A Note on Spectral Clustering Method Based on Normalized Cut Criterion

Recently spectral clustering has become one of the most popular clustering algorithms. Although it has many advantages, it still has a lot of shortcomings which should be resolved, such as there are a wide variety of spectral clustering algorithms that use the eigenvectors in slightly different ways and many of these algorithms have no proof that they will actually compute a reasonable clustering. The spectral clustering method based on normalized cut criterion is a very efficient spectral clustering method. In this paper, we give a note on why we choose the first k eigenvectors in the algorithm (rationality of the clustering) and the conditions for indicator vectors under which the clustering problem could lead to the problem of minimizing the objective function of the spectral clustering method based on normalized cut criterion.