AEPolytopes: Code and data for "Random Polytope Descriptors"
Michael Joswig, Marek Kaluba, Lukas Ruff · arXiv (Cornell University) · 2020
Code and data for random polytope descriptors (RPD): a family of random polytopes, built as intersections of random halfspaces with an outlier-removal parameter, that approximate the convex hull of a point set while remaining computationally benign (few vertices, fast double-description computation). This deposit accompanies the paper "Random Polytope Descriptors" by Michael Joswig, Marek Kaluba, and Lukas Ruff. Contents: - Julia source (`src/`, `scripts/`) implementing random polytope descriptors, dual bounding bodies, the vertex-barycenter approximation, and the classification/anomaly-detection experiments described in the paper.- Trained autoencoder (AE/VAE) embeddings of MNIST and Fashion-MNIST (`AE-PyTorch/`), used as the feature spaces analyzed in the paper's classification experiments.- Experiment logs (AUC scores from the Random Polytope Classifier and Voronoi/k-means baseline, `AE-PyTorch/log-30epochs/`) underlying the paper's Table 1 and Figure 2.- Saved dual bounding body polytopes (`dbd-data/`) backing the timing and f-vector numbers in the paper's case-study section.- Per-script documentation (`docs/`) and a Julia test suite (`test/`). See `README.md` in the archive for directory structure, system requirements (Julia 1.12, OSCAR 1.7, plus polymake 4.15 and Normaliz 3.10.3 for the case-study computation), and step-by-step reproduction instructions. Random seeds are fixed throughout, so results reproduce exactly given matching library versions. The paper's LaTeX source is maintained separately and is not part of this deposit. License: code is MIT-licensed (`LICENSE`); data (embeddings, logs, polytope files) is CC BY 4.0 (`LICENSE-DATA`).