Visualizing Topological Importance: A Class-Driven Approach
- URL: http://arxiv.org/abs/2309.13185v1
- Date: Fri, 22 Sep 2023 21:20:41 GMT
- Title: Visualizing Topological Importance: A Class-Driven Approach
- Authors: Yu Qin and Brittany Terese Fasy and Carola Wenk and Brian Summa
- Abstract summary: This work shows how proven explainable deep learning approaches can be adapted for use in topological classification.
It provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label.
This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data.
- Score: 8.131460996877944
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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