Point feature labeling is a classical problem in cartography and GIS that has been extensively studied for geospatial point data. At the same time, word clouds are a popular visualization tool to show the most important words in text data which has also been extended to visualize geospatial data (Buchin et al. PacificVis 2016). In this paper, we study a hybrid visualization, which combines aspects of word clouds and point labeling. In the considered setting, the input data consists of a set of points grouped into categories and our aim is to place multiple disjoint and axis-aligned rectangles, each representing a category, such that they cover points of (mostly) the same category under some natural quality constraints. In our visualization, we then place category names inside the computed rectangles to produce a labeling of the covered points which summarizes the predominant categories globally (in a word-cloud-like fashion) while locally avoiding excessive misrepresentation of points (i.e., retaining the precision of point labeling). We show that computing a minimum set of such rectangles is NP-hard. Hence, we turn our attention to developing heuristics and exact SAT models to compute our visualizations. We evaluate our algorithms quantitatively, measuring running time and quality of the produced solutions, on several artificial and real-world data sets. Our experiments show that the heuristics produce solutions of comparable quality to the SAT models while running much faster.

中文翻译：

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Worbel：将点标签聚合成词云

点要素标注是制图和 GIS 中的一个经典问题，已针对地理空间点数据进行了广泛研究。同时，词云是一种流行的可视化工具，用于显示文本数据中最重要的单词，该工具也已扩展到可视化地理空间数据（Buchin 等人。PacificVis 2016）。在本文中，我们研究了一种混合可视化，它结合了词云和点标记的各个方面。在考虑的设置中，输入数据由一组按类别分组的点组成，我们的目标是放置多个不相交且轴对齐的矩形，每个矩形代表一个类别，以便它们覆盖（大部分）相同类别下的点自然质量约束。在我们的可视化中，然后我们将类别名称放在计算的矩形内以生成覆盖点的标签，该标签在全局（以类似词云的方式）汇总主要类别，同时在局部避免点的过度错误表示（即，保留点标记的精度） . 我们表明计算此类矩形的最小集合是 NP 难的。因此，我们将注意力转向开发启发式和精确的 SAT 模型来计算我们的可视化。我们在几个人工和真实世界的数据集上定量评估我们的算法，测量生成的解决方案的运行时间和质量。我们的实验表明，启发式生成的解决方案与 SAT 模型的质量相当，同时运行速度要快得多。