Can neural networks learn persistent homology features?
This work addresses the problem of efficiently extracting and utilizing topological features from data for researchers and practitioners using topological data analysis, though the abstract does not specify a particular bottleneck or strong specific gain, making it an exploratory and potentially incremental contribution.
This paper explores whether neural networks can learn various features extracted from persistence diagrams, which describe the lifetime of topological invariants across one-parameter families of spaces associated with data. The study investigates the feasibility of this learning process for different types of persistence diagram features.
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.