Gramian Angular Fields for leveraging pretrained computer vision models with anomalous diffusion trajectories

Abstract

Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and the migration patterns of birds. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent {$\alpha$} with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge ge (Munoz-Gil et al., 2021). Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian Angular Fields (GAF) to encode one-dimensional trajectories as images (Gramian Matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pre-trained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime, and infer the anomalous diffusion exponent {$\alpha$}. Short raw trajectories, of lengths between 10 and 50, are commonly encountered in single-particle tracking experiments and are the most difficult to characterize. We show that by using GAF images, we can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting.

arXiv comment19 pages, 15 figures

References in corpus (26)

• An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Imaging Time-Series to Improve Classification and Imputation
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Machine learning method for single trajectory characterization
• Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach
• Spectral content of a single non-Brownian trajectory
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Noisy continuous time random walks
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Finite-time effects and ultraweak ergodicity breaking in superdiffusive dynamics
• Fractional kinetics emerging from ergodicity breaking in random media
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Nonergodic Diffusion of Single Atoms in a Periodic Potential
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• Characterization of anomalous diffusion classical statistics powered by deep learning (CONDOR)
• Implementation of Deep Neural Networks to Classify EEG Signals using Gramian Angular Summation Field for Epilepsy Diagnosis
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features
• Characterization of anomalous diffusion through convolutional transformers
• Continuous-time random walk for a particle in a periodic potential
• A statistical-inference approach to reconstruct inter-cellular interactions in cell-migration experiments

Cited by in corpus (2)

• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Recurrent neural network analysis of single trajectories switching between anomalous diffusion states