  Biclustering is widely used in different kinds of fields including gene
information analysis, text mining, and recommendation system by effectively
discovering the local correlation between samples and features. However, many
biclustering algorithms will collapse when facing heavy-tailed data. In this
paper, we propose a robust version of convex biclustering algorithm with Huber
loss. Yet, the newly introduced robustification parameter brings an extra
burden to selecting the optimal parameters. Therefore, we propose a tuning-free
method for automatically selecting the optimal robustification parameter with
high efficiency. The simulation study demonstrates the more fabulous
performance of our proposed method than traditional biclustering methods when
encountering heavy-tailed noise. A real-life biomedical application is also
presented. The R package RcvxBiclustr is available at
https://github.com/YifanChen3/RcvxBiclustr.
