Understanding deep crustal structure can provide us with insights into tectonic processes and how they affect the geological record. The deep crustal structure can be studied using a variety of seismological techniques such as receiver function analysis, and surface and body wave tomography. Using models of crustal structure derived from these methods, it is possible to delineate tectonic boundaries and regions that have been affected by similar processes. However, often velocity models are grouped in a somewhat subjective manner, potentially meaning that some geological insight may be missed. Cluster analysis, based on unsupervised machine learning, can be used to more objectively group together similar velocity profiles and, thus, put additional constraints on the deep crustal structure. In this study, we apply hierarchical agglomerative clustering to the shear wave velocity profiles obtained by Gilligan et. al. (2016) from the joint inversion of receiver functions and surface wave dispersion data at 59 sites surrounding Hudson Bay. This location provides an ideal natural laboratory to study Precambrian tectonic processes, including the 1.8Ga Trans-Hudson Orogen. We use Ward linkage to define the distance between clusters, as it gives the most physically realistic results, and after testing the number of clusters from 2 to 10, we find there are 5 main stable clusters of velocity models. We then compare our results with different inversion parameters, clustering schemes (K-means and GMM), as well as results obtained for profiles from receiver functions in different azimuths and found that, overall, the clustering results are consistent. The clusters that form correlate well with the surface geology, crustal thickness, regional tectonics, and previous geophysical studies concentrated on specific regions. The profiles in the Archean domains (Rae, Hearne, and Superior) were clearly distinguished from the profiles in the Proterozoic domains (Southern Baffin Island and Ungava Peninsula). Further, the crust of Melville Peninsula is found to be in the same cluster as the crust of the western coast of Ungava Peninsula, suggesting a similar crustal structure. Our study shows the promising use of unsupervised machine learning in interpreting deep crustal structures to gain new geological insights.