A method of iterative spectral clustering based on the inverse stereographic projection is proposed. The proposed method contains two steps for data clustering, one by the polarization theorem as the spectral clustering, the other by the inverse stereographic projection. Firstly, the affinity matrix of input data is eigen-decomposed, leading to the embedding of data in a low-dimensional space. The Euclidean distance matrix of the embedded data is then projected to its nearest
doubly stochastic matrix. This approach is shown as a critical step to implicitly call the inverse stereographic projection that maps data into a hyper sphere. The last step is to solve the center and the scale factor of the hyper sphere. Experiments on the challenging synthetic data and the Iris and Wine data sets demonstrate the successful use of the proposed method in modifying the affinity matrix, and the modified affinity matrix can obtain better clustering results than the original one.