Optimal Transport for Latent Integration with An Application to Heterogeneous Neuronal Activity Data

Music City Center 

Detecting dynamic patterns of task-specific responses shared across heterogeneous datasets
is an essential and challenging problem in many scientific applications in medical science and
neuroscience. In our motivating example of rodent electrophysiological data, identifying the
dynamical patterns in neuronal activity associated with ongoing cognitive demands and behavior
is key to uncovering the neural mechanisms of memory. One of the greatest challenges
in investigating a cross-subject biological process is that the systematic heterogeneity across
individuals could significantly undermine the power of existing machine learning methods to
identify the underlying biological dynamics. In addition, many technically challenging neurobiological
experiments are conducted on only a handful of subjects where rich longitudinal
data are available for each subject. The low sample sizes of such experiments could further reduce
the power to detect common dynamic patterns among subjects. In this paper, we propose
a novel heterogeneous data integration framework based on optimal transport to extract shared
patterns in complex biological processes. The key advantages of the proposed method are that
it can increase discriminating power in identifying common patterns by reducing heterogeneity
unrelated to the signal by aligning the extracted latent spatiotemporal information across
subjects. Our approach is effective even with a small number of subjects, and does not require
auxiliary matching information for the alignment. In particular, our method can align longitudinal
data across heterogeneous subjects in a common latent space to capture the dynamics of
shared patterns while utilizing temporal dependency within subjects. Our numerical studies on both simulation settings and neuronal activity data indicate that the proposed data integration
approach improves prediction accuracy compared to existing machine learning methods.

Distribution alignment

Electrophysiological study

Gromov-Wasserstein barycenter,


Latent embedding