Linear Optimal Transport Subspaces for Point Set Classification

Area of Science:

• Computer Vision
• Machine Learning
• Geometric Deep Learning

Background:

• Modeling unordered, permutation-invariant point sets is challenging, especially under spatial deformations.
• Existing methods struggle with affine deformations common in real-world data.
• Developing robust point set classification techniques is crucial for various applications.

Purpose of the Study:

• To propose a new framework for classifying point sets under spatial deformations, particularly affine transformations.
• To leverage the linear optimal transport (LOT) transform for efficient set-structured data embedding.
• To simplify point set classification by creating a convex data space.

Main Methods:

• Employed the linear optimal transport (LOT) transform to create a linear embedding of set-structured data.
• Constructed a convex data space using LOT transform properties to handle point set variations.
• Utilized a nearest-subspace algorithm within the LOT space for classification.

Main Results:

• The proposed method demonstrates label efficiency and requires no hyperparameter tuning.
• Achieved competitive accuracy compared to state-of-the-art methods on diverse point set classification tasks.
• Showcased robustness in out-of-distribution scenarios with varying deformation magnitudes.

Conclusions:

• The LOT transform provides an effective way to model and classify point sets under spatial deformations.
• The framework simplifies classification by creating a convex data space, enhancing efficiency and accuracy.
• The method offers a robust and adaptable solution for point set classification challenges.