Galaxy Formation and Evolution via Phase-temporal Clustering with FuzzyCat $\circ$ AstroLink

We demonstrate how the composition of two unsupervised clustering algorithms, $\texttt{AstroLink}$ and $\texttt{FuzzyCat}$, makes for a powerful tool when studying galaxy formation and evolution. $\texttt{AstroLink}$ is a general-purpose astrophysical clustering algorithm built for extracting meaningful hierarchical structure from point-cloud data defined over any feature space, while $\texttt{FuzzyCat}$ is a generalised soft-clustering algorithm that propagates the dynamical effects of underlying data processes into a fuzzy hierarchy of stable fuzzy clusters. Their composition, $\texttt{FuzzyCat}$ $\circ$ $\texttt{AstroLink}$, can therefore identify a fuzzy hierarchy of astrophysically- and statistically-significant fuzzy clusters within any point-based data set whose representation is subject to changes caused by some underlying process. Furthermore, the pipeline achieves this without relying upon strong assumptions about the data, the change process, the number/importance of specific structure types, or much user input -- thereby making itself applicable to a wide range of fields in the physical sciences. We find that for the task of structurally decomposing simulated galaxies into their constituents, our context-agnostic approach has a substantial impact on the diversity and completeness of the structures extracted as well as on their relationship within the broader galactic structural hierarchy -- revealing dwarf galaxies, infalling groups, stellar streams (and their progenitors), stellar shells, galactic bulges, and star-forming regions.