# Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia

arXiv: https://arxiv.org/abs/2407.17329 · HTML: https://mlsanity.com/paper/2407.17329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations](https://mlsanity.com/paper/2008.09165/) (2020)
- [Stochastic Wasserstein Barycenters](https://mlsanity.com/paper/1802.05757/) (2018)
- [Supervised learning of sheared distributions using linearized optimal transport](https://mlsanity.com/paper/2201.10590/) (2022)
- [The Linearized Hellinger--Kantorovich Distance](https://mlsanity.com/paper/2102.08807/) (2021)
- [The Gene Mover's Distance: Single-cell similarity via Optimal Transport](https://mlsanity.com/paper/2102.01218/) (2021)
- [Log-PCA versus Geodesic PCA of histograms in the Wasserstein space](https://mlsanity.com/paper/1708.08143/) (2017)
- [Sequential Dirichlet Process Mixtures of Multivariate Skew t-distributions for Model-based Clustering of Flow Cytometry Data](https://mlsanity.com/paper/1702.04407/) (2017)
- [optimalFlow: Optimal-transport approach to flow cytometry gating and population matching](https://mlsanity.com/paper/1907.08006/) (2019)
- [Point Cloud Classification via Deep Set Linearized Optimal Transport](https://mlsanity.com/paper/2401.01460/) (2024)

## Built on by (most cited first, 1 of 1)

- [Scalable Learning from Probability Measures with Mean Measure Quantization](https://mlsanity.com/paper/2502.04907/) (2025)

## Abstract (arXiv)

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.