Visualizing Topological Importance: A Class-Driven Approach
Visualizing Topological Importance: A Class-Driven Approach
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DOI：
10.1109/topoinvis60193.2023.00016
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Yu Qin;Brittany Terese Fasy;C. Wenk;B. Summa
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文献类型：
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作者：
Yu Qin;Brittany Terese Fasy;C. Wenk;B. Summa
本文提出了第一种方法来可视化的拓扑特征，定义类的数据的重要性。拓扑特征能够抽象复杂数据的基本结构，是可视化和分析管道的组成部分。尽管并非数据中存在的所有拓扑特征都具有同等重要性。到目前为止，特征重要性的默认定义通常是假设和固定的。这项工作展示了经过验证的可解释深度学习方法如何适用于拓扑分类。在这样做的过程中，它提供了第一种技术，说明了在每个数据集中关于它们的类标签的拓扑结构是重要的。特别是，该方法使用一个学习的度量分类器的持久性图的点的密度估计作为输入。该度量学习如何重新加权该密度，使得分类准确度高。通过提取该权重，可以创建关于持久点密度的重要性字段。这提供了持久点重要性的直观表示，可用于驱动新的可视化。这项工作提供了两个例子：直接在每个图上的可视化，以及在图像上的子级集过滤的情况下，直接在图像本身上。这项工作突出了现实世界的例子，这种方法可视化图形，3D形状和医学图像数据中的重要拓扑特征。
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data.