Analysis of Topological Invariants of Manifold Embedding for Waveform Signals
파형 신호에 대한 다양체 임베딩의 위상학적 불변항의 분석

Hee-Il Hahn
2016 The Journal of The Institute of Internet Broadcasting and Communication  
This paper raises a question of whether a simple periodic phenomenon is associated with the topology and provides the convincing answers to it. A variety of music instrumental sound signals are used to prove our assertion, which are embedded in Euclidean space to analyze their topologies by computing the homology groups. A commute time embedding is employed to transform segments of waveforms into the corresponding geometries, which is implemented by organizing patches according to the
more » ... d metric. It is shown that commute time embedding generates the intrinsic topological complexities although their geometries are varied according to the spectrums of the signals. This paper employs a persistent homology to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, and discusses their applications.
doi:10.7236/jiibc.2016.16.1.291 fatcat:enehkhmxszb3vffxrljsedgbm4