Inferring pointwise diffusion properties of single trajectories with deep learning.

To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5ß1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.

Objective comparison of methods to decode anomalous diffusion.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

Shopper intent prediction from clickstream e-commerce data with minimal browsing information.

We address the problem of user intent prediction from clickstream data of an e-commerce website via two conceptually different approaches: a hand-crafted feature-based classification and a deep learning-based classification. In both approaches, we deliberately coarse-grain a new clickstream proprietary dataset to produce symbolic trajectories with minimal information. Then, we tackle the problem of trajectory classification of arbitrary length and ultimately, early prediction of limited-length trajectories, both for balanced and unbalanced datasets. Our analysis shows that k-gram statistics with visibility graph motifs produce fast and accurate classifications, highlighting that purchase prediction is reliable even for extremely short observation windows. In the deep learning case, we benchmarked previous state-of-the-art (SOTA) models on the new dataset, and improved classification accuracy over SOTA performances with our proposed LSTM architecture. We conclude with an in-depth error analysis and a careful evaluation of the pros and cons of the two approaches when applied to realistic industry use cases.