# Joint segmentation of many aCGH profiles using fast group LARS

## TL;DR

This paper presents a fast, group LARS-based algorithm for jointly segmenting multiple aCGH profiles, effectively identifying shared breakpoints and smoothing data for better interpretation, especially useful in cancer research.

## Contribution

Introduces a novel constrained optimization algorithm for joint segmentation of many aCGH profiles, efficiently finding shared breakpoints using a fast group LARS approach.

## Key findings

- Shared breakpoints are identified first by the algorithm even with noise.
- The method provides a low-dimensional, smoothed representation of profiles.
- Application to bladder cancer data demonstrates practical utility.

## Abstract

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.