Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds
This provides a toolkit for machine learning on point clouds, particularly in domains like biology, but it is incremental as it applies existing LOT methods to new data.
The paper introduces the pyLOT library, which implements linearized optimal transport (LOT) techniques to embed probability distributions into a Hilbert space, enabling the use of linear machine learning algorithms for downstream tasks like classification and clustering, as demonstrated in a case study on 3D scans of lemur teeth.
The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributions into a Hilbert space via the Optimal Transport maps from a fixed reference distribution, and this linearization allows downstream tasks to be completed using off the shelf (linear) machine learning algorithms. We provide a case study of performing ML on 3D scans of lemur teeth, where the original questions of classification, clustering, dimension reduction, and data generation reduce to simple linear operations performed on the LOT embedded representations.