Scaling Invariant Multidimensional Projections for Visualization

缩放不变多维投影以实现可视化

• 批准号: 509315541
• 负责人: Professor Dr.-Ing. Holger Theisel
• 金额: --
• 依托单位: Institut für Simulation und Graphik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/509315541?language=en
• 关键词: Scaling; Invariant; Multidimensional; Projections; Visualization

Finding good projections from multi-dimensional data domains to the 2D screen is a standard problem in many fields. Multidimensional data usually considered in Multifield Visualization (a subfield of Scientific Visualization) often comes with the property that the dimensions are measured in different physical units, making the ratio between arbitrary. We propose to develop projection techniques that are independent of the chosen physical unit of each dimension, i.e., they are invariant on the scaling of each dimension. While many standard measures and features do not have this scaling invariance (such as relative Euclidean distance, PCA, t-SNE), simple solutions like normalization of each dimension does not solve the problem adequately. We propose to develop scaling invariant versions of standard automatic non-linear projection techniques such as t-SNE. Also, we search for scaling invariant versions of linear projections (such as PCA), as well as for standard clustering techniques.We see the main application of scaling invariant projection techniques in the visual analysis of multifield data.

寻找从多维数据域到二维屏幕的良好投影是许多领域的标准问题。通常在多场可视化（科学可视化的一个子领域）中考虑的多维数据通常具有以不同的物理单位测量维度的属性，使得它们之间的比率是任意的。我们建议开发独立于每个维度所选择的物理单位的投影技术，即它们在每个维度的缩放上是不变的。虽然许多标准度量和特征不具有这种尺度不变性（如相对欧几里得距离、PCA、t-SNE），但像每个维度的归一化这样的简单解决方案并不能充分解决问题。我们建议开发标准自动非线性投影技术（如t-SNE）的缩放不变版本。此外，我们还搜索线性投影的缩放不变版本（如PCA），以及标准聚类技术。我们看到了尺度不变投影技术在多场数据可视化分析中的主要应用。