Reviews: Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds

This paper investigates Dimensionality Reduction (DR) maps in an information retrieval setting. In particular, they showed that no DR map can attain both perfect precision and perfect recall. Further, they showed the theoretical bounds for the precision and the Wasserstein distance of a continuous DR map. They also run simulations in various settings. Quality: They have theoretical equivalences of precision and recall (Proposition 1) and show that perfect map does not exist (Theorem 1).