  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.
