Clustering with Adaptive Manifold Structure Learning

Construction of a reliable similarity matrix is fundamental for graph-based clustering methods. However, most of the current work is built upon some simple manifold structure, whereas limited work has been conducted on nonlinear data sets where data reside in a union of manifolds rather than a union of subspaces. Therefore, we construct a similarity graph to capture both global and local manifold structures of the input data set. The global structure is exploited based on the self-expressive property of data in an implicit feature space using kernel methods. Since the similarity graph computation is independent of the subsequent clustering, the final results may be far from optimal. To overcome this limitation, we simultaneously learn similarity graph and clustering structure in a principled way. Experimental studies demonstrate that our proposed algorithms deliver consistently superior results to other state-of-the-art algorithms.