  Array-Based Comparative Genomic Hybridization (aCGH) is a method used to
search for genomic regions with copy numbers variations. For a given aCGH
profile, one challenge is to accurately segment it into regions of constant
copy number. Subjects sharing the same disease status, for example a type of
cancer, often have aCGH profiles with similar copy number variations, due to
duplications and deletions relevant to that particular disease. We introduce a
constrained optimization algorithm that jointly segments aCGH profiles of many
subjects. It simultaneously penalizes the amount of freedom the set of profiles
have to jump from one level of constant copy number to another, at genomic
locations known as breakpoints. We show that breakpoints shared by many
different profiles tend to be found first by the algorithm, even in the
presence of significant amounts of noise. The algorithm can be formulated as a
group LARS problem. We propose an extremely fast way to find the solution path,
i.e., a sequence of shared breakpoints in order of importance. For no extra
cost the algorithm smoothes all of the aCGH profiles into piecewise-constant
regions of equal copy number, giving low-dimensional versions of the original
data. These can be shown for all profiles on a single graph, allowing for
intuitive visual interpretation. Simulations and an implementation of the
algorithm on bladder cancer aCGH profiles are provided.
