利用拓扑景观对高维点云进行可视化分析

P. Oesterling, Christian Heine, H. Leitte, G. Scheuermann
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引用次数: 31

摘要

在本文中,我们提出了一种新的三阶段过程来可视化任意维度的点云结构。为了深入了解数据集的结构和复杂性,我们最好只是观察它,例如通过绘制相应的点云。不幸的是,对于正交散点图,这只适用于三个维度,而其他可视化,如平行坐标或散点图矩阵,在处理多个维度和数据实体的视觉重叠方面也存在问题。该方法通过可视化点云密度分布的拓扑结构,间接解决了点云的可视化问题。这种方法的好处是可以在任意维度上计算该拓扑。与检查散点图类似,这提供了诸如累积区域的数量、大小和嵌套结构等重要信息。我们把我们的方法看作是集群可视化的另一种选择。为了创建可视化,我们首先使用一种新的高维插值方案来估计密度函数。其次,我们通过连接树计算该函数的拓扑,使用Weber等人(2007)引入的拓扑景观隐喻生成相应的3-D地形,最后通过将原始数据点放置在合适的位置来增强该景观。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Visual analysis of high dimensional point clouds using topological landscapes
In this paper, we present a novel three-stage process to visualize the structure of point clouds in arbitrary dimensions. To get insight into the structure and complexity of a data set, we would most preferably just look into it, e.g. by plotting its corresponding point cloud. Unfortunately, for orthogonal scatter plots, this only works up to three dimensions, and other visualizations, like parallel coordinates or scatterplot matrices, also have problems handling many dimensions and visual overlap of data entities. The presented solution tackles the problem of visualizing point clouds indirectly by visualizing the topology of their density distribution. The benefit of this approach is that this topology can be computed in arbitrary dimensions. Similar to examining scatter plots, this gives the important information like the number, size and nesting structure of accumulated regions. We view our approach as an alternative to cluster visualization. To create the visualization, we first estimate the density function using a novel high-dimensional interpolation scheme. Second, we compute that function's topology by means of the join tree, generate a corresponding 3-D terrain using the topological landscape metaphor introduced by Weber et al. (2007), and finally augment that landscape by placing the original data points at suitable locations.
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