Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909478684721152 |
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| author | Linwu, Jun Khurana, Varun Karris, Nicholas Cloninger, Alexander |
| author_facet | Linwu, Jun Khurana, Varun Karris, Nicholas Cloninger, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds Linwu, Jun Khurana, Varun Karris, Nicholas Cloninger, Alexander Machine Learning Mathematical Software Computation 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. |
| title | Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds |
| topic | Machine Learning Mathematical Software Computation |
| url | https://arxiv.org/abs/2502.03439 |