  Data obtained from Flow Cytometry present pronounced variability due to
biological and technical reasons. Biological variability is a well-known
phenomenon produced by measurements on different individuals, with different
characteristics such as illness, age, sex, etc. The use of different settings
for measurement, the variation of the conditions during experiments and the
different types of flow cytometers are some of the technical causes of
variability. This mixture of sources of variability makes the use of supervised
machine learning for identification of cell populations difficult. The present
work is conceived as a combination of strategies to facilitate the task of
supervised gating.
  We propose $optimalFlowTemplates$, based on a similarity distance and
$\text{Wasserstein barycenters}$, which clusters cytometries and produces
prototype cytometries for the different groups. We show that supervised
learning, restricted to the new groups, performs better than the same
techniques applied to the whole collection. We also present
$optimalFlowClassification$, which uses a database of gated cytometries and
optimalFlowTemplates to assign cell types to a new cytometry. We show that this
procedure can outperform state of the art techniques in the proposed datasets.
Our code is freely available as $optimalFlow$ a Bioconductor R package at
https://bioconductor.org/packages/optimalFlow.
  optimalFlowTemplates+optimalFlowClassification addresses the problem of using
supervised learning while accounting for biological and technical variability.
Our methodology provides a robust automated gating workflow that handles the
intrinsic variability of flow cytometry data well. Our main innovation is the
methodology itself and the optimal-transport techniques that we apply to flow
cytometry analysis.
