QuadratiK 1.1.1

QuadratiK includes test for multivariate normality, test for uniformity on the Sphere, non-parametric two- and k-sample tests, random generation of points from the Poisson kernel-based density and clustering algorithm for spherical data.

Introduction

The QuadratiK package is implemented in both R and Python, providing a comprehensive set of goodness-of-fit tests and a clustering technique using kernel-based quadratic distances. This framework aims to bridge the gap between the statistical and machine learning literatures. It includes:

• Goodness-of-Fit Tests : The software implements one, two, and k-sample tests for goodness of fit, offering an efficient and mathematically sound way to assess the fit of probability distributions. Expanded capabilities include supporting tests for uniformity on the \(d\)-dimensional Sphere based on Poisson kernel densities.

• Clustering Algorithm for Spherical Data: the package incorporates a unique clustering algorithm specifically tailored for spherical data. This algorithm leverages a mixture of Poisson-kernel-based densities on the sphere, enabling effective clustering of spherical data or data that has been spherically transformed. This facilitates the uncovering of underlying patterns and relationships in the data. Additionally, the package also includes Poisson Kernel-based Densities random number generation.

• Additional Features: Alongside these functionalities, the software includes additional graphical functions, aiding users in validating cluster results as well as visualizing and representing clustering results. This enhances the interpretability and usability of the analysis.

• User Interface: We also provide a dashboard application built using streamlit allowing users to access the methods implemented in the package without the need for programming.

Authors

Giovanni Saraceno <[e-mail]>, Marianthi Markatou <[e-mail]>, Raktim Mukhopadhyay <[e-mail]>, Mojgan Golzy <[e-mail]>

Mantainer: Raktim Mukhopadhyay <[e-mail]>

Documentation

The documentation is hosted on Read the Docs at - https://quadratik.readthedocs.io/en/latest/

Installation using pip

pip install QuadratiK

Examples

Find basic examples at QuadratiK Examples

You can also execute the examples on Binder .

Community

Development Version Installation

For installing the development version, please download the code files from the master branch of the Github repository. Please note that installation from Github might be buggy, for latest stable release please download using pip. For downloading from Github use the following instructions,

git clone https://github.com/rmj3197/QuadratiK.git
cd QuadratiK
pip install -e .

Contributing Guide

Please refer to the Contributing Guide.

Code of Conduct

The code of conduct can be found at Code of Conduct.

License

This project uses the GPL-3.0 license, with a full version of the license included in the repository here.

Funding Information

The work has been supported by Kaleida Health Foundation, Food and Drug Administration, and Department of Biostatistics, University at Buffalo.

References

Saraceno G., Markatou M., Mukhopadhyay R., Golzy M. (2024). Goodness-of-Fit and Clustering of Spherical Data: the QuadratiK package in R and Python. arXiv preprint arXiv:2402.02290.

Ding Y., Markatou M., Saraceno G. (2023). “Poisson Kernel-Based Tests for Uniformity on the d-Dimensional Sphere.” Statistica Sinica. DOI: 10.5705/ss.202022.0347.

Golzy M. & Markatou M. (2020) Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling, Journal of Computational and Graphical Statistics, 29:4, 758-770, DOI: 10.1080/10618600.2020.1740713.

Markatou M, Saraceno G, Chen Y (2023). “Two- and k-Sample Tests Based on Quadratic Distances.” Manuscript, (Department of Biostatistics, University at Buffalo).