A new Kmeans clustering model and its generalization achieved by joint spectral embedding and rotation

The Kmeans clustering and spectral clustering are two popular clustering methods for grouping similar data points together according to their similarities. However, the performance of Kmeans clustering might be quite unstable due to the random initialization of the cluster centroids. Generally, spectral clustering methods employ a two-step strategy of spectral embedding and discretization postprocessing to obtain the cluster assignment, which easily lead to far deviation from true discrete solution during the postprocessing process. In this paper, based on the connection between the Kmeans clustering and spectral clustering, we propose a new Kmeans formulation by joint spectral embedding and spectral rotation which is an effective postprocessing approach to perform the discretization, termed KMSR. Further, instead of directly using the dot-product data similarity measure, we make generalization on KMSR by incorporating more advanced data similarity measures and call this generalized model as KMSR-G. An efficient optimization method is derived to solve the KMSR (KMSR-G) model objective whose complexity and convergence are provided. We conduct experiments on extensive benchmark datasets to validate the performance of our proposed models and the experimental results demonstrate that our models perform better than the related methods in most cases.