# Optimal interval clustering: Application to Bregman clustering and statistical mixture learning

arXiv: https://arxiv.org/abs/1403.2485 · HTML: https://mlsanity.com/paper/1403.2485/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2014.

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

- [Addressing Negative Transfer in Diffusion Models](https://mlsanity.com/paper/2306.00354/) (2023)
- [Minimum Distortion Quantization with Specified Output Distribution](https://mlsanity.com/paper/2606.10458/) (2026)
- [Spectral partitioning for k-block averaging kernels of finite Markov chains](https://mlsanity.com/paper/2608.21466/) (2026)

## Abstract (arXiv)

We present a generic dynamic programming method to compute the optimal clustering of n scalar elements into k pairwise disjoint intervals. This case includes 1D Euclidean k-means, k-medoids, k-medians, k-centers, etc. We extend the method to incorporate cluster size constraints and show how to choose the appropriate k by model selection. Finally, we illustrate and refine the method on two case studies: Bregman clustering and statistical mixture learning maximizing the complete likelihood.