  Different cell types aggregate and sort into hierarchical architectures
during the formation of animal tissues. The resulting spatial organization
depends (in part) on the strength of adhesion of one cell type to itself
relative to other cell types. However, automated and unsupervised
classification of these multicellular spatial patterns remains challenging,
particularly given their structural diversity and biological variability.
Recent developments based on topological data analysis are intriguing to reveal
similarities in tissue architecture, but these methods remain computationally
expensive. In this article, we show that multicellular patterns organized from
two interacting cell types can be efficiently represented through persistence
images. Our optimized combination of dimensionality reduction via autoencoders,
combined with hierarchical clustering, achieved high classification accuracy
for simulations with constant cell numbers. We further demonstrate that
persistence images can be normalized to improve classification for simulations
with varying cell numbers due to proliferation. Finally, we systematically
consider the importance of incorporating different topological features as well
as information about each cell type to improve classification accuracy. We
envision that topological machine learning based on persistence images will
enable versatile and robust classification of complex tissue architectures that
occur in development and disease.
