Locally discriminative spectral clustering with composite manifold

A large number of data are generated in many real-world applications, e.g., photos of albums in social networks. Discovering meaningful patterns from them is desirable and still remains a big challenge. To this end, spectral clustering has established itself as a very useful tool for data analysis. It considers the manifold geometrical structure of the data and desires to estimate the intrinsic manifold. However, there exists no principled way for estimating such manifold. Thus, the clustering performance might even degrade seriously when the estimated manifold deviates far from the intrinsic manifold. To address this problem, we propose to employ composite manifold to approximate the intrinsic manifold as much as possible. This composite manifold is derived from a convex combination of some pre-given candidate manifolds in a convex hull. The diversity nature of these manifolds provides richer structure information, which is helpful to maximally estimate the intrinsic manifold. Besides, traditional spectral clustering neglects the discriminant information latent in the data space, so we incorporate the locally discriminative structure into the partition matrix by explicitly using local linear regression, for better clustering. Therefore, in this paper, we present an integrated clustering approach named Spectral Clustering via Composite manifold and Local discriminant learning, referred to as SCCL for short, which addresses the aforementioned two problems. To optimize the objective function, an alternating optimization framework is adopted to derive both the cluster membership matrix and the composite manifold coefficient. Extensive experiments are carried out on several real-world databases. Results have validated the efficacy of the proposed algorithm.