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Several modern genomic technologies, such as DNA-Methylation arrays, measurespatially registered probes that number in the hundreds of thousands acrossmultiplechromosomes. The measured probes are by themselves less interestingscientifically; instead scientists seek to discover biologically interpretablegenomic regions comprised of contiguous groups of probes which may act asbiomarkers of disease or serve as a dimension-reducing pre-processing step fordownstream analyses. In this paper, we introduce an unsupervised featurelearning technique which maps technological units (probes) to biological units(genomic regions) that are common across all subjects. We use ideas from fusionpenalties and convex clustering to introduce a method for Spatial ConvexClustering, or SpaCC. Our method is specifically tailored to detectingmulti-subject regions of methylation, but we also test our approach on thewell-studied problem of detecting segments of copy number variation. Weformulate our method as a convex optimization problem, develop a massivelyparallelizable algorithm to find its solution, and introduce automatedapproaches for handling missing values and determining tuning parameters.Through simulation studies based on real methylation and copy number variationdata, we show that SpaCC exhibits significant performance gains relative toexisting methods. Finally, we illustrate SpaCC's advantages as a pre-processingtechnique that reduces large-scale genomics data into a smaller number ofgenomic regions through several cancer epigenetics case studies on subtypediscovery, network estimation, and epigenetic-wide association.

Genomic Region Detection via Spatial Convex Clustering