Clustering via adaptive and locality-constrained graph learning and unsupervised ELM

In this paper an effective graph learning method is proposed for clustering based on adaptive graph regularizations. Many graph learning methods focus on optimizing a global constraint on sparsity, low-rankness or weighted pair-wise distances, but they often fail to consider local connectivities. We demonstrate the importance of locality by generalizing the Locality-constrained Linear Coding (LLC) for unsupervised learning. Each data sample is expressed as a representation of its nearest neighbors, which naturally leads to a combination of distance regularized features and a Locally Linear Embedding (LLE) decomposition. The representation enforces a locally sparse connection on the data graph that exhibits high discrimination power and is easy to optimize. To improve the learned graph structure and incorporate cluster information, a rank constraint is further imposed on the Laplacian matrix of the data graph so that the connected components match the class number. The obtained representations are smoothed via manifold regularizations on a predefined graph which serves as a prior for graph learning. Finally, we utilize unsupervised Extreme Learning Machine (US-ELM) to learn a flexible and discriminative data embedding. Extensive evaluations show that the proposed algorithm outperforms graph learning counterpart methods on a wide range of benchmark datasets