Data sets in the real world are often complex and to some degree hierarchical, with groups and subgroups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these data sets is an important task that has many practical applications. To address this challenge, we present a general method for building relational data trees by exploiting the learning dynamics of the restricted Boltzmann machine. 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 data set and on three different real-world data sets (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.

• Received 16 March 2023
• Revised 19 May 2023
• Accepted 9 June 2023

DOI:https://doi.org/10.1103/PhysRevE.108.014110