Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes occurring in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of the particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the cost of much longer processing times. Moreover, there are still some borderline cases in which the classical methods perform better than CNN.

Figure 1

Comparison between (a) random forest and (b) gradient boosting methods. In the random forest, $N$ independent learners (trees) are built in parallel from random subsets of the input data set. In gradient boosting, the next tree is constructed from the pseudoresiduals of the ensemble and added to it.

Figure 2

A schematic architecture of a CNN. The network consists of two components: hidden layers responsible for feature extraction from input data and fully connected layers carrying out the classification.

Figure 3

Confusion matrices for (a) the random forest and (b) the gradient boosting classifiers.

Figure 4

Feature importance in (a) the random forest model and (b) the gradient boosting models.

Figure 5

Cumulative importance of features for both models. The dashed line is the 97% level of importance and indicates a threshold for feature selection.

Figure 6

Comparison of the feature-based classifiers. (a) Number of features required to achieve the given threshold of cumulative importance. (b) Accuracy of classifiers trained with the reduced number of features.

Figure 7

Impact of (a) the number of architectures in the random search and of (b) the number of epochs in training the final model on the loss, accuracy, and execution time. In the random search procedure, 10 epochs were used to train the models on a small subset of the training data. The final model analyzed in the right column was selected from 20 architectures.

Figure 8

Architecture of the best performing network model found by mcfly.

Figure 9

Confusion matrix of the CNN classifier.

Figure 10

Average accuracy of the methods in some limiting cases. (a) Performance of the classifiers for anomalous diffusion for four different ranges of the exponent $\alpha$. The lines in the plot are used to guide the eye. (b) Same for directed motion with small velocities, corresponding to $R\in \{1,2,3\}$ [see Eq. (7) for the definition of $R]$.