Structured Graph Reconstruction for Scalable Clustering

Spectral clustering is a quite simple but effective method for solving graph clustering problem. It projects the original data points into a lower dimensional space with spectral embedding, and then relies on an algorithm to obtain the cluster labels. Since it involves eigendecomposition of the graph Laplacian matrix for embedding, spectral clustering has high time complexity and is not able to process large scale data. The performance of spectral clustering is also limited by a post-processing algorithm such as kmeans. To tackle the two issues, we propose a method called Orthogonal and Nonnegative Graph Reconstruction (ONGR) for large scale clustering. The two constraints serve as a structure constraint with which the graph reconstructed by the indicator matrix is structured. The proposed method has linear time complexity with respect to the data size that it mainly needs to implicitly construct a graph and iteratively perform economical singular value decomposition for a small size matrix. Moreover, the interpretability of the indicator matrix is offered due to the nonnegative constraint, and thus our method can provide the cluster labels with no post-processing. The experiments on benchmark datasets show the effectiveness of the proposed scalable clustering method.