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Linear optimal transport subspaces for point set classification.

Mohammad Shifat-E-Rabbi1, Naqib Sad Pathan2, Shiying Li3

  • 1Department of Electrical and Computer Engineering, North South University, Dhaka, Bangladesh.

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|April 2, 2024
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Summary
This summary is machine-generated.

This study introduces a new framework for classifying point sets, even with spatial deformations. Using the Linear Optimal Transport (LOT) transform, it simplifies complex data for accurate and efficient classification.

Keywords:
optimal transportparticle-LOTpoint set classificationsubspace modeling

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Area of Science:

  • Computer Vision
  • Machine Learning
  • Data Science

Background:

  • Modeling unordered, permutation-invariant point sets is difficult, especially with spatial deformations.
  • Point set classification faces challenges due to variations in spatial arrangements.

Purpose of the Study:

  • To develop a robust framework for classifying point sets under spatial deformations, particularly affine transformations.
  • To simplify the complex data space of point sets for effective classification.

Main Methods:

  • Employed the Linear Optimal Transport (LOT) transform for 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:

  • Achieved competitive accuracies on various point set classification tasks.
  • Demonstrated label efficiency, non-iterative processing, and no need for hyper-parameter tuning.
  • Showcased robustness in out-of-distribution scenarios with varying deformation magnitudes.

Conclusions:

  • The proposed LOT-based framework effectively simplifies point set classification.
  • The method offers an efficient, robust, and accurate solution for handling spatial deformations in point sets.
  • This approach advances point set analysis in computer vision and machine learning.