circlus: An R Package for Circular and Spherical Clustering Using Poisson Kernel-Based and Spherical Cauchy Distributions

This paper introduces circlus, an R package designed for clustering circular and spherical data using Poisson kernel-based (PKB) distributions and spherical Cauchy distributions. The package leverages the general framework for Expectation-Maximization (EM) estimation implemented by package flexmix and provides model drivers for estimating PKB and spherical Cauchy distributions in the components. The drivers implement two approaches for the M-step. The first is a direct maximization approach implemented in C++ via Rcpp, while the second incorporates covariates by solving the M-step using neural networks with the torch package. The package is particularly suited for highdimensional clustering tasks, such as text embeddings on a spherical space, and supportsmodels both with and without covariates. As a case study, we apply circlus to cluster the abstracts of papers co-authored by Fritz Leisch and demonstrate the use with and without the inclusion of co-author count as a covariate.