Multiparameter Persistence Landscapes
Authors: Oliver Vipond
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally we provide example calculations and statistical tests to demonstrate a range of potential applications and how one can interpret the landscapes associated to a multiparameter module. We provide three computational examples together with the application of a basic statistical test and standard SVM classifier. |
| Researcher Affiliation | Academia | Oliver Vipond EMAIL Mathematical Institute University of Oxford Oxford, OX2 7DT, UK |
| Pseudocode | No | The paper describes algorithms (e.g., for computing persistence landscapes and birth-death pairs) but does not present any structured pseudocode or algorithm blocks within its content. |
| Open Source Code | No | We use the RIVET software (The RIVET Developers, 2018) for computations of 2-parameter persistence modules presented in Lesnick and Wright (2015). As far as we know, RIVET is the only publicly available TDA software package supporting multiparameter persistent homology calculations. The paper discusses using a third-party open-source tool, but does not provide its own implementation code for the methodology described. |
| Open Datasets | Yes | For this example we work on meteorite data which we have lifted from Good and Gaskins (1980). |
| Dataset Splits | Yes | We randomly partition our samples into 160 training samples and 40 test samples and evaluate the accuracy by the proportion of test samples correctly classified. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | We use the RIVET software (The RIVET Developers, 2018) for computations of 2-parameter persistence modules presented in Lesnick and Wright (2015). Using the Python package Linear SVC, we train a Support Vector Machine (SVM) with linear kernel. The paper mentions software names but does not provide specific version numbers for any of them (e.g., Python, Linear SVC, or a specific RIVET version beyond the publication year). |
| Experiment Setup | Yes | We produce a filtration on each pointcloud with the Rips filtration in the first parameter and the colour parameter in the second parameter. Using the Python package Linear SVC, we train a Support Vector Machine (SVM) with linear kernel on discretizations of the first 10 landscapes for the samples of the hyperbolic discs and elliptic discs, using l2 penalty and squared hinge loss function. |