Convergence rates for persistence diagram estimation in Topological Data Analysis
Authors: Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel
ICML 2014 | Conference 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. |
| Researcher Affiliation | Academia | Fr ed eric Chazal FREDERIC.CHAZAL@INRIA.FR INRIA Saclay ˆIle-de-France, Palaiseau, France Marc Glisse MARC.GLISSE@INRIA.FR INRIA Saclay ˆIle-de-France, Palaiseau, France Catherine Labru ere CLABRUER@U-BOURGOGNE.FR Institut de Math ematiques de Bourgogne, France Bertrand Michel BERTRAND.MICHEL@UPMC.FR LSTA, Universit e Pierre et Marie Curie, Paris |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository for the methodology described. |
| Open Datasets | Yes | M2 is a space of images: we used a 3D character from the SCAPE database (Anguelov et al., 2005) |
| Dataset Splits | No | The paper describes generating data through sampling ('sampled k sets of n points') and uses these samples for estimation and illustration of theoretical results, but it does not specify or mention any training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, or memory) used to conduct the experiments described. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., programming languages, libraries, or solvers) used for its implementation or experiments. |
| Experiment Setup | Yes | From each of the measured metric spaces M1 and M2, 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 we have computed the persistence diagrams for the 1-dimensional homology of the α-complex built on top of the sampled sets. For M2, we computed the persistence diagrams for the 1-dimensional homology of the Vietoris-Rips complex built on top of the sampled sets. |