Fractional Fourier Transform based Visibility Graphs

The fractional Fourier transform (FrFT) is a generalization of the conventional Fourier transform with a fractional parameter that interpolates between the time and frequency domains in a flexible manner. Recent work introduced the FrFT into machine learning and graph signal processing, the latter motivating graph constructions whose topology is directly induced by the underlying signal. Visibility graphs (VGs) provide such signal-driven graph representations by mapping time series into graphs, yielding simple and interpretable structures. However, the integration of VGs with spectral transformations has largely been restricted to the conventional Fourier transform. We introduce an approach where the FrFT is used to assign edge weights to the visibility graph of both scalar and vector signals. We propose the fractional order as a learnable parameter such that the optimal fractional Fourier domain can be determined based on the data. Extensive experiments on six biomedical, industrial, and energy time series benchmarks, together with evaluations on two additional multivariate time series benchmarks, show that FrFT-based edge weighting in VGs achieves superior performance compared with unweighted, fixed Fourier-domain, alternative weighted VG, and graph signal processing baselines.