Visually guided exploration of point cloud data in Euclidean space

欧几里得空间中的点云数据已经变得无处不在。有时点云数据表示是真实的，比如在物理和生物化学测量和模拟中，否则像图像、形状或文本这样的给定数据可以很容易地转换为点云数据：图像可以表示为灰度或颜色值的向量，文本文档可以表示为术语频率向量，该向量存储每个术语（在术语集合中）在文档中出现的频率。形状、音频和视频数据也有类似的转换。因此，分析欧几里得空间中的点云数据是机器学习的核心任务，为此已经开发了各种算法。其中许多算法具有可自由调整的参数，其设置会严重影响分析结果。因此，有必要系统地探索参数设置。有趣的是，有相当多已知的算法，它们对所有参数设置应用算法（计算由参数参数化的解决方案路径）并不比计算单个解决方案贵多少。对于如何利用这一点来选择一个好的参数设置或识别有趣的参数区域，我们所知甚少。在这里，我们建议开发和验证以下范例：计算分析算法的整个参数解路径，并以一种允许数据分析师交互式识别有趣参数设置的方式可视化地表示该路径。

Point cloud data in Euclidean space have become ubiquitous. Sometimes the point cloud data representation is genuine like in physical and bio-chemical measurements and simulations, otherwise given data like images, shapes or text can be easily transformed into point cloud data: an image can be represented as a vector of gray-scale or color values, and a text document can be represented as a term frequency vector that stores for each term (in a collection of terms) how often it appears in the document. Similar transformations are known for shapes, audio- and video data. Hence analyzing point cloud data in Euclidean space is a core task in machine learning and various algorithms have been developed to that means. Many of these algorithms have freely adaptable parameters whose setting can heavily influence the results of the analysis. Hence there is a well recognized need to explore the parameter settings systematically. Interestingly, there are quite a number of algorithms known for which applying the algorithm for all parameter settings (computing the solution path parameterized by the parameter) is not much more expensive than computing a single solution. Much less is known on how to exploit this for choosing a good parameter setting or identifying interesting parameter regions. Here we propose to develop and validate the following paradigm: compute the whole parameter solution path of an analysis algorithm and visually represent this path in a way that allows the data analyst to identify interesting parameter settings interactively.