Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality metrics have been studied in the literature, in the field of dimensionality reduction only a few over-simplistic metrics has been proposed. In this work, we aim to introduce the first highly non-trivial dimensionality reduction performance metric. This metric is based on the sectional curvature behaviour arising from Riemannian geometry. To test its feasibility, this metric has been used to evaluate the performance of the most commonly used dimension reduction algorithms in the state of the art. Furthermore, to make the evaluation of the algorithms robust and representative, using curvature properties of planar curves, a new parameterized problem instance generator has been constructed in the form of a function generator. Experimental results are consistent with what could be expected based on the design and characteristics of the evaluated algorithms and the features of the data instances used to feed the method.
翻译:无监督机器学习由于定义而缺乏地面真相。这在设计评估这些算法性能的指标时带来了主要困难。与有监督学习形成鲜明对比的是,对于评估质量已经在文献中研究了大量质量指标,在降维领域中只提出了一些过度简化的指标。在这项工作中,我们意在引入第一个高度非平凡的降维绩效度量。该度量基于从Riemann几何中得出的截面曲率行为。为了测试其可行性,该度量已用于评估当前使用的最常见的降维算法的性能。此外,为使算法的评估鲁棒且具有代表性,利用平面曲线的曲率属性,构造了一个新的参数化问题实例生成器,其形式为函数生成器。实验结果与评估算法的设计和特性以及用于提供方法的数据实例的特征相一致。