Can neural networks learn persistent homology features?

• URL: http://arxiv.org/abs/2011.14688v1
• Date: Mon, 30 Nov 2020 10:58:53 GMT
• Title: Can neural networks learn persistent homology features?
• Authors: Guido Mont\'ufar, Nina Otter, Yuguang Wang
• Abstract summary: Topological data analysis uses tools from topology to create representations of data. In our work, we explore the possibility of learning several types of features extracted from persistence diagrams using neural networks.
• Score: 1.1816942730023885
• License: http://creativecommons.org/licenses/by/4.0/
• 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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