Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds

TL;DR

The pyLOT library implements linearized optimal transport techniques in Python, enabling efficient machine learning tasks on point cloud data by embedding distributions into a Hilbert space for simplified linear operations.

Contribution

It introduces a Python toolkit for linearized optimal transport, facilitating machine learning on point clouds through Hilbert space embeddings and demonstrating its application on 3D scan data.

Findings

Effective classification, clustering, and data generation using LOT embeddings.

Simplified linear operations enable complex ML tasks on point clouds.

Case study on lemur teeth scans showcases practical utility.

Abstract

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.