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Discriminant cuts for data clustering and analysis

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 since it relaxes the intractable graph cut problem into a mild eigenvalue decomposition problem. Toy-data and real-data experiments show that Dcut is pronounced comparing with other spectral clustering methods.