Defines the walk-length filtration for persistent homology on directed graphs, establishes stability under a generalized L1-style network distance, supplies a computation algorithm, and compares it to the Dowker filtration on cycle and synthetic hippocampal networks.
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A standardized pipeline converts time series to graphs, computes persistence diagrams, and extracts features that classify UCR benchmarks, with diffusion distance outperforming shortest-path metrics and performance varying by graph type.
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The Walk-Length Filtration for Persistent Homology on Weighted Directed Graphs
Defines the walk-length filtration for persistent homology on directed graphs, establishes stability under a generalized L1-style network distance, supplies a computation algorithm, and compares it to the Dowker filtration on cycle and synthetic hippocampal networks.
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Persistent Homology of Time Series through Complex Networks
A standardized pipeline converts time series to graphs, computes persistence diagrams, and extracts features that classify UCR benchmarks, with diffusion distance outperforming shortest-path metrics and performance varying by graph type.