  Dimensionality reduction (DR) is an important technique for data exploration
and knowledge discovery. However, most of the main DR methods are either linear
(e.g., PCA), do not provide an explicit mapping between the original data and
its lower-dimensional representation (e.g., MDS, t-SNE, isomap), or produce
mappings that cannot be easily interpreted (e.g., kernel PCA, neural-based
autoencoder). Recently, genetic programming (GP) has been used to evolve
interpretable DR mappings in the form of symbolic expressions. There exists a
number of ways in which GP can be used to this end and no study exists that
performs a comparison. In this paper, we fill this gap by comparing existing GP
methods as well as devising new ones. We evaluate our methods on several
benchmark datasets based on predictive accuracy and on how well the original
features can be reconstructed using the lower-dimensional representation only.
Finally, we qualitatively assess the resulting expressions and their
complexity. We find that various GP methods can be competitive with
state-of-the-art DR algorithms and that they have the potential to produce
interpretable DR mappings.
