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，就像在物理和生物化学测量和模拟中一样，否则，给定的数据(如图像、形状或文本)可以很容易地转换为点云数据：图像可以表示为灰度值或颜色值的矢量，文本文档可以表示为术语频率矢量，该术语频率矢量存储每个术语(在术语集合中)在文档中出现的频率。类似的变换对于形状、音频和视频数据也是已知的。因此，在欧氏空间中分析点云数据是机器学习的核心任务，各种算法都已发展到这一目的。这些算法中的许多算法都具有可自由调整的参数，其设置会严重影响分析结果。因此，有一种公认的需要系统地探索参数设置。有趣的是，有相当多的已知算法将该算法应用于所有参数设置(计算由该参数参数化的解路径)并不比计算单个解昂贵得多。关于如何利用这一点来选择好的参数设置或识别感兴趣的参数区域，我们知道的要少得多。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求解路径，并以一种允许数据分析师以交互方式识别感兴趣的参数设置的方式直观地表示该路径。

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.