This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance. We detail the construction methods, generation time complexity, theoretical guarantees, and conditions for each strategy. Additionally, we provide insights into their suitability for sliced optimal transport in theory. Extensive experiments on both simulated and real-world data offer a representative comparison of the strategies, culminating in practical recommendations for their best usage.

翻译：本文旨在为切片最优传输的采样策略提供一份用户指南。我们回顾了切片Wasserstein距离的相关性质，并补充了额外的正则性结果。针对每种策略，我们详细阐述了其构建方法、生成时间复杂度、理论保证条件。此外，我们从理论角度深入分析了这些策略对切片最优传输的适用性。通过在模拟数据和真实数据上进行大量实验，我们对各策略进行了具有代表性的比较，最终提出了关于其最佳使用场景的实践建议。