We present a method for data sampling in scatterplots by jointly optimizing point selection for different views or classes. Our method uses space-filling curves (Z-order curves) that partition a point set into subsets that, when covered each by one sample, provide a sampling or coreset with good approximation guarantees in relation to the original point set. For scatterplot matrices with multiple views, different views provide different space-filling curves, leading to different partitions of the given point set. For multi-class scatterplots, the focus on either per-class distribution or global distribution provides two different partitions of the given point set that need to be considered in the selection of the coreset. For both cases, we convert the coreset selection problem into an Exact Cover Problem (ECP), and demonstrate with quantitative and qualitative evaluations that an approximate solution that solves the ECP efficiently is able to provide high-quality samplings.

中文翻译：

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通过Set Cover Optimization在多视图和多类散点图中进行数据采样。

我们通过联合优化不同视图或类的点选择，提出了一种散点图数据采样方法。我们的方法使用空间填充曲线（Z阶曲线），该曲线将点集划分为子集，当每个子集被一个样本覆盖时，该子集为样本或核心集提供与原始点集相关的良好近似保证。对于具有多个视图的散点图矩阵，不同的视图提供不同的空间填充曲线，导致给定点集的不同分区。对于多类散点图，对每个类分布或全局分布的关注提供了给定点集的两个不同分区，在选择核心集时需要考虑这些分区。对于这两种情况，我们都将核心集选择问题转换为精确覆盖问题（ECP），