Improving Spectral Clustering Using Spectrum-Preserving Node Aggregation

Spectral clustering is an important graph clustering technique. However, it suffers from a scalability problem due to the involved computationally expensive eigen-decomposition procedure and is highly sensitive to noisy nodes in the graph. In this work we solve the two problems simultaneously by using spectrum-preserving node aggregation to generate a nearly-noiseless concise representation of the data set. Specifically, we create a small set of spectral-representative pseudo-nodes based on spectral analysis. Then, standard spectral clustering algorithm is performed on the smaller node set. Finally, we map the clusters of pseudo nodes back to find the cluster memberships of the data points in the original data set. The proposed framework has a nearly-linear time complexity. Meanwhile, the clustering accuracy can be significantly improved. The experimental results show dramatically improved clustering performance when compared with state-of-the-art methods.