  Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid
Leukemia (AML), a type of cancer that affects the blood and bone marrow, is
essential in the prognosis and follow-up of AML patients. As traditional
cytological analysis cannot detect leukemia cells below 5\%, the analysis of
flow cytometry dataset is expected to provide more reliable results. In this
paper, we explore statistical learning methods based on optimal transport (OT)
to achieve a relevant low-dimensional representation of multi-patient flow
cytometry measurements (FCM) datasets considered as high-dimensional
probability distributions. Using the framework of OT, we justify the use of the
K-means algorithm for dimensionality reduction of multiple large-scale point
clouds through mean measure quantization by merging all the data into a single
point cloud. After this quantization step, the visualization of the intra and
inter-patients FCM variability is carried out by embedding low-dimensional
quantized probability measures into a linear space using either Wasserstein
Principal Component Analysis (PCA) through linearized OT or log-ratio PCA of
compositional data. Using a publicly available FCM dataset and a FCM dataset
from Bordeaux University Hospital, we demonstrate the benefits of our approach
over the popular kernel mean embedding technique for statistical learning from
multiple high-dimensional probability distributions. We also highlight the
usefulness of our methodology for low-dimensional projection and clustering
patient measurements according to their level of MRD in AML from FCM. In
particular, our OT-based approach allows a relevant and informative
two-dimensional representation of the results of the FlowSom algorithm, a
state-of-the-art method for the detection of MRD in AML using multi-patient
FCM.
