A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in matrix-format set, which can provide results checkerboard-like pattern for visualization exploratory analysis wide array of domains. Multiple biclustering algorithms have been developed the past two decades, among convex guarantee global optimum by formulating as optimization problem. On other hand, application has not progressed parallel with algorithm techniques. For example, increasingly popular microbiome research under-applied possibly due to its compositional constraints each sample. In this manuscript, we propose new algorithm, called bi-ADMM, under general setups based on ADMM free extra smoothing steps visualize informative biclusters required existing algorithms. Furthermore, tailor it named biC-ADMM specifically tackle confronted data. The key step our methods utilize Sylvester Equation derive research. effectiveness proposed examined through variety numerical experiments application.