Fast approximate spectral clustering is a general framework we proposed recently for the spectral clustering of large datasets. The aim is to preserve the virtue of spectral clustering yet being able to meet the scability challenge of emerging data mining tasks. It grows out of our work on the perturbation analysis of spectral clustering  as well as extensive empirical studies. The main idea is to perform a distortion minimizing local transformation on the data to get a small number of representative points on which the cluster membership of all data points can be derived. There are three steps involved:
Since the distortion minimizing local transformation can be computed with fast procedures while the expensive spectral clustering is only performed on the representative points, large speedup can be achieved. Our theory predicts that if the distortion resulted from the data "compression" is small, then algorithms implemented within our framework will incur very little loss in clustering "accuracy".
Currently we have two implementations for distortion minimizing local transformation, one based on K-means clustering and the other on random projection trees. These two are chosen for their favorable empirical computational efficiency and the simplicity of their implementation. Evidently other approaches can be adopted if the resulting distortion can be made small. For more details on the general framework, please refer to .