  Unsupervised machine learning methods are used to identify structural changes
using the melting point transition in classical molecular dynamics simulations
as an example application of the approach. Dimensionality reduction and
clustering methods are applied to instantaneous radial distributions of atomic
configurations from classical molecular dynamics simulations of metallic
systems over a large temperature range. Principal component analysis is used to
dramatically reduce the dimensionality of the feature space across the samples
using an orthogonal linear transformation that preserves the statistical
variance of the data under the condition that the new feature space is linearly
independent. From there, k-means clustering is used to partition the samples
into solid and liquid phases through a criterion motivated by the geometry of
the reduced feature space of the samples, allowing for an estimation of the
melting point transition. This pattern criterion is conceptually similar to how
humans interpret the data but with far greater throughput, as the shapes of the
radial distributions are different for each phase and easily distinguishable by
humans. The transition temperature estimates derived from this machine learning
approach produce comparable results to other methods on similarly small system
sizes. These results show that machine learning approaches can be applied to
structural changes in physical systems.
