Regularized Spectral Clustering With Entropy Perturbation

Spectral clustering is a popular clustering method because it gives a natural way to reduce the dimensionality of data using eigenvectors. It is well known that the performance of spectral clustering could be improved via regularization. Nevertheless, it is hard to cope with the different cases by only one constant regularization parameter. To solve such a problem, a novel regularized spectral clustering method is proposed. Specifically, two modules are integrated in the proposed method. First, under matrix perturbation analysis, we prove that the entropy can be used as a rank score function to reveal the informative eigenvector, and the eigenvector corresponding to the minimal entropy will be the regularization to regularize the data matrix instead of a constant regularization parameter. Second, in order to ensure the perturbation on eigenspace is within the effective range, a perturbation boundary on eigenvectors is given. Numerical results showed that our proposal has superior performance than spectral clustering and k-means algorithm.