Linear Optimal Partial Transport Embedding
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929324625494016 |
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| author | Bai, Yikun Medri, Ivan Martin, Rocio Diaz Khan, Rana Muhammad Shahroz Kolouri, Soheil |
| author_facet | Bai, Yikun Medri, Ivan Martin, Rocio Diaz Khan, Rana Muhammad Shahroz Kolouri, Soheil |
| contents | Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear Optimal Partial Transport Embedding Bai, Yikun Medri, Ivan Martin, Rocio Diaz Khan, Rana Muhammad Shahroz Kolouri, Soheil Machine Learning Optimization and Control Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. |
| title | Linear Optimal Partial Transport Embedding |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2302.03232 |