Linear Optimal Partial Transport Embedding
This is an incremental improvement for researchers and practitioners in machine learning and statistics who need efficient OPT calculations.
The paper tackled the computational inefficiency of optimal partial transport (OPT) distances by proposing a linear optimal partial transport (LOPT) embedding, which extends linearization techniques to OPT, resulting in faster computation for positive measures.
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.