  Several modern genomic technologies, such as DNA-Methylation arrays, measure
spatially registered probes that number in the hundreds of thousands across
multiplechromosomes. The measured probes are by themselves less interesting
scientifically; instead scientists seek to discover biologically interpretable
genomic regions comprised of contiguous groups of probes which may act as
biomarkers of disease or serve as a dimension-reducing pre-processing step for
downstream analyses. In this paper, we introduce an unsupervised feature
learning technique which maps technological units (probes) to biological units
(genomic regions) that are common across all subjects. We use ideas from fusion
penalties and convex clustering to introduce a method for Spatial Convex
Clustering, or SpaCC. Our method is specifically tailored to detecting
multi-subject regions of methylation, but we also test our approach on the
well-studied problem of detecting segments of copy number variation. We
formulate our method as a convex optimization problem, develop a massively
parallelizable algorithm to find its solution, and introduce automated
approaches for handling missing values and determining tuning parameters.
Through simulation studies based on real methylation and copy number variation
data, we show that SpaCC exhibits significant performance gains relative to
existing methods. Finally, we illustrate SpaCC's advantages as a pre-processing
technique that reduces large-scale genomics data into a smaller number of
genomic regions through several cancer epigenetics case studies on subtype
discovery, network estimation, and epigenetic-wide association.
