🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.004962s)

  1. Topological Autoencoders (2020)

    Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt
    Abstract We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

  2. Topological Graph Neural Networks (2021)

    Max Horn, Edward De Brouwer, Michael Moor, Yves Moreau, Bastian Rieck, Karsten Borgwardt
    Abstract Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures, such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive in terms of the Weisfeiler--Lehman test of isomorphism. Augmenting GNNs with our layer leads to beneficial predictive performance, both on synthetic data sets, which can be trivially classified by humans but not by ordinary GNNs, and on real-world data.