Coarse graining of data via inhomogeneous diffusion condensation

Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyle, Manik Kuchroo, David van Dijk, Kevin R. Moon, Daniel Colon-Ramos, Guy Wolf, Matthew Hirn, Smita Krishnaswamy

Abstract:

Big data often has emergent structure that exists at
multiple levels of abstraction, which are useful for characterizing
complex interactions and dynamics of the observations. Here,
we consider multiple levels of abstraction via a multiresolution
geometry of data points at different granularities. To construct
this geometry we define a time-inhomogemeous diffusion process
that effectively condenses data points together to uncover nested
groupings at larger and larger granularities. This inhomogeneous
process creates a deep cascade of intrinsic low pass filters on the
data affinity graph that are applied in sequence to gradually eliminate local variability while adjusting the learned data geometry
to increasingly coarser resolutions. We provide visualizations to
exhibit our method as a “continuously-hierarchical” clustering
with directions of eliminated variation highlighted at each step.
The utility of our algorithm is demonstrated via neuronal
data condensation, where the constructed multiresolution data
geometry uncovers the organization, grouping, and connectivity
between neurons.