A novel ranking distance measure combining Cayley and Spearman footrule metrics

作者：Sipos Laszlo; Gere Attila; Popp Jozsef; Kovacs Sandor

来源：Journal of Chemometrics, 2018, 32(4): e3011.

DOI：10.1002/cem.3011

• Cayley distance
• cross-validation
• distance metrics
• Kendall tau
• sum of ranking differences (SRDs)

Defining the appropriate ranking distance measures among rankings is a classic area of study. The goal of our work is to identify a combination of methodologies, which is proven to be capable for the determination of a proper ranking system. In our study, we used 3 well-established metrics: Kendall tau, Spearman footrule, and Cayley distance and a novel metric created by the combination of Cayley and Spearman footrule metrics. The results of the newly introduced metric depend on how fast we can trade a permutation of items to the reference permutation according to the Spearman footrule. On the other hand, the distance also depends on the number of cycles and the inversions in the cycle. Two case studieschemometric data of phytonutrients of tomato varieties and sensometric data of orange juiceswere used to test the performance of the studied ranking distance metrics. The properties of the new metric were compared to the traditional metrics regarding the normality of their distributions, significant number of differences between the rating objects, and the quality of the rankings. Results were validated by leave-one-out cross-validation and significant differences by Wilcoxon matched pairs test.

• 出版日期2018-4