A study on manifolds of acoustic responses

The construction of a meaningful metric between acoustic responses which respects the source locations, is addressed. By comparing three alternative distance measures, we verify the existence of the acoustic manifold and give an insight into its nonlinear structure. From such a geometric view point, we demonstrate the limitations of linear approaches to infer physical adjacencies. Instead, we introduce the diffusion framework, which combines local and global processing in order to find an intrinsic nonlinear embedding of the data on a low dimensional manifold. We present the diffusion distance which is related to the geodesic distance on the manifold. In particular, simulation results demonstrate the ability of the diffusion distance to organize the samples according to the source direction of arrival (DOA).