Spectral clustering based on multinomial manifold

The Dirichlet distribution offers high flexibility for modeling data. Dirichlet compound multinomial manifold (DCM manifold) is proposed in the paper, which is homeomorphic and isometric to positive sphere. Geodesic distance of DCM manifold may be derived by pullback mapping geodesic distance of positive sphere. According to the geodesic distance, we present diffusion kernel based on DCM manifold, and diffusion kernel based spectral clustering algorithm. Experiments are made to compare performance of our spectral clustering algorithm with other clustering algorithms, and results show our algorithm gets better accuracy.