Extreme learning machine for the characterization of anomalous diffusion from single trajectories (AnDi-ELM)

Abstract

The study of the dynamics of natural and artificial systems has provided several examples of deviations from Brownian behavior, generally defined as anomalous diffusion. The investigation of these dynamics can provide a better understanding of diffusing objects and their surrounding media, but a quantitative characterization from individual trajectories is often challenging. Efforts devoted to improving anomalous diffusion detection using classical statistics and machine learning have produced several new methods. Recently, the anomalous diffusion challenge (AnDi, www.andi-challenge.org) was launched to objectively assess these approaches on a common dataset, focusing on three aspects of anomalous diffusion: the inference of the anomalous diffusion exponent; the classification of the diffusion model; and the segmentation of trajectories. In this article, I describe a simple approach to tackle the tasks of the AnDi challenge by combining extreme learning machine and feature engineering (AnDi-ELM). The method reaches satisfactory performance while offering a straightforward implementation and fast training time with limited computing resources, making it a suitable tool for fast preliminary screening of anomalous diffusion.

Bayesian deep learning for error estimation in the analysis of anomalous diffusion

“…Complementing the discussion of the regression in section V A, we now evaluate the trained Multi-SWAG models on the test data set. The achieved accuracies depicted in figure 9a are in line with the best performing participants of the AnDi-Challenge [59,62,63,[65][66][67][68][69][70][71][72][73][74][75][76][77]. As one would expect the achieved accuracy increases with trajectory length, starting from 44.9% for T = 10 and reaching 91.7% for T = 500.…”

“…In order to quantify the performance of our Multi-SWAG [88] models we test them on a new set of computer generated trajectories using the andi-datasets package. For the general prediction of the anomalous diffusion exponent α we obtain results comparable to the best participants in the AnDi-Challenge [59,62,63,[65][66][67][68][69][70][71][72][73][74][75][76][77]. The achieved mean average error for different trajectory lengths in figure 4a shows an expected decreasing trend with trajectory length.…”

“…The challenge consisted of three tasks, among them the determination of the anomalous diffusion exponent α and the underlying diffusion model from single particle trajectories. The entries included a wide variety of methods ranging from mathematical analysis of trajectory features [63,64], to Bayesian Inference [65][66][67], to a wide variety of machine learning techniques [59,[68][69][70][71][72][73][74][75][76][77]. While the best results were achieved by deep learning (neural networks), this approach suffers from the so-called Black Box Problem, delivering answers without providing explanations as to how these are obtained or how reliable they are [78].…”

Objective comparison of methods to decode anomalous diffusion

“…Methods were classified based on the type of approach (as machine learning (ML), or classical statistics (Stat)); their input data (as raw/lightly preprocessed trajectories (Traj), or features (Feat)); and their training procedure (as length-specific ( L -specific, Yes), or not (No)). Label Team name Method Class Input Tasks L -specific A Anomalous Unicorns Ensemble of CNN and RNN 45 , 76 ML Traj T1(1D), T2(1D) No B BIT Bayesian inference 77 , 78 Stat Traj All No C DecBayComp Graph neural networks 79 ML Traj + Feat T1, T2(1D, 2D) No D DeepSPT ResNet + XGBoost 80 , 81 ML Traj + Feat T1(1D), T2(1D) No E eduN RNN + Dense NN 82 ML Traj All Yes F Erasmus MC bi-LSTM + Dense NN 31 ML Feat T1, T2 Yes G HNU LSTM 83 ML Traj T1 Yes H NOA CNN + bi-LSTM 84 ML Traj T1(1D) No I QUBI ELM 85 ML Feat T1(1D), T2(1D) …”

Classification-based motion analysis of single-molecule trajectories using DiffusionLab

“…The classification is done using these features, either by setting thresholds manually or with feature-based machine learning methods on a user-generated training set. Recently, machine learning methods have been developed for the detection and classification of the different diffusion types, which are mostly focussed on the recognition of anomalous diffusion 19 – 25 . In contrast to the approach employed in DiffusionLab, these models are trained by simulated trajectories with a known set of diffusion models.…”