  AI-enabled precision medicine promises a transformational improvement in
healthcare outcomes by enabling data-driven personalized diagnosis, prognosis,
and treatment. However, the well-known "curse of dimensionality" and the
clustered structure of biomedical data together interact to present a joint
challenge in the high dimensional, limited observation precision medicine
regime. To overcome both issues simultaneously we propose a simple and scalable
approach to joint clustering and embedding that combines standard embedding
methods with a convex clustering penalty in a modular way. This novel,
cluster-aware embedding approach overcomes the complexity and limitations of
current joint embedding and clustering methods, which we show with
straightforward implementations of hierarchically clustered principal component
analysis (PCA), locally linear embedding (LLE), and canonical correlation
analysis (CCA). Through both numerical experiments and real-world examples, we
demonstrate that our approach outperforms traditional and contemporary
clustering methods on highly underdetermined problems (e.g., with just tens of
observations) as well as on large sample datasets. Importantly, our approach
does not require the user to choose the desired number of clusters, but instead
yields interpretable dendrograms of hierarchically clustered embeddings. Thus
our approach improves significantly on existing methods for identifying patient
subgroups in multiomics and neuroimaging data, enabling scalable and
interpretable biomarkers for precision medicine.
