## arXiv Analytics

### arXiv:1905.05604 [cs.LG]AbstractReferencesReviewsResources

#### Embeddings of Persistence Diagrams into Hilbert Spaces

Published 2019-05-11Version 1

Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessarily distort the metric on persistence diagrams. We show that persistence diagrams with the bottleneck distance do not admit a coarse embedding into a Hilbert space. As part of our proof, we show that any separable, bounded metric space isometrically embeds into the space of persistence diagrams with the bottleneck distance. As corollaries, we also calculate the generalized roundness, negative type, and asymptotic dimension of this space.

Categories: cs.LG, math.AT, math.MG, stat.ML
Subjects: 55N99, 46C05
Related articles: Most relevant | Search more
arXiv:2002.05715 [cs.LG] (Published 2020-02-13)
Self-Distillation Amplifies Regularization in Hilbert Space
arXiv:1902.09722 [cs.LG] (Published 2019-02-26)
Topological Bayesian Optimization with Persistence Diagrams
arXiv:1910.06741 [cs.LG] (Published 2019-10-13)
Adaptive template systems: Data-driven feature selection for learning with persistence diagrams