# Cascade of Phase Transitions for Multi-Scale Clustering

arXiv: https://arxiv.org/abs/2010.07955 · HTML: https://mlsanity.com/paper/2010.07955/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Cascade of phase transitions in the training of Energy-based models](https://mlsanity.com/paper/2405.14689/) (2024)
- [Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physics](https://mlsanity.com/paper/2307.06797/) (2023)
- [Unsupervised hierarchical clustering using the learning dynamics of RBMs](https://mlsanity.com/paper/2302.01851/) (2023)
- [Regularization of Mixture Models for Robust Principal Graph Learning](https://mlsanity.com/paper/2106.09035/) (2021)

## Abstract (arXiv)

We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularised Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.