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Topological Analysis of Spaces of Waveform Signals
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 Title & Authors
Topological Analysis of Spaces of Waveform Signals
Hahn, Hee Il;
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This paper presents methods to analyze the topological structures of the spaces composed of patches extracted from waveform signals, which can be applied to the classification of signals. Commute time embedding is performed to transform the patch sets into the corresponding geometries, which has the properties that the embedding geometries 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, which can be used to discriminate between the groups of waveforms topologically.
Topology;Commute Time Embedding;Manifold Learning;Homology;Persistent Homology;
 Cited by
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