In more details, to create a combined ranking of length n, we learn the fraction (phi_{kappa}) of pairs which are extracted from each input ranking (r_{kappa}).
Note that most of the functions in pmr require the input ranking data to be organized in an aggregated format, that is, a summary matrix with rankings and their corresponding frequencies.
The median performance for all single inputs is then analysed and the inputs ranked accordingly.
Reconstruction using Optshrink LR + S method is robust to input rank specification.
Moreover, Optshrink LR + S results are similar with different input rank specification.
An optimal ensemble ranking approach seeks for a permutation (sigma ) that has the minimum number of pairwise disagreements with all input ranks (S^{r_i}) [3, 12, 19, 80].
Also, in [31], it has been shown that the solution of Optshrink is quite robust to input rank specification, and hence a rough estimate of rank [= m in (7)] at the input is sufficient.
Hierarchical Cluster was used to analyze expression profiles of different samples, and was carried out using UPGMA (Unweighted Pair Group Method with Arithmetic Mean) analysis, with an ordering function based on the input rank.
Similarity measure was the Euclidean distance, the clustering method was Unweighted Pair Group Method with Arithmetic Mean, and input rank was the ordering function.
