Can neural networks learn persistent homology features?

Guido Montufar, Nina Otter, Yu Guang Wang

Keywords: persistent homology, CNN, neural networks, learning representations

TL;DR: We show that neural networks can learn several types of features associated with persistence diagrams, using the data sets MNIST and CIFAR-10.

Abstract: Topological data analysis uses tools from topology — the mathematical area that studies shapes — to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data, and persistence diagrams describe the lifetime of topological invariants, such as connected components or holes, across the one-parameter family. In many applications, one is interested in working with features associated with persistence diagrams rather than the diagrams themselves. In our work, we explore the possibility of learning several types of features extracted from persistence diagrams using neural networks.

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