We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies of depth functions in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we analyze the distribution of different classifier performances over a sample of standard benchmark data sets. Our results promisingly demonstrate that our approach differs substantially from existing benchmarking approaches and, therefore, adds a new perspective to the vivid debate on the comparison of classifiers.

翻译：我们提出一个基于深度函数概念对偏序集进行描述性分析的框架。尽管深度函数在线性空间和度量空间中的研究已相当深入，但在偏序集等非标准数据类型上的深度函数探讨仍十分有限。我们将经典的单纯形深度概念创新性地引入全体偏序集空间，提出了无并泛化（ufg）深度。进一步地，我们利用所提出的ufg深度，基于多维性能指标对机器学习算法进行比较分析。具体而言，我们针对一组标准基准数据集，对不同分类器性能的分布特征进行分析。实验结果表明，本文方法与传统基准比较方法存在本质差异，从而为当前关于分类器比较的热点讨论提供了全新视角。