A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings
A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings
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用于比较和汇总非严格和不完整排名的新相关系数
DOI：
10.1016/j.ejor.2020.02.027
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发表时间：
2020
影响因子：
6.4
通讯作者：
Skolfield, J. Kyle
中科院分区：
文献类型：
--
作者：
Yoo, Yeawon;Escobedo, Adolfo R.;Skolfield, J. Kyle
我们引入了一个相关系数，旨在处理各种排名格式，包括那些包含非严格（即，带结）和不完整（即，未知的偏好。相关系数的设计是为了执行一个中立的不完整性处理，其中没有假设涉及未排名的对象的个人偏好。新的措施，这可以被看作是一个推广的种子肯德尔tau相关系数，被证明是满足一组度量公理，并相当于最近开发的排序距离函数与Kemeny聚集。为了进一步统一和增强这两种强大的排名方法，这项工作证明了一个额外的距离和相关系数配对的非严格不完整的排名空间中的等价性。这些连接导致新的精确优化方法：一个专门的分支和界限算法和一个精确的整数规划制定。此外，这些互补的理论的桥接加强了奇异的适用性的特征相关系数，以解决一般的共识排名问题。后一个前提是由一组随机实例，这是通过本文开发的抽样技术与经典的马洛分布的排名数据连接生成的实验支持。与分支和界限算法的相关实验表明，随着数据变得嘈杂，特征相关系数产生相对较少的替代最佳解决方案，并且聚合排名往往更接近于大多数人共享的基本事实。
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects. The new measure, which can be regarded as a generalization of the seminal Kendall tau correlation coefficient, is proven to satisfy a set of metric-like axioms and to be equivalent to a recently developed ranking distance function associated with Kemeny aggregation. In an effort to further unify and enhance both robust ranking methodologies, this work proves the equivalence of an additional distance and correlation-coefficient pairing in the space of non-strict incomplete rankings. These connections induce new exact optimization methodologies: a specialized branch and bound algorithm and an exact integer programming formulation. Moreover, the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem. The latter premise is bolstered by an accompanying set of experiments on random instances, which are generated via a herein developed sampling technique connected with the classic Mallows distribution of ranking data. Associated experiments with the branch and bound algorithm demonstrate that, as data becomes noisier, the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority.
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影响因子：
2.7
作者：
MALLOWS, CL
通讯作者：
MALLOWS, CL
影响因子：
6.4
作者：
Amodio, S.;D'Ambrosio, A.;Siciliano, R.
通讯作者：
Siciliano, R.
MicroClAn：微阵列聚类分析
DOI：
--
发表时间：
2013
期刊：
J. Parallel Distributed Comput.
影响因子：
--
作者：
G. Bruno;A. Fiori
通讯作者：
A. Fiori
基于距离的集体弱排序
DOI：
--
发表时间：
2001
期刊：
影响因子：
--
作者：
Slim Ben Khelifa;J. Martel
通讯作者：
J. Martel
影响因子：
3.2
作者：
Lin, Shili
通讯作者：
Lin, Shili