EMBED: Essential Microbiome Dynamics, a dimensionality reduction method for longitudinal microbiome data

Dimensionality reduction techniques are crucial in deciphering high dimensional biological data. Gut microbiome is an example of complex and dynamical systems comprising thousands of bacteria whose abundances change stochastically and substantially. To understand the collective dynamics of the gut microbiome as a combination of simple dynamical patterns, we propose Essential MicroBiomE Dynamics (EMBED); a matrix factorization method that embeds longitudinal microbiome abundance data onto a series of lower dimensional Boltzmann Distributions. EMBED learns uniquely from data features (Hamiltonians) and orthogonal latents (Intensive variables) akin to “normal modes” in soft matter physics. We use EMBED to investigate three gut microbiome datasets that represent pathogenesis, diet, and drug related perturbations respectively. For all datasets considered, < 5 modes are sufficient to capture the dynamics with significant accuracy. Notably, EMBED identifies the collective modes representing typical dynamics of gut bacteria that have clear physiological interpretations. Moreover, features can be used to identify bacteria with similar dynamical profiles. We believe that EMBED will be a significant tool in the analysis of other longitudinal sequencing data as well.