Dimensionality Reduction (DR) techniques are commonly used for the visual exploration and analysis of high-dimensional data due to their ability to project datasets of high-dimensional points onto the 2D plane. However, projecting datasets in lower dimensions often entails some distortion, which is not necessarily easy to recognize but can lead users to misleading conclusions. Several Projection Quality Metrics (PQMs) have been developed as tools to quantify the goodness-of-fit of a DR projection; however, they mostly focus on measuring how well the projection captures the global or local structure of the data, without taking into account the visual distortion of the resulting plots, thus often ignoring the presence of outliers or artifacts that can mislead a visual analysis of the projection. In this work, we introduce the Warping Index (WI), a new metric for measuring the quality of DR projections onto the 2D plane, based on the assumption that the correct preservation of empty regions between points is of crucial importance towards a faithful visual representation of the data.

翻译：降维技术因其能够将高维数据点集投影至二维平面，常被用于高维数据的可视化探索与分析。然而，在低维空间中投影数据集通常会导致一定程度的失真，这种失真不易被察觉，却可能使用户得出误导性结论。已有多种投影质量度量方法被开发为量化降维投影拟合优度的工具；但这些方法主要关注投影捕获数据全局或局部结构的能力，未考虑生成图表的视觉失真，因而常忽略可能误导投影视觉分析的离群点或伪影的存在。本研究基于正确保持数据点间空白区域对数据忠实视觉表征至关重要的假设，提出了翘曲指数——一种用于度量二维平面降维投影质量的新指标。