Fig. 1: Overview of the Multiscale PHATE algorithm.

a, Multiscale PHATE process involves four successive steps. The first step (i) learns the manifold geometry via diffusion potential calculation. The second step (ii) iteratively coarse grains the manifold construction through a fast diffusion condensation process to learn data topology. The third step (iii) involves the selection of salient granularities via gradient analysis before finally visualizing and clustering the manifold in the fourth step (iv). coef, coefficient. b, Gradient analysis identifies a range of scales for visualization by computing shifts in data density from one iteration of the diffusion condensation process to the next. c, Multiscale PHATE allows for high-level summarizations of data and zoom ins of data subsets for additional detail. d. Multiscale PHATE abstractions of data are amenable to downstream analyses with algorithms like MELD (ref. ¹²) and DREMI (ref. ³⁶).