Goodness-of-Fit and Clustering of Spherical Data: the QuadratiK package in R and Python

TL;DR

The QuadratiK package in R and Python provides advanced goodness-of-fit tests and clustering methods for spherical data, utilizing kernel-based quadratic distances to improve statistical analysis and visualization.

Contribution

This work introduces a comprehensive software package that combines novel goodness-of-fit tests and a specialized clustering algorithm for spherical data, bridging statistical and machine learning approaches.

Findings

Implemented tests for distribution fit and uniformity on spheres.

Developed a unique clustering algorithm for spherical data.

Enhanced data analysis with visualization tools.

Abstract

We introduce the QuadratiK package that incorporates innovative data analysis methodologies. The presented software, implemented in both R and Python, offers a comprehensive set of goodness-of-fit tests and clustering techniques using kernel-based quadratic distances, thereby bridging the gap between the statistical and machine learning literatures. Our software implements one, two and k-sample tests for goodness of fit, providing an efficient and mathematically sound way to assess the fit of probability distributions. Expanded capabilities of our software include supporting tests for uniformity on the d-dimensional Sphere based on Poisson kernel densities. Particularly noteworthy is the incorporation of a unique clustering algorithm specifically tailored for spherical data that leverages a mixture of Poisson kernel-based densities on the sphere. Alongside this, our software includes additional graphical functions, aiding the users in validating, as well as visualizing and representing clustering results. This enhances interpretability and usability of the analysis. In summary, our R and Python packages serve as a powerful suite of tools, offering researchers and practitioners the means to delve deeper into their data, draw robust inference, and conduct potentially impactful analyses and inference across a wide array of disciplines.