Abstract

In high-dimensional data analysis, the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space. Contrary to this, is that projected data tends to clump at the center. This gives a sense that any structure near the center of the projection is obscured, whether this is true or not. A geometric transformation to reverse the curse, is defined in this article, which uses radial transformations on the projected data. It is integrated seamlessly into the grand tour algorithm, and we have called it a burning sage tour, to indicate that it reverses the curse. The work is implemented into the tourr package in R. Several case studies are included that show how the sage visualizations enhance exploratory clustering and classification problems. Supplementary files for this article are available online.

摘要

在高维数据分析中，维数灾难导致点往往远离分布的中心，位于高维空间的边缘。与此相反的是，预测数据往往集中在中心。这给人一种感觉，即投影中心附近的任何结构都被遮挡了，无论这是否属实。本文定义了一种几何变换来扭转诅咒，它对投影数据使用径向变换。它与大巡演算法无缝集成，我们称其为燃烧贤者巡演，表示它逆转了诅咒。这项工作被实施到 R 中的 tourr 包中。包括几个案例研究，展示了 sage 可视化如何增强探索性聚类和分类问题。