The reviews were mixed, but given the competitive nature of the conference, this paper probably doesn't make the threshold. Since the paper deals with adaptive dimensionality reduction, the following paper seems quite relevant: Lee-Ad Gottlieb, Aryeh Kontorovich, Robert Krauthgamer: Adaptive metric dimensionality reduction. Theor. Comput. Sci. 620: 105-118 (2016) Finally, "principle" in the title and abstract should be *principal*.