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A well-rounded feature selection (FS) method should consider relevance, redundancy and complementarity of the features. Yet most existing FS methods focus on gene relevance to the cell types but neglect redundancy and complementarity, which undermines the cell clustering performance. We develop a novel computational method GeneClust to select feature genes for scRNA-seq cell clustering. GeneClust groups genes based on their expression profiles, then selects genes with the aim of maximizing relevance, minimizing redundancy and preserving complementarity. It can work as a plug-in tool for FS with any existing cell clustering method. Extensive benchmark results demonstrate that GeneClust significantly improve the clustering performance. Moreover, GeneClust can group cofunctional genes in biological process and pathway into clusters, thus providing a means of investigating gene interactions and identifying potential genes relevant to biological characteristics of the dataset. 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