Analyzing the Topological Structures of Waveform Signals

DOI: 10.5176/2251-1911_CMCGS16.20

Authors: Hee Il Hahn

Abstract: The manifold learning algorithms basically generate geometries intrinsic to the signal characteristics under the conditions that each signal is smooth enough and sufficient number of patches are extracted from it. It is shown that commute time embedding results of periodic or quasi-periodic waveforms are represented as closed curves on the low dimensional Euclidean space, while those of aperiodic signals have the shape of open curves. Persistent homology is employed to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms.

Keywords: component; topology; persistent homology; manifold learning; commute time embeding