Datasets for intrinsic dimension estimation

Intrinsic Dimension Estimation Dataset This repository is dedicated to datasets for testing intrinsic dimension estimators. It contains code for generating datasets and sample datasets in CSV format. 📊 Included Dataset Dataset Description Hyper Ball A dataset sampled from a d-dimensional hyperball. Hyper Sphere A dataset sampled from the d-dimensional hypersphere. Hyper Twin Peaks Plane with protruding peaks Swiss Roll with Spheres A Swiss roll surface combined with a uniform distribution of points from a 3-sphere inside the roll. Toroidal Spiral A looped spiral on the surface of a torus Torus 2-dimensional torus Lorenz Attractor Attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid Hilbert Curve Points sampled along a space-filling Hilbert curve, illustrating fractal geometry Dumbbell Piecewise linear model of a 2-dimensional dumbbell in 3-dimensional space SO(n) Special Orthogonal group in dimension n Benchmark Manifolds Commonly used benchmark set of synthetic manifolds with known intrinsic dimension described by Hein et al. and Campadelli et al. MNIST Handwritten digit images from the MNIST dataset 💻 Code Attached code is a snippet from our fork of the scikit-dimension repository. Main Features Added in the Fork - Sampling Hilbert curve- Sampling torus- Sampling toroidal spiral- Sampling Lorenz attractor- Sampling a piecewise linear model of a 2-dimensional dumbbell- Sampling an arbitrary surface of Revolution- Sampling a special orthogonal group- Ensuring uniform (with respect to the Hausdorff measure) sampling Hyper Twin Peaks - Fetching the MNIST dataset 📁 Dataset Format Each dataset is provided as a `.csv` file. Each row corresponds to a single data point. Information about the intrinsic dimension of presented datasets and parameters used in generation files are stored in json files in the 'parameters' folder. 📦 Repository Structure /<root>├── data/│ └── BenchmarkManifolds/├── README.md├── parameters│ └── BenchmarkManifolds/└── code/ 🧪 Credits Original scikit-dimension code for generating datasets was created by Jonathan Bac. The BenchmarkManifold class has been adapted from the implementation by Mokrov Nikita, Marina Gomtsyan, Maxim Panov, and Yury Yanovich. The authors of the new features are John Harvey, Ka Man Yim, and James Binnie. The method for sampling from the Lorenz attractor incorporates code by Christian Hill. The method for sampling from the Hilbert curve is based on Kyle Finn's javascript code.