# Unsupervised hierarchical clustering using the learning dynamics of RBMs

arXiv: https://arxiv.org/abs/2302.01851 · HTML: https://mlsanity.com/paper/2302.01851/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Restricted Boltzmann Machine, recent advances and mean-field theory](https://mlsanity.com/paper/2011.11307/) (2020)
- [Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2105.13889/) (2021)
- [Thermodynamics of Restricted Boltzmann Machines and related learning dynamics](https://mlsanity.com/paper/1803.01960/) (2018)
- [Emergence of Compositional Representations in Restricted Boltzmann Machines](https://mlsanity.com/paper/1611.06759/) (2016)
- [Explaining the effects of non-convergent sampling in the training of Energy-Based Models](https://mlsanity.com/paper/2301.09428/) (2023)
- [Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling](https://mlsanity.com/paper/2206.01310/) (2022)
- [A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines](https://mlsanity.com/paper/1702.03260/) (2017)
- [Cascade of Phase Transitions for Multi-Scale Clustering](https://mlsanity.com/paper/2010.07955/) (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)
- [Interpretable machine learning of amino acid patterns in proteins: a statistical ensemble approach](https://mlsanity.com/paper/2303.15228/) (2023)
- [Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplings](https://mlsanity.com/paper/2507.05147/) (2025)

## Abstract (arXiv)

Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these datasets is an important task that has many practical applications. To address this challenge, we present a new and general method for building relational data trees by exploiting the learning dynamics of the Restricted Boltzmann Machine (RBM). Our method is based on the mean-field approach, derived from the Plefka expansion, and developed in the context of disordered systems. It is designed to be easily interpretable. We tested our method in an artificially created hierarchical dataset and on three different real-world datasets (images of digits, mutations in the human genome, and a homologous family of proteins). The method is able to automatically identify the hierarchical structure of the data. This could be useful in the study of homologous protein sequences, where the relationships between proteins are critical for understanding their function and evolution.