Persistence Images: A Stable Vector Representation of Persistent Homology
Authors: Henry Adams, Tegan Emerson, Michael Kirby, Rachel Neville, Chris Peterson, Patrick Shipman, Sofya Chepushtanova, Eric Hanson, Francis Motta, Lori Ziegelmeier
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The paper includes a dedicated section titled "6. Experiments" where it details: "We perform several experiments in order to assess the added value of our vector representation of PDs. First, in 6.1, we compare the performance of PDs, PLs, and PIs in a classification task for a synthetic data set..." and later "Lastly, 6 contains examples of ML techniques applied to PIs generated from samples of common topological spaces, an applied dynamical system modeling turbulent mixing, and a partial differential equation describing pattern formation in extended systems driven far from equilibrium." |
| Researcher Affiliation | Academia | All listed authors are affiliated with universities: "Colorado State University", "Wilkes University", "Texas Christian University", "Duke University", and "Macalester College". All email addresses provided are also academic domains (.edu). |
| Pseudocode | No | The paper describes methods and processes in prose and mathematical formulations but does not contain any explicitly labeled "Pseudocode" or "Algorithm" blocks or figures. |
| Open Source Code | Yes | Our code for producing PIs is publicly available at https://github.com/CSU-TDA/Persistence Images. |
| Open Datasets | No | The paper describes generating its own synthetic data: "Our synthetic data set consists of six shape classes: a unit cube, a circle of diameter one, a sphere of diameter one, three clusters with centers randomly chosen in the unit cube... We produce 25 point clouds of 500 points sampled uniformly at random from each of the six shapes, and then add a level of Gaussian noise." There is no mention of using or providing access to any external publicly available dataset. |
| Dataset Splits | Yes | In Section 6.4.2, when describing the classification for the Kuramoto-Sivashinsky equation, it states: "Accuracy reported is averaged over 100 different training and testing partitions. ...a normal distribution was fit to a training set of 2/3 of the variances for each parameter value, and the testing data was classified based on a z-test for each of the different models." |
| Hardware Specification | Yes | All timings are computed on a laptop with a 1.3 GHz Intel Core i5 processor and 4 GB of memory. |
| Software Dependencies | No | The paper mentions using "the software of Kerber et al. (2016)", "the Persistence Landscapes Toolbox by Bubenik and Dlotko (2016)", and "Our MATLAB code". However, it does not provide specific version numbers for any of these software components. |
| Experiment Setup | Yes | The paper provides specific parameter choices for generating Persistence Images (PIs) in various experiments. For example, in Section 6.1: "For PIs in this experiment, we use variance σ = 0.1, resolution 20 × 20, and the weighting function defined in § 4." In Section 6.3: "The PIs were generated using resolution 20 × 20, variance 0.0001, and noise level 0.05." |