How to determine the scale parameter and the cluster number are two important open issues of spectral clustering remained to be studied. In this paper, it is aimed to overcome these two problems. Firstly, we analyze the principle of spectral clustering from normalized cut. Secondly, on one hand, a weighted local scale was proposed to improve both the classification performance and robustness. On the other hand, we proposed an automatic cluster number estimation method from standpoint of Eigenvectors of its affinity matrix. Finally, a framework of robust and smart spectral clustering method was concluded; it is robust enough to deal with arbitrary distributed datasets and smart enough to estimate cluster number automatically. The proposed method was tested both on artificial datasets and UCI datasets, and experiments prove its availability.
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