Interpretable and unsupervised phase classification

Fully automated classification methods that provide direct physical insights into phase diagrams are of current interest. Interpretable, i.e., fully explainable, methods are desired for which we understand why they yield a given phase classification. Ideally, phase classification methods should also be unsupervised. That is, they should not require prior labeling or knowledge of the phases of matter to be characterized. Here, we demonstrate an unsupervised machine-learning method for phase classification, which is rendered interpretable via an analytical derivation of the functional relationship between its optimal predictions and the input data. Based on these findings, we propose and apply an alternative, physically-motivated, data-driven scheme, which relies on the difference between mean input features. This mean-based method does not rely on any predictive model and is thus computationally cheap and directly explainable. As an example, we consider the physically rich ground-state phase diagram of the spinless Falicov-Kimball model.

Automated summary

The current interest lies in fully automated classification methods that offer direct physical insights into phase diagrams. It is desired to have interpretable methods that can explain why they classify phases as they do, and ideally these methods should be unsupervised, not requiring prior labeling or knowledge of phases. An unsupervised machine-learning method for phase classification is demonstrated here, made interpretable through an analytical derivation of the functional relationship between its predictions and input data, showcasing a physically-motivated, mean-based approach that is computationally efficient and directly explainable.