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Unsupervised machine learning lacks ground truth by definition. This poses amajor difficulty when designing metrics to evaluate the performance of suchalgorithms. In sharp contrast with supervised learning, for which plenty ofquality metrics have been studied in the literature, in the field ofdimensionality reduction only a few over-simplistic metrics has been proposed.In this work, we aim to introduce the first highly non-trivial dimensionalityreduction performance metric. This metric is based on the sectional curvaturebehaviour arising from Riemannian geometry. To test its feasibility, thismetric has been used to evaluate the performance of the most commonly useddimension reduction algorithms in the state of the art. Furthermore, to makethe evaluation of the algorithms robust and representative, using curvatureproperties of planar curves, a new parameterized problem instance generator hasbeen constructed in the form of a function generator. Experimental results areconsistent with what could be expected based on the design and characteristicsof the evaluated algorithms and the features of the data instances used to feedthe method.

An evaluation framework for dimensionality reduction through sectional curvature