Visually guided exploration of point cloud data in Euclidean space

欧氏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，如物理和生物化学测量和模拟，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或颜色值的矢量，并且文本文档可以被表示为术语频率向量，该术语频率向量存储每个术语（在术语集合中）在文档中出现的频率。对于形状、音频和视频数据，类似的变换是已知的。因此，在欧氏空间中分析点云数据是机器学习的核心任务，并且已经开发了各种算法。这些算法中的许多算法具有可自由调整的参数，这些参数的设置可以严重影响分析的结果。因此，有一个公认的需要，探索系统的参数设置。有趣的是，已知有相当多的算法，对于这些算法，将算法应用于所有参数设置（计算由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一个好的参数设置或识别感兴趣的参数区域，人们知之甚少。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决方案路径，并以一种允许数据分析师交互式识别有趣的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.