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Abstract   Biclustering is a generalization of clustering used to identify simultaneous grouping patterns in observations (rows) and features (columns) of a data matrix. Recently, the biclustering task has been formulated as a convex optimization problem. While this convex recasting of the problem has attractive properties, existing algorithms do not scale well. To address this problem and make convex biclustering a practical tool for analyzing larger data, we propose an implementation of fast convex biclustering called COBRAC to reduce the computing time by iteratively compressing problem size along the solution path. We apply COBRAC to several gene expression datasets to demonstrate its effectiveness and efficiency. Besides the standalone version for COBRAC, we also developed a related online web server for online calculation and visualization of the downloadable interactive results. Availability The source code and test data are available at https://github.com/haidyi/cvxbiclustr or https://zenodo.org/record/4620218. The web server is available at https://cvxbiclustr.ericchi.com. Supplementary information Supplementary data are available at Bioinformatics online. 

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting. Our unsupervised approach consists of three components. We first solve a family of optimization problems to estimate a complete matrix at multiple scales of smoothness. We then use this collection of smooth matrix estimates to compute pairwise distances on the rows and columns based on a new multi-scale metric that implicitly introduces a coupling between the rows and the columns. Finally, we construct row and column representations from these multi- scale metrics. We demonstrate that our approach outperforms competing methods in both data visualization and clustering.