  The value of supervised dimensionality reduction lies in its ability to
uncover meaningful connections between data features and labels. Common
dimensionality reduction methods embed a set of fixed, latent points, but are
not capable of generalizing to an unseen test set. In this paper, we provide an
out-of-sample extension method for the random forest-based supervised
dimensionality reduction method, RF-PHATE, combining information learned from
the random forest model with the function-learning capabilities of
autoencoders. Through quantitative assessment of various autoencoder
architectures, we identify that networks that reconstruct random forest
proximities are more robust for the embedding extension problem. Furthermore,
by leveraging proximity-based prototypes, we achieve a 40% reduction in
training time without compromising extension quality. Our method does not
require label information for out-of-sample points, thus serving as a
semi-supervised method, and can achieve consistent quality using only 10% of
the training data.
