Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when discretisation becomes problematic. In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach. The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data.
翻译:肯德尔转换是将一个定序特性转换成单个值之间对称顺序关系的矢量。 这样, Kendall 转换可以保留观察的排序,并以绝对的形式代表它。 这种转换可以将要求绝对输入的方法加以概括化,特别是在观测数量有限的情况下,当分解出现问题时。 特别是,许多信息理论方法可以直接应用到肯德尔转换的连续数据中,而不必依赖不同的英特罗比或任何额外的参数。 此外,通过筛选排名中所包含的信息,Kendall 转换可以以合理成本降低尖端相互作用,从而导致更稳健,而这种成本是不可能正确估计的。 在双轨分析中,Kendall 转换可以与流行的非参数方法相联系,显示该方法的健全性。 文件还展示了它在多变式问题中的效率,并提供了真实世界数据的实例分析。