Anomalous diffusion is characterized by nonlinear growth in the mean square displacement of a trajectory. Recent advances using statistical methods and recurrent neural networks have made it possible to detect such phenomena, even in noisy conditions. In this work, we explore feature extraction through parametric and non-parametric spectral analysis methods to decode anomalously diffusing trajectories, achieving reduced computational costs compared with other approaches that require additional data or prior training. Specifically, we propose the use of higher-order statistics, such as the bispectrum, and a hybrid algorithm that combines kurtosis with a multiple-signal classification technique. Our results demonstrate that the type of trajectory can be identified based on amplitude and kurtosis values. The proposed methods deliver accurate results, even with short trajectories and in the presence of noise.
The paper is available at:
M.E. Iglesias Martínez, Ò. Garibo-i-Orts, J.A. Conejero, J.A. Decoding anomalous diffusion using higher-order spectral analysis and multiple signal classification. Photonics 2025, 12, 145. https://doi.org/10.3390/photonics12020145
