Linear Optimal Partial Transport Embedding

• URL: http://arxiv.org/abs/2302.03232v5
• Date: Tue, 23 Apr 2024 16:30:40 GMT
• Title: Linear Optimal Partial Transport Embedding
• Authors: Yikun Bai, Ivan Medri, Rocio Diaz Martin, Rana Muhammad Shahroz Khan, Soheil Kolouri,
• Abstract summary: Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. We propose the Linear partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem.
• Score: 8.23887869467319
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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