Learning interpretable shared space via rank constraint for multi-view clustering

Multi-view clustering aims to assign appropriate labels for multiple views data in an unsupervised manner, which explores the underlying clustering structures shared by multi-view data. Currently, multi-view data is commonly collected from various feature spaces with different properties or distributions. Existing methods mainly utilize the original features to reconstruct the low-dimensional representation of all views, which fail to take the latent relationship and complementarity from multiple views in a unified space into consideration. Therefore, it is urgent to explore a unified space from multi-view ensemble to address the distribution differences between views. In light of this, we learn an interpretable shared space via rank constraint for multi-view clustering (SSRC), which directly reconstructs multi-view data into shared space to explore the underlying complementarity and low-dimensional representation from multiple views. Specifically, SSRC embeds the low-dimensional representation into a reproducing kernel Hilbert space to learn the similarity matrix, which ensures the high correlation between the shared similarity matrix and low-dimensional representation. Furthermore, the rank constraint is imposed on the Laplacian matrix so that the connected component of the similarity matrix is equal to the number of clusters. It can directly obtain the final clustering results in a unified framework through regularization constraints. Then, an ADMM based optimization scheme is devised to seek the optimal solution efficiently. Experiments on 6 benchmark multi-view datasets corroborate that our approach outperforms the state-of-the-art methods.