  Learning multi-view data is an emerging problem in machine learning research,
and nonnegative matrix factorization (NMF) is a popular
dimensionality-reduction method for integrating information from multiple
views. These views often provide not only consensus but also complementary
information. However, most multi-view NMF algorithms assign equal weight to
each view or tune the weight via line search empirically, which can be
infeasible without any prior knowledge of the views or computationally
expensive. In this paper, we propose a weighted multi-view NMF (WM-NMF)
algorithm. In particular, we aim to address the critical technical gap, which
is to learn both view-specific weight and observation-specific reconstruction
weight to quantify each view's information content. The introduced weighting
scheme can alleviate unnecessary views' adverse effects and enlarge the
positive effects of the important views by assigning smaller and larger
weights, respectively. Experimental results confirm the effectiveness and
advantages of the proposed algorithm in terms of achieving better clustering
performance and dealing with the noisy data compared to the existing
algorithms.
