Robust Group Fused Lasso for Multisample CNV Detection under Uncertainty

One of the most important needs in the post-genome era is providing the researchers with reliable and efficient computational tools to extract and analyze this huge amount of biological data, in which DNA copy number variation (CNV) is a vitally important one. Array-based comparative genomic hybridization (aCGH) is a common approach in order to detect CNVs. Most of methods for this purpose were proposed for one-dimensional profile. However, slightly this focus has moved from one- to multi-dimensional signals. In addition, since contamination of these profiles with noise is always an issue, it is highly important to have a robust method for analyzing multisample aCGH data. In this paper, we propose Robust Grouped Fused Lasso (RGFL) which utilizes the Robust Group Total Variations (RGTV). Instead of l2;1 norm, the l1-l2 M-estimator is used which is more robust in dealing with non-Gaussian noise and high corruption. More importantly, Correntropy (Welsch M-estimator) is also applied for fitting error. Extensive experiments indicate that the proposed method outperforms the state-of-the art algorithms and techniques under a wide range of scenarios with diverse noises.

Mat-aCGH: a Matlab toolbox for simultaneous multisample aCGH data analysis and visualization

Mat-aCGH is an application toolbox for analysis and visualization of microarray-comparative genomic hybridization (array-CGH or aCGH) data which is based on Matlab. Full process of aCGH analysis, from denoising of the raw data to the visualization of the desired results, can be obtained via Mat-aCGH straight-forwardly. The main advantage of this toolbox is that it is collection of recent well-known statistical and information theoretic methods and algorithms for analyzing aCGH data. More importantly, the proposed toolbox is developed for multisample analysis which is one of the current challenges in this area. Mat-aCGH is convenient to apply for any format of data, robust against diverse noise and provides the users with valuable information in the form of diagrams and metrics. Therefore, it eliminates the needs of another software or package for multisample aCGH analysis.

Alternating Proximal Regularized Dictionary Learning

We present an algorithm for dictionary learning that is based on the alternating proximal algorithm studied by Attouch, Bolte, Redont, and Soubeyran ( 2010 ), coupled with a reliable and efficient dual algorithm for computation of the related proximity operators. This algorithm is suitable for a general dictionary learning model composed of a Bregman-type data fit term that accounts for the goodness of the representation and several convex penalization terms on the coefficients and atoms, explaining the prior knowledge at hand. As Attouch et al. recently proved, an alternating proximal scheme ensures better convergence properties than the simpler alternating minimization. We take care of the issue of inexactness in the computation of the involved proximity operators, giving a sound stopping criterion for the dual inner algorithm, which keeps under control the related errors, unavoidable for such a complex penalty terms, providing ultimately an overall effective procedure. Thanks to the generality of the proposed framework, we give an application in the context of genome-wide data understanding, revising the model proposed by Nowak, Hastie, Pollack, and Tibshirani ( 2011 ). The aim is to extract latent features (atoms) and perform segmentation on array-based comparative genomic hybridization (aCGH) data. We improve several important aspects that increase the quality and interpretability of the results. We show the effectiveness of the proposed model with two experiments on synthetic data, which highlight the enhancements over the original model.