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Analysis of Topological Invariants of Manifold Embedding for Waveform Signals
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 Title & Authors
Analysis of Topological Invariants of Manifold Embedding for Waveform Signals
Hahn, Hee-Il;
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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.
Manifold learning;Commute time embedding;Topological analysis;Persistent homology;
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