Comparing dimensionality reduction methods for local structural identification in colloidal systems

Quantifying local structures in self-assembled systems is a central challenge in soft matter and materials science. When no \emph{a priori} knowledge of the relevant structures is available, traditional order parameters often fall short. Unsupervised machine learning provides a convenient route to autonomously uncover structural motifs directly from particle configurations. In this work, we systematically compare three popular dimensionality reduction techniques; Principal Component Analysis (PCA), Autoencoders (AE), and Uniform Manifold Approximation and Projection (UMAP), for classifying local environments in self-assembled systems. We first apply these methods to fluid and crystal configurations of hard and charged spheres. Thereafter, we apply it to an icosahedral arrangement of spheres that self-assembled in spherical confinement, both from simulations as well as from experiments. We demonstrate that UMAP consistently outperforms the other methods in capturing complex structural features, offering a robust tool for structural classification without supervision.