Improved Normalized Cut for Multi-View Clustering

Spectral clustering (SC) algorithms have been successful in discovering meaningful patterns since they can group arbitrarily shaped data structures. Traditional SC approaches typically consist of two sequential stages, i.e., performing spectral decomposition of an affinity matrix and then rounding the relaxed continuous clustering result into a binary indicator matrix. However, such a two-stage process could make the obtained binary indicator matrix severely deviate from the ground true one. This is because the former step is not devoted to achieving an optimal clustering result. To alleviate this issue, this paper presents a general joint framework to simultaneously learn the optimal continuous and binary indicator matrices for multi-view clustering, which also has the ability to tackle the conventional single-view case. Specially, we provide theoretical proof for the proposed method. Furthermore, an effective alternate updating algorithm is developed to optimize the corresponding complex objective. A number of empirical results on different benchmark datasets demonstrate that the proposed method outperforms several state-of-the-arts in terms of six clustering metrics.