It is well known that \({\mathbb {C}}H^n\) has the structure of a solvable Lie group with left invariant metric constant holomorphic sectional curvature. In this paper we give full classification all possible Riemannian metrics on group. We prove each those negative scalar curvature, only one them being Einstein (up to isometry and scaling).

In this paper, a method for multi-pitch detection which exploits the temporal evolution of musical sounds is presented. The proposed method extends the shift-invariant probabilistic latent component analysis algorithm by introducing temporal constraints using multiple Hidden Markov Models, while supporting multiple-instrument spectral templates. Thus, this model can support the representation o...

We introduce novel multiscale kernels using the random walk framework and derive corresponding embeddings and pairwise distances. The fractional moments of the rate of continuous time random walk (equivalently diffusion rate) are used to discover higher order kernels (or similarities) between pair of points. The formulated kernels are isometry, scale, and tessellation invariant, can be made glo...