Robust multi-view subspace clustering with missing data by aligning nonlinear manifolds

We study the clustering of high-dimensional multi-view data with randomly missing features. Most existing methods employ the low-dimensional subspace assumption, which ignore the fact that data may reside close to multiple nonlinear manifolds, let alone nonlinear relationships between multiple views. Usually, they give multiple views equal weights, making them sensitive to redundant and noisy views. In most cases, completion and clustering are treated as separate processes, preventing them from reinforcing each other. To address these problems, we propose a Robust Nonlinear Multi-view Subspace Clustering and Completion (RNMSCC) algorithm, which projects multi-view data to high-dimensional feature spaces and integrates data completion and clustering therein. For data completion, the minimum intrinsic rank of sub-manifold is promoted while for clustering, an adaptive weighting technique is developed to automatically adjust the importance of multiple views in self-expression. Integrated with manifold alignment, redundant and noisy views are selected out, thus the learning process enjoys robust mutual reinforcement. The optimization problem is solved by an alternating algorithm. Experiments on real-world datasets validate its performance advantage over state-of-the-art methods. •Unifies clustering and imputation of nonlinear manifold data with missing at random.•A nonlinear dependence measure facilitates the alignment of nonlinear manifolds.•An adaptive weighting technique enhances the algorithm’s robustness against noise.