Spectral clustering with discriminant cuts

Recently, many k-way spectral clustering algorithms have been proposed, satisfying one or both of the following requirements: between-cluster similarities are minimized and within-cluster similarities are maximized. In this paper, a novel graph-based spectral clustering algorithm called discriminant cut (Dcut) is proposed, which first builds the affinity matrix of a weighted graph and normalizes it with the corresponding regularized Laplacian matrix, then partitions the vertices into k parts. Dcut has several advantages. First, it is derived from graph partition and has a straightforward geometrical explanation. Second, it emphasizes the above requirements simultaneously. Besides, it is computationally feasible because the NP-hard intractable graph cut problem can be relaxed into a mild eigenvalue decomposition problem. Toy-data and real-data experimental results show that Dcut is pronounced comparing with other spectral clustering methods.