Self-weighted multi-view clustering with soft capped norm

Real-world data sets are often comprised of multiple representations or modalities which provide different and complementary aspects of information. Multi-view clustering plays an indispensable role in analyzing multi-view data. In multi-view learning, one key step is assigning a reasonable weight to each view according to the view importance. Most existing work learn the weights by introducing a hyperparameter, which is undesired in practice. In this paper, our proposed model learns an optimal weight for each view automatically without introducing an additive parameter as previous methods do. Furthermore, to deal with different level noises and outliers, we propose to use 'soft' capped norm, which caps the residual of outliers as a constant value and provides a probability for certain data point being an outlier. An efficient updating algorithm is designed to solve our model and its convergence is also guaranteed theoretically. Extensive experimental results on several real-world data sets show that our proposed model outperforms state-of-the-art multi-view clustering algorithms.