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Multi-view unsupervised feature selection (MUFS) has been demonstrated as aneffective technique to reduce the dimensionality of multi-view unlabeled data.The existing methods assume that all of views are complete. However, multi-viewdata are usually incomplete, i.e., a part of instances are presented on someviews but not all views. Besides, learning the complete similarity graph, as animportant promising technology in existing MUFS methods, cannot achieve due tothe missing views. In this paper, we propose a complementary and consensuslearning-based incomplete multi-view unsupervised feature selection method(C$^{2}$IMUFS) to address the aforementioned issues. Concretely, C$^{2}$IMUFSintegrates feature selection into an extended weighted non-negative matrixfactorization model equipped with adaptive learning of view-weights and asparse $\ell_{2,p}$-norm, which can offer better adaptability and flexibility.By the sparse linear combinations of multiple similarity matrices derived fromdifferent views, a complementary learning-guided similarity matrixreconstruction model is presented to obtain the complete similarity graph ineach view. Furthermore, C$^{2}$IMUFS learns a consensus clustering indicatormatrix across different views and embeds it into a spectral graph term topreserve the local geometric structure. Comprehensive experimental results onreal-world datasets demonstrate the effectiveness of C$^{2}$IMUFS compared withstate-of-the-art methods.

C$^{2}$IMUFS: Complementary and Consensus Learning-based Incomplete Multi-view Unsupervised Feature Selection