Correlation measures are among the most basic tools in statistical data analysis and machine learning.

They are applied to pairs of observations to measure to which extent the two observations

comply with a certain model. The most prominent representative is surely Pearson’s product

moment coefficient [1, 13], often nonchalantly called correlation coefficient for short. Pearson’s

product moment coefficient can be applied to numerical data and assumes a linear relationship as

the underlying model; therefore, it can be used to detect linear relationships, but no non-linear

ones.

Rank correlation measures [7, 10, 12] are intended to measure to which extent a monotonic

function is able to model the inherent relationship between the two observables. They neither

assume a specific parametric model nor specific distributions of the observables. They can be

applied to ordinal data and, if some ordering relation is given, to numerical data too. Therefore,

rank correlation measures are ideally suited for detecting monotonic relationships, in particular, if

more specific information about the data is not available. The two most common approaches are

Spearman’s rank correlation coefficient (short Spearman’s rho) [14, 15] and Kendall’s tau (rank

correlation coefficient) [2, 9, 10]. Another simple rank correlation measure is the gamma rank

correlation measure according to Goodman and Kruskal [7].

The rank correlation measures cited above are designed for ordinal data. However, as argued in

[5], they are not ideally suited for measuring rank correlation for numerical data that are perturbed

by noise. Consequently, [5] introduces a family of robust rank correlation measures. The idea

is to replace the classical ordering of real numbers used in Goodman’s and Kruskal’s gamma [7]

by some fuzzy ordering [8, 3, 4] with smooth transitions — thereby ensuring that the correlation

measure is continuous with respect to the data.

cited from "RoCoCo-An R Package Implementing a Robust Rank Correlation Coefficient and a Corresponding Test".