# Spherical Wards clustering and generalized Voronoi diagrams

## TL;DR

This paper introduces a novel spherical Gaussian-based clustering method that operates in non-Euclidean spaces, automatically determines the number of clusters, and uses generalized Voronoi diagrams for visualization.

## Contribution

It combines spherical Cross-Entropy Clustering with a generalized Wards approach to handle arbitrary dissimilarity measures in non-Euclidean spaces.

## Key findings

- Automatically finds the optimal number of clusters.
- Supports scale-invariant, spherical clusters of arbitrary sizes.
- Uses generalized Voronoi diagrams for visualization.

## Abstract

Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning data sets with respect to arbitrary dissimilarity measure. The proposed method is a combination of spherical Cross-Entropy Clustering with a generalized Wards approach. The algorithm finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, it is scale invariant and allows for forming of spherically-shaped clusters of arbitrary sizes. In order to graphically represent and interpret the results the notion of Voronoi diagram was generalized to non Euclidean spaces and applied for introduced clustering method.