Cancer progression is often driven by an accumulation of genetic changes but also accompanied by increasing genomic instability. These processes lead to a complicated landscape of copy number alterations (CNAs) within individual tumors and great diversity across tumor samples. High resolution array-based comparative genomic hybridization (aCGH) is being used to profile CNAs of ever larger tumor collections, and better computational methods for processing these data sets and identifying potential driver CNAs are needed. Typical studies of aCGH data sets take a pipeline approach, starting with segmentation of profiles, calls of gains and losses, and finally determination of frequent CNAs across samples. A drawback of pipelines is that choices at each step may produce different results, and biases are propagated forward. We present a mathematically robust new method that exploits probe-level correlations in aCGH data to discover subsets of samples that display common CNAs. Our algorithm is related to recent work on maximum-margin clustering. It does not require pre-segmentation of the data and also provides grouping of recurrent CNAs into clusters. We tested our approach on a large cohort of glioblastoma aCGH samples from The Cancer Genome Atlas and recovered almost all CNAs reported in the initial study. We also found additional significant CNAs missed by the original analysis but supported by earlier studies, and we identified significant correlations between CNAs.