Visualizing the Stability of 2D Point Sets from Dimensionality Reduction Techniques,Computer Graphics Forum

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Visualizing the Stability of 2D Point Sets from Dimensionality Reduction Techniques
Computer Graphics Forum ( IF 2.7 ) Pub Date : 2019-09-06 , DOI: 10.1111/cgf.13806
Christian Reinbold ₁ , Alexander Kumpf ₁ , Rüdiger Westermann ₁

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We use k‐order Voronoi diagrams to assess the stability of k‐neighbourhoods in ensembles of 2D point sets, and apply it to analyse the robustness of a dimensionality reduction technique to variations in its input configurations. To measure the stability of k‐neighbourhoods over the ensemble, we use cells in the k‐order Voronoi diagrams, and consider the smallest coverings of corresponding points in all point sets to identify coherent point subsets with similar neighbourhood relations. We further introduce a pairwise similarity measure for point sets, which is used to select a subset of representative ensemble members via the PageRank algorithm as an indicator of an individual member's value. The stability information is embedded into the k‐order Voronoi diagrams of the representative ensemble members to emphasize coherent point subsets and simultaneously indicate how stable they lie together in all point sets. We use the proposed technique for visualizing the robustness of t‐distributed stochastic neighbour embedding and multi‐dimensional scaling applied to high‐dimensional data in neural network layers and multi‐parameter cloud simulations.

中文翻译：

从降维技术可视化二维点集的稳定性

我们使用 k 阶 Voronoi 图来评估 2D 点集集合中 k 邻域的稳定性，并将其应用于分析降维技术对其输入配置变化的鲁棒性。为了测量集合上 k 邻域的稳定性，我们使用 k 阶 Voronoi 图中的单元格，并考虑所有点集中对应点的最小覆盖来识别具有相似邻域关系的相干点子集。我们进一步引入了点集的成对相似性度量，用于通过 PageRank 算法选择具有代表性的集合成员的子集作为单个成员价值的指标。稳定性信息被嵌入到代表性集合成员的 k 阶 Voronoi 图中，以强调连贯的点子集，并同时指示它们在所有点集中在一起的稳定性。我们使用所提出的技术来可视化应用于神经网络层和多参数云模拟中的高维数据的 t 分布随机邻居嵌入和多维缩放的鲁棒性。

更新日期：2019-09-06

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