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用户指南。我们回顾了切片Wasserstein距离的基本概念并补充了其正则性结果。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、理论保证及适用条件。此外，我们从理论角度深入分析了各策略对切片最优传输的适配性。通过模拟数据与真实数据的广泛实验，我们对各策略进行了代表性比较，最终提出了实际应用中的最佳使用建议。