2023/09/22 by Yu Qin, Qin, Yu, Brittany Terese Fasy +5
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cell Image Analysis Techniques #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning (cs.LG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2309.13185
openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.