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The rapidly expanding Gravitational-Wave Transient Catalog (GWTC) necessitates the development of model-independent techniques to uncover trends and subpopulations within the binary black hole (BBH) population. We present the first usage of the Uniform Manifold Approximation and Projection (UMAP) algorithm, a novel dimensionality-reduction technique, for the purpose of analyzing BBH mergers in GWTC-3. We show that UMAP, paired with a clustering algorithm, effectively partitions the population into four well-segregated subgroups principally via their primary and secondary mass components along with an outlier event, GW$190521\_030229$. UMAP clearly identifies objects in the ${\sim}10~M_\odot$ buildup in the BBH mass spectrum as their own group with aligned spins and mass ratios of ${\sim}0.2{-}0.7$ while objects in or above the ${\sim}35~M_\odot$ overdensity are all in the same, largest group and display typically lower effective spins as well as larger mass ratios (${\sim}0.5{-}0.9$) on average. With the aid of hierarchical population inference, we interpret these as subpopulations from different formation pathways, consistent with previous findings. We also find a transitional group of a handful of objects with masses in between the aforementioned buildups and broad support for anti-aligned spins. We examine the low-mass UMAP subgroup, which exhibits anti-correlation between the mass ratio and effective spin, and show that it drives such anti-correlation for the entire GWTC-3 sample. Overall, we demonstrate that UMAP is an interpretable, non-parametric framework that can not only be used for visualization but also for probing the astrophysics of the BBH population.
