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