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 Shift Toward Open and Reproducible AI Research," Under Review, 2026. doi: 10.48550/arXiv.2606.16974..
Outlier-Robust Subsampling Techniques for Persistent Homology
Authors: Bernadette J. Stolz
JMLR 2023 | Venue PDF | LLM Run Details | Input Tokens: 25,148 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 3,491 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test our landmarks on artiļ¬cial data sets which contain diļ¬erent levels of noise and compare them to standard landmark selection techniques. We demonstrate that our landmark selection outperforms standard methods as well as a subsampling technique based on an outlier-robust version of the k-means algorithm for low sampling densities in noisy data with respect to robustness to outliers. |
| Researcher Affiliation | Academia | Bernadette J. Stolz1,2 EMAIL 1 Ecole Polytechnique F ed erale de Lausanne Station 8, 1015 Lausanne, Switzerland 2 Mathematical Institute University of Oxford, Woodstock Rd Oxford OX2 6GG, United Kingdom |
| Pseudocode | Yes | We show pseudocode for the procedure in Algorithm 3 in Appendix A.1. We show our modiļ¬ed version of the k-means algorithm for landmark selection in Algorithm 2. We show the pseudocode for PH landmarks I in Algorithm 1, an algorithm for PH landmarks II can be formulated accordingly. |
| Open Source Code | Yes | We make an improved python version of our code for PH landmarks available on https://github.com/stolzbernadette/Outlier-robust-subsampling-techniques-f or-persistent-homology. |
| Open Datasets | No | We introduce the data sets to which we apply the diļ¬erent landmark selection methods. The data sets are chosen to be simple to allow us to determine eļ¬ects of the landmark selection. The data sets consist of signal points that are sampled from a topologically interesting structure a sphere, a Klein bottle, or a torus and noise points that we design to be topologically diļ¬erent from the signal. We consider four 3-dimensional data sets. ... We use the Laplacian random number generator code (Chen, 2019) to generate Ī±. |
| Dataset Splits | No | For a given number of points N and probability p we sample signal points uniformly at random from the surface of the unit sphere with probability p and noise points from the (ļ¬lled) cube [ 1, 1]3 R3 with probability 1 p. This corresponds to a landmark sampling density of m/N. For the k landmarks, we deļ¬ne the number of clusters to be k = pm and the number of outliers to be j = (1 p)m, where p is the probability with which a point in the respective data set was sampled from the signal data, i.e. the sphere, torus, or Klein bottle. |
| 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 | Yes | We implement PH landmark selection method in Matlab using Ripser (Bauer, 2021) for the computation of the local Vietoris-Rips complexes. We also implement the k landmarks algorithm in Matlab. For the calculation of maxmin landmarks, random landmarks, and dense core subsets we use the inbuilt functions in the java Plex package (Tausz et al., 2014). |
| Experiment Setup | Yes | For the k landmarks, we deļ¬ne the number of clusters to be k = pm and the number of outliers to be j = (1 p)m, where p is the probability with which a point in the respective data set was sampled from the signal data, i.e. the sphere, torus, or Klein bottle. ... For the PH landmarks we choose Ī“ = 0.2 for the 3-dimensional data sets, Ī“ = 0.5 for the torus data and Ī“ = 0.6 for the Klein bottle. In all our data sets, we ļ¬nd that when looking for the maximal persistence of a feature across all dimensions, the value of out0,1,2 PH (y) is exclusively determined by dimension 0. ... For the maxmin, random and k landmarks we show the average fraction of signal points and its standard deviation across 20 realisations of the selection algorithms. |