# Pheno-GS: Phenoscape-scale Geodesic Sinkhorn

arXiv: https://arxiv.org/abs/2609.27633 · HTML: https://mlsanity.com/paper/2609.27633/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithm](https://mlsanity.com/paper/2002.03293/) (2020)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [Diffusion Earth Mover's Distance and Distribution Embeddings](https://mlsanity.com/paper/2102.12833/) (2021)
- [Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds](https://mlsanity.com/paper/2211.00805/) (2022)
- [Fast Multiscale Diffusion on Graphs](https://mlsanity.com/paper/2104.14652/) (2021)

## Abstract (arXiv)

High-throughput single-cell data is now collected across large patient cohorts. Understanding patient-level heterogeneity from cellular-level data motivates phenoscaping: embedding each single-cell distribution as a "datapoint," with distances given by optimal transport (OT). Computing geometry-aware OT at this scale, between all pairs of patient datasets, remains an open challenge, since existing methods either rely on Euclidean ground metrics that distort manifold structure or fail under sparse, unevenly sampled, or large-scale data. We present Pheno-GS (Phenoscape-scale Geodesic Sinkhorn), which computes accurate, scalable geodesic transport distances under noisy, unbalanced, large-scale settings via three components: (1) graph connectivity regularization for well-defined geodesics on sparse/disconnected manifolds; (2) an unbalanced OT formulation via KL marginal penalties; and (3) a batched matrix algorithm computing all pairwise distances in one heat diffusion (over 200 × faster than Geodesic Sinkhorn for 500 distributions). We validate Pheno-GS on synthetic benchmarks and a CyTOF perturbation dataset.