Entropy steered Kendall's tau measure for a fair Rank Aggregation

Rank Aggregation, in layman's term, is a technique of inferring a consensus ranking when multiple ranked lists of a set objects are given. Rank Aggregation has importance in a wide spectrum of fields including spam reduction in meta search, social choice theory of welfare economics, microarray analysis in bioinformatics etc. Unfortunately an ample Rank Aggregation is computationally a hard task to do even for a small set of objects. Till the date several heuristic algorithms have been devised towards its improvement. Almost all these heuristics rely on certain notion of disagreement between two ranked lists. Kendall's tau distance is undoubtedly quite popular among them, for its various desirable features. Kendall's tau distance is often used by different heuristics for approximating the consensus list. We in this article point out an important drawback of the Kendall's tau distance and propose a modified measure by using Shanon's Entropy formula. We also explain its benefit through some artificial and real data.

[1]  Jie Ding,et al.  Integration of Ranked Lists via Cross Entropy Monte Carlo with Applications to mRNA and microRNA Studies , 2009, Biometrics.

[2]  S. Falcon,et al.  Combining Results of Microarray Experiments: A Rank Aggregation Approach , 2006, Statistical applications in genetics and molecular biology.

[3]  Anton J. Enright,et al.  Human MicroRNA Targets , 2004, PLoS biology.

[4]  A. Hatzigeorgiou,et al.  A guide through present computational approaches for the identification of mammalian microRNA targets , 2006, Nature Methods.

[5]  Michel Truchon.  An Extension of the Concordet Criterion and Kemeny Orders , 1998 .

[6]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[7]  Michael Kertesz,et al.  The role of site accessibility in microRNA target recognition , 2007, Nature Genetics.

[8]  Ujjwal Maulik,et al.  A novel measure for evaluating an ordered list: application in microRNA target prediction , 2010 .

[9]  Tongbin Li,et al.  miRecords: an integrated resource for microRNA–target interactions , 2008, Nucleic Acids Res..

[10]  Y. Li,et al.  Incorporating structure to predict microRNA targets. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Ronald Fagin,et al.  Comparing top k lists , 2003, SODA '03.

[12]  D. Bartel,et al.  MicroRNAs Modulate Hematopoietic Lineage Differentiation , 2004, Science.

[13]  Sanghamitra Bandyopadhyay,et al.  TargetMiner: microRNA target prediction with systematic identification of tissue-specific negative examples , 2009, Bioinform..

[14]  K. Kosik,et al.  MicroRNA-21 is an antiapoptotic factor in human glioblastoma cells. , 2005, Cancer research.

[15]  Dang D. Long,et al.  Potent effect of target structure on microRNA function , 2007, Nature Structural &Molecular Biology.

[16]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[17]  Vasyl Pihur,et al.  Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach , 2007, Bioinform..

[18]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[19]  Moni Naor,et al.  Rank aggregation methods for the Web , 2001, WWW '01.

[20]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[21]  F. Slack,et al.  Oncomirs — microRNAs with a role in cancer , 2006, Nature Reviews Cancer.

[22]  Julius Brennecke,et al.  Identification of Drosophila MicroRNA Targets , 2003, PLoS biology.

[23]  Vasyl Pihur,et al.  RankAggreg, an R package for weighted rank aggregation , 2009, BMC Bioinformatics.

[24]  K. Gunsalus,et al.  Combinatorial microRNA target predictions , 2005, Nature Genetics.

[25]  H. Young.  Condorcet's Theory of Voting , 1988, American Political Science Review.

[26]  Susmita Datta,et al.  Finding common genes in multiple cancer types through meta-analysis of microarray experiments: a rank aggregation approach. , 2008, Genomics.

[27]  Alfred De Grazia,et al.  Mathematical Derivation of an Election System , 1953 .

[28]  R. Giegerich,et al.  Fast and effective prediction of microRNA/target duplexes. , 2004, RNA.

[29]  H. Young,et al.  A Consistent Extension of Condorcet’s Election Principle , 1978 .

[30]  N. Greenberg,et al.  Down‐regulation of prostasin serine protease: A potential invasion suppressor in prostate cancer , 2001, The Prostate.

[31]  D. Bartel.  MicroRNAs Genomics, Biogenesis, Mechanism, and Function , 2004, Cell.