No abstract

We propose a new family of algorithms for bounding/approximating the optimal solution of rank aggregation problems based on weighted Kendall distances. The algorithms represent linear programming relaxations of integer programs that involve variables reflecting partial orders of three or more candidates. Our simulation results indicate that the linear programs give near-optimal performance for a number of important voting parameters, and outperform methods based on PageRank and Weighted Bipartite Matching.

LIST OF FIGURES 3.1 (a) Sorted MRI signal coefficient values in Wavelet domain (b) Sorted proposed signal model coefficient values in Wavelet domain. .. .. .. 4.1 Normalized MSE (NMSE), number of extras and number of misses over time for CS, modified CS, modified BPDN, and regularized modified CSN. In part (b) and (c), NMSE for CS was more than 20%.

Gene prioritization is a class of methods for discovering genes implicated in the onset and progression of a disease. As candidate genes are ranked based on similarity to known disease genes according to different set of criteria, the overall aggregation of these ranked datasets is a vital step of the prioritization procedure. Aggregation of different lists of ordered genes is accomplished either via classical order statistics analysis or via combinatorial ordinal data fusion. We propose a novel approach to combinatorial gene prioritization via Linear Programming (LP) optimization and use the recently introduced weighted Kendall τ distance to assess similarities between rankings. The weighted Kendall τ distance allows for constructing aggregates that have higher accuracy at the top of the ranking, usually tested experimentally, and it can also accommodate ties in rankings and handle negative outliers. In addition, the Kendall distance does not use quantitative data which in many instances may be unreliable. We illustrate the performance of the prioritization method on a set of test genes pertaining to the Bardet-Biedl syndrome, schizophrenia, and HIV and show that the combinatorial method matches or outperforms state-of-the art algorithms such as ToppGene.