  Low-dimensional embedding techniques such as tSNE and UMAP allow visualizing
high-dimensional data and therewith facilitate the discovery of interesting
structure. Although they are widely used, they visualize data as is, rather
than in light of the background knowledge we have about the data. What we
already know, however, strongly determines what is novel and hence interesting.
In this paper we propose two methods for factoring out prior knowledge in the
form of distance matrices from low-dimensional embeddings. To factor out prior
knowledge from tSNE embeddings, we propose JEDI that adapts the tSNE objective
in a principled way using Jensen-Shannon divergence. To factor out prior
knowledge from any downstream embedding approach, we propose CONFETTI, in which
we directly operate on the input distance matrices. Extensive experiments on
both synthetic and real world data show that both methods work well, providing
embeddings that exhibit meaningful structure that would otherwise remain
hidden.
