Multidimensional projections (MP) are among the most essential approaches in the visual analysis of multidimensional data. It transforms multidimensional data into two-dimensional representations that may be shown as scatter plots while preserving their similarity with the original data. Human visual perception is frequently used to evaluate the quality of MP. In this work, we propose to study and improve on a well-known map called Local Affine Multidimensional Projection (LAMP), which takes a multidimensional instance and embeds it in Cartesian space via moving least squares deformation. We propose a new visual quality metric based on human perception. The new metric combines three previously used metrics: silhouette coefficient, neighborhood preservation, and silhouette ratio. We show that the proposed metric produces more precise results in analyzing the quality of MP than other previously used metrics. Finally, we describe an algorithm that attempts to overcome a limitation of the LAMP method which requires a similar scale for control points and their counterparts in the Cartesian space.

翻译：多维投影（MP）是多维数据可视化分析中最基本的方法之一。它将多维数据转换为可显示为散点图的二维表示，同时保持其与原始数据的相似性。人类视觉感知常被用于评估MP的质量。在本研究中，我们提出对一种称为局部仿射多维投影（LAMP）的著名映射方法进行研究和改进，该方法通过移动最小二乘变形将多维实例嵌入笛卡尔空间。我们提出了一种基于人类感知的新视觉质量度量。该新度量结合了三种先前使用的度量：轮廓系数、邻域保持度和轮廓比。我们证明，在分析MP质量时，所提出的度量比其他先前使用的度量能产生更精确的结果。最后，我们描述了一种算法，旨在克服LAMP方法的一个局限性，即要求控制点与其在笛卡尔空间中的对应点具有相似尺度。