🍩 Database of Original & Non-Theoretical Uses of Topology

1. Graph Filtration Learning (2020)

   Christoph Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, Roland Kwitt

   Abstract

   We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.

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   • Graph classification
   • Machine learning
   • Graphs
   • Innovate
   • Filtration
   • Neural network layer
   • Persistence diagrams
   • Persistent homology