# Linear optimal transport subspaces for point set classification

## TL;DR

This paper introduces a new method for classifying point sets using linear optimal transport to handle spatial deformations effectively.

## Contribution

The novel framework uses Linear Optimal Transport to create a convex data space for efficient and robust point set classification.

## Key findings

- The LOT transform simplifies point set classification by creating a convex embedding space.
- The method achieves competitive accuracy without hyper-parameter tuning.
- It shows robustness in out-of-distribution scenarios with varying deformation magnitudes.

## Abstract

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.