  Nowadays, multi-view clustering has attracted more and more attention. To
date, almost all the previous studies assume that views are complete. However,
in reality, it is often the case that each view may contain some missing
instances. Such incompleteness makes it impossible to directly use traditional
multi-view clustering methods. In this paper, we propose a Doubly Aligned
Incomplete Multi-view Clustering algorithm (DAIMC) based on weighted
semi-nonnegative matrix factorization (semi-NMF). Specifically, on the one
hand, DAIMC utilizes the given instance alignment information to learn a common
latent feature matrix for all the views. On the other hand, DAIMC establishes a
consensus basis matrix with the help of $L_{2,1}$-Norm regularized regression
for reducing the influence of missing instances. Consequently, compared with
existing methods, besides inheriting the strength of semi-NMF with ability to
handle negative entries, DAIMC has two unique advantages: 1) solving the
incomplete view problem by introducing a respective weight matrix for each
view, making it able to easily adapt to the case with more than two views; 2)
reducing the influence of view incompleteness on clustering by enforcing the
basis matrices of individual views being aligned with the help of regression.
Experiments on four real-world datasets demonstrate its advantages.
