Spectral Clustering Based on k-Nearest Neighbor Graph

Finding clusters in data is a challenging task when the clusters differ widely in shapes, sizes, and densities. We present a novel spectral algorithm Speclus with a similarity measure based on modified mutual nearest neighbor graph. The resulting affinity matrix reflex the true structure of data. Its eigenvectors, that do not change their sign, are used for clustering data. The algorithm requires only one parameter - a number of nearest neighbors, which can be quite easily established. Its performance on both artificial and real data sets is competitive to other solutions.