Data sets containing multi-manifold structures are ubiquitous in real-world tasks, and effective grouping of such data is an important yet challenging problem. Though there were many studies on this problem, it is not clear on how to design principled methods for the grouping of multiple hybrid manifolds. In this paper, we show that spectral methods are potentially helpful for hybrid manifold clustering when the neighborhood graph is constructed to connect the neighboring samples from the same manifold. However, traditional algorithms which identify neighbors according to Euclidean distance will easily connect samples belonging to different manifolds. To handle this drawback, we propose a new criterion, i.e., local and structural consistency criterion, which considers the neighboring information as well as the structural information implied by the samples. Based on this criterion, we develop a simple yet effective algorithm, named Local and Structural Consistency (LSC), for clustering with multiple hybrid manifolds. Experiments show that LSC achieves promising performance.
['Yong Wang', 'Yuan Jiang', 'Yi Wu', 'Zhi-Hua Zhou']
Local and structural consistency for multi-manifold clustering