On the Impact of Post-clustering Phase in Multi-way Spectral Partitioning

Spectral clustering is one of the most popular modern graph clustering techniques in machine learning. By using the eigenvalue analysis, spectral methods partition the given set of points into number of disjoint groups. Spectral methods are very useful in determining non-convex shaped clusters, identifying such clusters is not trivial for many traditional clustering methods including hierarchical and partitional methods. Spectral clustering may be carried out either as recursive bi-partitioning using fiedler vector (second eigenvector) or as muti-way partitioning using first k eigenvectors, where k is the number of clusters. Although spectral methods are widely discussed, there has been a little attention on which post-clustering algorithm (for eg. K-means) should be used in multi-way spectral partitioning. This motivated us to carry out an experimental study on the influence of post-clustering phase in spectral methods. We consider three clustering algorithms namely K-means, average linkage and FCM. Our study shows that the results of multi-way spectral partitioning strongly depends on the post-clustering algorithm.