  Clustering has long been a popular unsupervised learning approach to identify
groups of similar objects and discover patterns from unlabeled data in many
applications. Yet, coming up with meaningful interpretations of the estimated
clusters has often been challenging precisely due to its unsupervised nature.
Meanwhile, in many real-world scenarios, there are some noisy supervising
auxiliary variables, for instance, subjective diagnostic opinions, that are
related to the observed heterogeneity of the unlabeled data. By leveraging
information from both supervising auxiliary variables and unlabeled data, we
seek to uncover more scientifically interpretable group structures that may be
hidden by completely unsupervised analyses. In this work, we propose and
develop a new statistical pattern discovery method named Supervised Convex
Clustering (SCC) that borrows strength from both information sources and guides
towards finding more interpretable patterns via a joint convex fusion penalty.
We develop several extensions of SCC to integrate different types of
supervising auxiliary variables, to adjust for additional covariates, and to
find biclusters. We demonstrate the practical advantages of SCC through
simulations and a case study on Alzheimer's Disease genomics. Specifically, we
discover new candidate genes as well as new subtypes of Alzheimer's Disease
that can potentially lead to better understanding of the underlying genetic
mechanisms responsible for the observed heterogeneity of cognitive decline in
older adults.
