Representation-dependent topology of visibility and recurrence networks under adaptive decomposition and coordinate compression

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Abstract

Time-series-to-network mappings are widely used in statistical physics and econophysics, often treating graph topology as intrinsic to observed dynamics. We test how strongly inferred topology depends on representation choices in multiscale financial signals. Four adaptive decomposition methods are evaluated on controlled non-stationary signals. Cross-mode coupling of stochastic ensemble methods is assessed over 30 Monte Carlo replications, while known-drift recovery is evaluated on a prespecified reference realization. No method is universally superior, so the operational choice is completed on the empirical panel. Five financial series are decomposed, their oscillatory modes compressed by fast independent component analysis (FastICA), and native and compressed representations mapped to natural visibility (NVG), horizontal visibility (HVG), and recurrence networks. HVG edge counts retain their order of magnitude after compression, but mean clustering increases and the native scale-ordered gradient is lost. Dense NVGs on slow native modes arise from natural-visibility geometry and disappear after FastICA recombination and truncation; native NVGs exceed FastICA NVGs by 0.706 on the mean log10 edge-count scale. Recurrence networks remain sparse and fragmented under local-distance calibration, with stronger fragmentation after compression; fixed recurrence-rate and Theiler-window checks show this result is protocol-dependent. Multi-seed and full-rank FastICA controls distinguish truncation loss from invertible linear recombination. Thus, these mappings provide complementary rather than interchangeable descriptions, and their descriptors must be interpreted jointly with the decomposition, coordinate representation, and encoding rule.