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http://dx.doi.org/10.7236/JIIBC.2016.16.1.291

Analysis of Topological Invariants of Manifold Embedding for Waveform Signals  

Hahn, Hee-Il (Dept. of Information and Communications Engineering, Hankuk University of Foreign Studies)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.16, no.1, 2016 , pp. 291-299 More about this Journal
Abstract
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 graph-based 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.
Keywords
Manifold learning; Commute time embedding; Topological analysis; Persistent homology;
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Times Cited By KSCI : 3  (Citation Analysis)
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