Robust Subspace Clustering for Multi-View Data by Exploiting Correlation Consensus

More often than not, a multimedia data described by multiple features, such as color and shape features, can be naturally decomposed of multi-views. Since multi-views provide complementary information to each other, great endeavors have been dedicated by leveraging multiple views instead of a single view to achieve the better clustering performance. To effectively exploit data correlation consensus among multi-views, in this paper, we study subspace clustering for multi-view data while keeping individual views well encapsulated. For characterizing data correlations, we generate a similarity matrix in a way that high affinity values are assigned to data objects within the same subspace across views, while the correlations among data objects from distinct subspaces are minimized. Before generating this matrix, however, we should consider that multi-view data in practice might be corrupted by noise. The corrupted data will significantly downgrade clustering results. We first present a novel objective function coupled with an angular based regularizer. By minimizing this function, multiple sparse vectors are obtained for each data object as its multiple representations. In fact, these sparse vectors result from reaching data correlation consensus on all views. For tackling noise corruption, we present a sparsity-based approach that refines the angular-based data correlation. Using this approach, a more ideal data similarity matrix is generated for multi-view data. Spectral clustering is then applied to the similarity matrix to obtain the final subspace clustering. Extensive experiments have been conducted to validate the effectiveness of our proposed approach.