6 papers
Encoding the Euler Characteristic Transform
Nello Blaser, Odin Hoff Gardaa, Lars M. Salbu +2
The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Cha…
The Kinetic Hourglass Data Structure for Computing the Bottleneck Distance of Dynamic Data
Elizabeth Munch, Elena Xinyi Wang, Carola Wenk
The kinetic data structure (KDS) framework is a powerful tool for maintaining various geometric configurations of continuously moving objects. In this work, we introduce the kineti…
Geometry-Aware Simplicial Message Passing
Elena Xinyi Wang, Bastian Rieck
The Weisfeiler--Lehman (WL) test and its simplicial extension (SWL) characterize the combinatorial expressivity of message passing networks, but they are blind to geometry, i.e., m…
Persistence-Augmented Neural Networks
Elena Xinyi Wang, Arnur Nigmetov, Dmitriy Morozov
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when…
Computing the Bottleneck Distance between Persistent Homology Transforms
Michael Kerber, Elena Xinyi Wang
The Persistent Homology Transform (PHT) summarizes a shape in by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathb…
On the Stability of the Euler Characteristic Transform for a Perturbed Embedding
Jasmine George, Oscar Lledo Osborn, Elizabeth Munch +2
The Euler Characteristic Transform (ECT) is a robust method for shape classification. It takes an embedded shape and, for each direction, computes a piecewise constant function rep…