Manifold embedding based visualization of signals

We address the problem of transforming statistically stationary waveform signals into their intrinsic geometries by embedding them into two or three dimensional space for the purpose of visualizing them. The graph Laplacian based manifold embedding algorithms basically generate geometries intrinsic to the signal characteristics under the conditions that it is smooth enough and sufficient number of patches are extracted from it. Especially, commute time is known to have the properties of shrinking the mutual distance between two points as the number of paths connecting them increases, which makes it possible to align the statistically different patches in the form of curves. Extensive experiment is conducted with speeches and musical instrumental sounds to investigate the relevance of the waveforms to their own inherent geometries.