Topology vs. Geometry in Data Analysis/Machine Learning

Dear Colleagues,

Recent years have witnessed a surging interest in the role geometric and topological tools play in machine learning and data science. Indeed topology and geometry have been proven to be natural tools that facilitate a concrete language and offer very useful set tools in solving many longstanding problems in these fields. For instance, geometry has played a key role in (nonlinear) dimension reduction models and geometric deep learning has great potential to revolutionize structure data analysis. Topological data analysis, in particular persistent homology has been overwhelmingly successful at solving a vast array of complex data problems within machine learning and beyond. On the other hand, the role that both geometry and topology play in machine learning is still mostly restricted to techniques that attempt to enhance machine learning models. However, we believe that both geometry and topology can and will play a central role in machine learning and AI in general and an entire set of tools that both geometry and topology can offer are yet to be discovered. Our purpose of this Topic call is to invite researchers to contribute to ongoing research interest in a new emerging area that intertwines topological and geometric tools with machine learning. We welcome contributions from theoretical and practical flavors. Specifically, the Topology vs. Geometry in Data Analysis/Machine Learning topic invites papers on theoretical and applied issues including, but not limited to: 

• Persistent Homology
• Generalized Persistence theories
• Applied Graph and Hypergraph Theory
• Dimensional reduction
• Discrete Morse Theory
• Spectral theory (spectral graph/simplicial complex/hypergraph)
• Discrete geometry and discrete exterior calculus
• Reeb graph
• Simplicial complex representations (Dowker complex, Hom complex, Path complex, etc.)
• Cellular Sheaves
• Hyperbolic embedding, Poincaré embedding
• Discrete Ricci curvature
• Hodge theory
• Conformal geometry
• Geometric deep learning
• Geometric signal processing
• Discrete optimal transport

This Topic will present the results of research describing recent advances in geometry and topology inspired by or applied to both Data Analysis and Machine Learning.

Prof. Massimo Ferri
Prof. Dr. Kelin Xia
Prof. Dr. Francesco Vaccarino
Prof. Dr. Mustafa Hajij
Prof. Dr. Nežka Mramor Kosta
Topic Editors