Dual regularized multi-view non-negative matrix factorization for clustering

Abstract Many real-world datasets are described by multiple modalities or views, which can provide compatible and complementary information to each other. Synthesizing multi-view features for data representation can lead to more comprehensive data description, which may further allow us to find more effective solutions for multi-view data clustering. In this paper, a novel algorithm, called Dual-regularized Multi-view Non-negative Matrix Factorization (DMvNMF), is developed for multi-view data clustering, which is able to preserve the geometric structures of multi-view data in both the data space and the feature space. A parameter-free strategy is developed for constructing the data graph in the multi-view context. Firstly, the affinity graph is learned for each view adaptively by using the self-expressiveness property and the principle of sparsity, i.e., reconstructing each data instance by using a few most similar instances. Secondly, these affinity graphs for different views are linearly combined to generate the global data graph, where the combination weights (importance weights) are learned automatically and the views with better explanations for data reconstruction can get larger importance weights. The feature graph for each view is also constructed in a similar way and it is treated as the affinity graph. For model optimization, an iterative updating scheme is developed to support our DMvNMF algorithm and its convergence proof is also provided. Our experimental results on three real-world datasets have demonstrated the effectiveness of our DMvNMF algorithm for multi-view data clustering and it can significantly outperform other baseline methods.