Intrinsic Persistent Homology via Density-based Metric Learning
Authors: Ximena Fernández, Eugenio Borghini, Gabriel Mindlin, Pablo Groisman
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We use these ideas to propose and implement a method for pattern recognition and anomaly detection in time series, which is evaluated in applications to real data. |
| Researcher Affiliation | Academia | Ximena Fern andez EMAIL Department of Mathematics Swansea University, UK Departamento de Matem atica and IMAS-CONICET FCEN, Universidad de Buenos Aires, Argentina; Eugenio Borghini EMAIL Departamento de Matem atica and IMAS-CONICET FCEN, Universidad de Buenos Aires, Argentina; Gabriel Mindlin EMAIL IFIBA, CONICET and Departamento de F ısica FCEN, Universidad de Buenos Aires, Argentina; Pablo Groisman EMAIL Departamento de Matem atica and IMAS-CONICET FCEN, Universidad de Buenos Aires, Argentina NYU-ECNU Institute of Mathematical Sciences NYU Shanghai |
| Pseudocode | No | The paper describes methods and algorithms (e.g., Isomap, MDS, persistent homology computation) but does not provide any explicitly labeled pseudocode or algorithm blocks for its own proposed method. Steps are described in narrative text. |
| Open Source Code | Yes | The code to replicate the computational examples and applications can be found at the repository by Fernandez (2021a). |
| Open Datasets | Yes | We consider the record sel102 of the QT Database from the freely-available repository of medical research data PhysioNet MIT, Figure 9. |
| Dataset Splits | No | The paper mentions data processing like "uniform downsampling from the original point cloud of 10000 points... to obtain a new point cloud of 3400 points" or "subsample of size 3000 from the original T 300000 points." However, it does not specify explicit training, validation, or testing splits commonly found in machine learning experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU models, CPU types, or memory configurations used for running the experiments. |
| Software Dependencies | Yes | Fermat and k-NN distances are computed using the library Fermat (Aristas, 2018), while Ripser by Bauer (2021) is employed for the computation of persistence diagrams associated to Vietoris Rips filtrations. |
| Experiment Setup | Yes | The persistence diagram of the delay embedding reconstruction is computed with time delay τ = 10 and embedding dimensions D = 3, 4 and 5... For a sample of 2000 points of the noisy signal in consideration at the interval [0, 100], the classic heuristic estimations of the optimal parameters outputs τ = 28 and D = 8... p was set equal to 6... All delay embeddings were computed with a stride of t = 2... here, the choice of p = 2... delay embedding of the time series X(t) with τ = 500 and D = 3, its associated persistence diagram computed using Fermat distance with p = 1.5. |