Convex Biclustering

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, identifying structure in high dimensional in genomic data motivates this work. In this context, biclustering enables us to identify subsets of genes that are co-expressed only within a subset of experimental conditions. We present a convex formulation of the biclustering problem that possesses a unique global minimizer and an iterative algorithm that is guaranteed to identify it. Our approach generates an entire solution path of possible biclusters as a single tuning regularization parameter is varied. We also introduce a data-driven method for selecting the number of biclusters through the regularization parameter.