# Multifractal-spectral features enhance classification of anomalous diffusion

arXiv: https://arxiv.org/abs/2401.07646 · HTML: https://mlsanity.com/paper/2401.07646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 181 references that are in the map.
- First posted on arXiv 15 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion](https://mlsanity.com/paper/2202.06355/) (2022)
- [Machine learning method for single trajectory characterization](https://mlsanity.com/paper/1903.02850/) (2019)
- [Unsupervised learning of anomalous diffusion data](https://mlsanity.com/paper/2108.03411/) (2021)
- [Bayesian inference of scaled versus fractional Brownian motion](https://mlsanity.com/paper/2201.00654/) (2021)
- [Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories](https://mlsanity.com/paper/2308.09414/) (2023)
- [Point estimates, Simpson's paradox and nonergodicity in biological sciences](https://mlsanity.com/paper/2009.00756/) (2020)
- [Ergodic descriptors of nonergodic stochastic processes](https://mlsanity.com/paper/2202.01091/) (2022)
- [Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series](https://mlsanity.com/paper/2204.00572/) (2022)

## Built on by (most cited first, 2 of 2)

- [Machine Learning Analysis of Anomalous Diffusion](https://mlsanity.com/paper/2412.01393/) (2024)
- [Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectories](https://mlsanity.com/paper/2512.08510/) (2025)

## Abstract (arXiv)

Anomalous diffusion processes pose a unique challenge in classification and characterization. Previously (Mangalam et al., 2023, Physical Review Research 5, 023144), we established a framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous time random walk, annealed transient time motion, and L'evy walk. To accomplish this, we generate extensive datasets comprising 106 trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. Furthermore, we explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p-variation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. Our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing classification of anomalous diffusion.