4 citations · 5 across the 15 of their papers we have counts for
8 papers · 1 filter
Point Cloud Synthesis Using Inner Product Transforms
Ernst Röell, Bastian Rieck
Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have bee…
Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform
Bastian Rieck
This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological…
Graph Classification Gaussian Processes via Hodgelet Spectral Features
Mathieu Alain, So Takao, Xiaowen Dong +2
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed…
Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms
Julius von Rohrscheidt, Bastian Rieck
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the…
MANTRA: The Manifold Triangulations Assemblage
Rubén Ballester, Ernst Röell, Daniel Bīn Schmid +4
The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data,…
CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphs
Davide Buffelli, Farzin Soleymani, Bastian Rieck
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neu…
Persistent Homology via Ellipsoids
Niklas Canova, Sara Kališnik, Aaron Moser +2
Persistent homology is one of the most popular methods in topological data analysis. An initial step in its use involves constructing a nested sequence of simplicial complexes. The…
The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning
Benjamin Holmgren, Eli Quist, Jordan Schupbach +2
We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques. Our approach adapts and extends Ripley's -function, and catego…