GiDR-DUN; Gradient Dimensionality Reduction -- Differences and Unification

TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been made toimproveonTSNE’scomputationalcomplexity,noexistingmethodcanobtainTSNEembeddingsatthespeedofUMAP.Inthiswork,weshowthatthisisindeedpossiblebycombiningthetwoap-proachesintoasinglemethod.WetheoreticallyandexperimentallyevaluatethefullspaceofparametersintheTSNEandUMAPalgo-rithmsandobservethatasingleparameter–thenormalization–isresponsibleforswitchingbetweenthem.This,inturn,impliesthatamajorityofthealgorithmicdifferencescanbetoggledwithoutaffectingtheembeddings.WediscusstheimplicationsthishasonseveraltheoreticclaimsunderpinningtheUMAPframework,aswellashowtoreconcilethemwithexistingTSNEinterpretations.Basedonouranalysis,weproposeanewdimensionalityre-ductionalgorithm,GDR,thatcombinespreviouslyincompatibletechniquesfromTSNEandUMAPandcanreplicatetheresultsofeitheralgorithmbychangingthenormalization.Asafurtheradvantage,GDRperformstheoptimizationfasterthanavailableUMAPmethodsandthusanorderofmagnitudefasterthanavail-ableTSNEmethods.Ourimplementationisplug-and-playwiththetraditionalUMAPandTSNElibrariesandcanbefoundathttps://github.com/Andrew-Draganov/GiDR-DUN.