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