Fast PCA in 1-D Wasserstein Spaces via B-splines Representation and Metric Projection
Authors: Matteo Pegoraro, Mario Beraha9342-9349
AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through extensive simulation studies, we show how our PCA performs similarly to the ones already proposed in the literature while retaining a much smaller computational cost. We apply our method to a real dataset of mortality rates due to Covid-19 in the US, concluding that our analyses are consistent with the current scientific consensus on the disease. |
| Researcher Affiliation | Academia | 1 MOX Department of Mathematics, Politecnico di Milano 2 Department of Mathematics, Politecnico di Milano 3 Department of Computer Science, Universit a di Bologna |
| Pseudocode | No | The paper describes mathematical formulations and optimization problems but does not include any explicit pseudocode blocks or algorithms. |
| Open Source Code | No | The paper mentions a public repository link: “The code is publicly available at https://github.com/ecazelles/ 2017-GPCA-vs-Log PCA-Wasserstein”. However, this link points to code for an existing method (Cazelles et al. 2017), which they used for comparison, not the open-source code for their novel projected PCA methodology described in the paper. |
| Open Datasets | Yes | Data are freely available at https://data.cdc.gov/NCHS/ Provisional-COVID-19-Death-Counts-by-Sex-Age-and-S/9bhghcku. |
| Dataset Splits | Yes | Each result displays the average 10-fold cross validation accuracy, averaged again over 20 repetitions one standard deviation. |
| Hardware Specification | Yes | All experiments were performed on a laptop equipped with a 8-core Intel i7-7700HQ CPU 2.80GHz and 16Gb of RAM. |
| Software Dependencies | Yes | The main numerical libraries employed consist of the Python packages numpy, scipy and qpsolvers (v 1.1) and of the optimization library Ipopt (v 3.12.12) interfaced with the Python package pyomo. |
| Experiment Setup | Yes | In the following, we will always center the PCA in the barycenter of the data, i.e. a0 = n 1 Pn i=1 ai. Moreover, we consider the spline basis {ψj}J j=1 with J = 20 and equispaced knots in [0, 1]... After performing a PCA, a Support Vector Machine (SVM) classifier is fit, with parameters C = 1.0, radial basis function kernel and default value for the parameter γ |