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

Factoring out prior knowledge from low-dimensional embeddings