An Efficient Algorithm for Convex Biclustering

We consider biclustering that clusters both samples and features and propose efficient convex biclustering procedures. The convex biclustering algorithm (COBRA) procedure solves twice the standard convex clustering problem that contains a non-differentiable function optimization. We instead convert the original optimization problem to a differentiable one and improve another approach based on the augmented Lagrangian method (ALM). Our proposed method combines the basic procedures in the ALM with the accelerated gradient descent method (Nesterov’s accelerated gradient method), which can attain O(1/k2) convergence rate. It only uses first-order gradient information, and the efficiency is not influenced by the tuning parameter λ so much. This advantage allows users to quickly iterate among the various tuning parameters λ and explore the resulting changes in the biclustering solutions. The numerical experiments demonstrate that our proposed method has high accuracy and is much faster than the currently known algorithms, even for large-scale problems.

Bayesian sparse convex clustering via global-local shrinkage priors

Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $$L_1$$ L 1 norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering method based on the ideas of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normal distributions. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.

A Novel Convex Clustering Method for High-Dimensional Data Using Semiproximal ADMM

Clustering is an important ingredient of unsupervised learning; classical clustering methods include K-means clustering and hierarchical clustering. These methods may suffer from instability because of their tendency prone to sink into the local optimal solutions of the nonconvex optimization model. In this paper, we propose a new convex clustering method for high-dimensional data based on the sparse group lasso penalty, which can simultaneously group observations and eliminate noninformative features. In this method, the number of clusters can be learned from the data instead of being given in advance as a parameter. We theoretically prove that the proposed method has desirable statistical properties, including a finite sample error bound and feature screening consistency. Furthermore, the semiproximal alternating direction method of multipliers is designed to solve the sparse group lasso convex clustering model, and its convergence analysis is established without any conditions. Finally, the effectiveness of the proposed method is thoroughly demonstrated through simulated experiments and real applications.

GDASC: a GPU parallel-based web server for detecting hidden batch factors

Summary We developed GDASC, a web version of our former DASC algorithm implemented with GPU. It provides a user-friendly web interface for detecting batch factors. Based on the good performance of DASC algorithm, it is able to give the most accurate results. For two steps of DASC, data-adaptive shrinkage and semi-non-negative matrix factorization, we designed parallelization strategies facing convex clustering solution and decomposition process. It runs more than 50 times faster than the original version on the representative RNA sequencing quality control dataset. With its accuracy and high speed, this server will be a useful tool for batch effects analysis. Availability and implementation http://bioinfo.nankai.edu.cn/gdasc.php. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.