# Bregman Power k-Means for Clustering Exponential Family Data

arXiv: https://arxiv.org/abs/2206.10860 · HTML: https://mlsanity.com/paper/2206.10860/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [The Information Geometry of Mirror Descent](https://mlsanity.com/paper/1310.7780/) (2013)
- [On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient](https://mlsanity.com/paper/1803.06573/) (2018)
- [Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning](https://mlsanity.com/paper/1402.4419/) (2014)
- [Statistical Properties of Convex Clustering](https://mlsanity.com/paper/1503.08340/) (2015)
- [Moment-based Uniform Deviation Bounds for k-means and Friends](https://mlsanity.com/paper/1311.1903/) (2013)
- [Uniform Concentration Bounds toward a Unified Framework for Robust Clustering](https://mlsanity.com/paper/2110.14148/) (2021)
- [Robust Bregman Clustering](https://mlsanity.com/paper/1812.04356/) (2018)
- [Bayesian Distance Clustering](https://mlsanity.com/paper/1810.08537/) (2018)

## Built on by (most cited first, 3 of 3)

- [Clustering above Exponential Families with Tempered Exponential Measures](https://mlsanity.com/paper/2211.02765/) (2022)
- [Variational Representations of Annealing Paths: Bregman Information under Monotonic Embedding](https://mlsanity.com/paper/2209.07481/) (2022)
- [DBGSA: A Novel Data Adaptive Bregman Clustering Algorithm](https://mlsanity.com/paper/2307.14375/) (2023)

## Abstract (arXiv)

Recent progress in center-based clustering algorithms combats poor local minima by implicit annealing, using a family of generalized means. These methods are variations of Lloyd's celebrated k-means algorithm, and are most appropriate for spherical clusters such as those arising from Gaussian data. In this paper, we bridge these algorithmic advances to classical work on hard clustering under Bregman divergences, which enjoy a bijection to exponential family distributions and are thus well-suited for clustering objects arising from a breadth of data generating mechanisms. The elegant properties of Bregman divergences allow us to maintain closed form updates in a simple and transparent algorithm, and moreover lead to new theoretical arguments for establishing finite sample bounds that relax the bounded support assumption made in the existing state of the art. Additionally, we consider thorough empirical analyses on simulated experiments and a case study on rainfall data, finding that the proposed method outperforms existing peer methods in a variety of non-Gaussian data settings.