Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis
Authors: Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel
JMLR 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Some numerical experiments are performed in various contexts to illustrate our results. 5. Experiments |
| Researcher Affiliation | Academia | Inria Saclay ˆIle de France, Universit e de Bourgogne, Universit e Pierre et Marie Curie Paris 6 |
| Pseudocode | No | The paper describes mathematical concepts and proofs, but does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about open-source code availability, specific repository links, or code in supplementary materials for the methodology described. |
| Open Datasets | Yes | M4 (rotating shape space): for this space we used a 3D character from the SCAPE database (Anguelov et al., 2005) and considered all the images of this character from a view rotating around it. |
| Dataset Splits | No | From each of the measured metric spaces M1, M2, M3 and M4 we sampled k sets of n points for different values of n from which we computed persistence diagrams for different geometric complexes (see Table 1). |
| Hardware Specification | No | The paper describes numerical experiments but does not provide specific details about the hardware used to run these experiments. |
| Software Dependencies | No | The paper describes numerical experiments but does not provide specific details about the software dependencies or their version numbers used in the implementation. |
| Experiment Setup | Yes | From each of the measured metric spaces M1, M2, M3 and M4 we sampled k sets of n points for different values of n from which we computed persistence diagrams for different geometric complexes (see Table 1). For M1, M2 and M3 we have computed the persistence diagrams for the 1 or 2-dimensional homology of the α-complex built on top of the sampled sets... For M4... we have computed the persistence diagrams for the 1-dimensional homology of the Vietoris-Rips complex built on top of the sampled sets. Table 1: Sampling parameters and geometric complexes where rn1 : h : n2s denotes the set of integers tn1, n1 h, n1 2h, n2u. |