results of microarray experiments: a rank aggregation approach. Statistical Applications in Genetics and Molecular Biology 5, 15

RepeatRanking

 ## Load toy gene expression data
data(toydata)
### class labels
yy <- toydata[1,]
### gene expression
xx <- toydata[-1,]
### get ranking 
ordT <- RankingTstat(xx, yy, type="unpaired")
### Generate Leave-One-Out
loo <- GenerateFoldMatrix(y = yy, k=1)
### Repeat Ranking with t-statistic
loor_ordT <- RepeatRanking(ordT, loo)
### assess stability
stab_dis_ordT <- GetStabilityDistance(loor_ordT, scheme  = "original", measure = "spearman", decay="linear")
### for a short summary
summary(stab_dis_ordT, display = "all")