Convex clustering has recently gained popularity due to its attractive theoretical and computational properties. Though it confers many advantages over traditional clustering methods, its merits become limited in the face of high-dimensional data due to numerical instability. To address these issues, biconvex clustering has been proposed recently to simultaneously optimize the feature weights as well as the centroids. In the biclustering problem, we seek to simultaneously group observations and features. For high-throughput bioinformatics data, we often also wish to perform feature selection. In this talk, we propose a novel biconvex algorithm to tackle the biclustering problem while simultaneously performing feature selection. Called `biconvex biclustering', the proposed method performs by selecting proper subsets in both the groups as well as the features throughout the clustering task. We demonstrate our method’s utility for exploring single cell RNA sequencing data.