Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis
Authors: Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel
JMLR 2015 | Venue PDF | 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. |