  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.
