Learning Signal Representations for EEG Cross-Subject Channel Selection and Trial Classification

First of all, ERNEST exploits a 1D-CNN to automatically extract channel-specific features from signals. To do that, it parametrizes a set of channel-specific embedding models optimized to separate between different classes of trials. The aforementioned classes might represent the health status of a patient, the onset of an epileptic seizure, the different responses to stimuli in an ERP trial or the imaginated motor task in a MI experiment. As mentioned, a notable aspect of the algorithm is the lack of signal preprocessing because of the end-to-end nature of 1DCNNs.
In particular, we can consider each 1DCNN as composed of an encoder and a subsequent classifier. The encoder maps the signals from the $J$-dimensional input space, into an $M$-dimensional embedding space, where $M<J$. The whole model is parametrized with supervised training to classify the signals in the classes of interest. After training, the embedded $M$-dimensional vectors from each of the $C$ channels are extracted from the encoder, and the algorithm builds a unique 1D representation of each trial by concatenating the $C$ embeddings into a trial vector $\textbf{t}\in\rm I\!R^{1\times(M\times C)}$.
The choice of training several parallel models was led by the idea that parametrizing in a supervised channel-wise fashion would generate rich embeddings for all channels and better capture the independent relationship each of those electrode locations has with the target. However, the information lying in the combination of several recording sources and their inter-relationships is not lost, as it is considered in the subsequent Autoencoder ensemble-based Channel Selection (CS) module applied to trial vectors, as described in the following.

The CS module relies on a supervised filtering (i.e. classifier-agnostic) Feature Selection method developed in [18]. This method exploits an Ensemble of Deep Sparse AutoEncoders (DSAEE) to select the most relevant features to discriminate between classes in a binary setting. The algorithm is adapted to select channels instead of single features and its AE-based nature is suited to consider complex non-linear inter-channel relationships while performing selection. In particular, after training of the Feature Extraction module, all training trial vectors t together form the matrix $\textbf{T}\in\rm I\!R^{N\times(CM)}$, where $CM$ is the product between the number of channels and the embedding dimension, that will be used to select the most relevant channels via DSAEE. We supply T to the algorithm that (repeating for each of the $B$ ensemble components) (i) builds the test set ($\textbf{T}_{test}$) by sampling a subset with the same number $L$ of observations from each class, (ii) builds the training set $\textbf{T}_{train}=\{\textbf{t}_{i}|y_{i}=0,\forall i\notin\textbf{T}_{test}\}$ with all observations from one of the classes ($y_{i}=0$) not included in the test set. Then (iii) it trains the DSAE to reconstruct $\textbf{T}_{train}$, and collects the RE on $\textbf{T}_{test}$ as the Squared Error between the input and its reconstruction. The final RE matrix $\textbf{R}\in\rm I\!R^{2BL\times CM}$ is the final output, $2BL$ being the total number of tested observations by the ensemble of models, and the features represent the testing RE committed by the DSAE on the $C$ concatenated $M$-dimensional channel-specific vectors. The RE by class for channel $c$ is then computed summing over the $M$-dimensional chunk in R associated with $c$ and taking the mean of the $BL$ trials of the class:

$$RE^{(c)}_{class}=\frac{1}{L}\sum_{\{i|y_{i}=class\}}\sum_{m=1}^{M}r^{(c)}_{i,m}$$

where the $class$ subscript represents the levels of $\textbf{y}\in\{0,1\}$, and each vector $\textbf{r}^{(c)}_{i}\in\rm I\!R^{M}$ is the subset vector of RE associated to channel $c$ for each trial $i$. The final metric to evaluate channels’ relevance is the difference in RE between classes, i.e. $\Delta RE^{(c)}=RE^{(c)}_{1}-RE^{(c)}_{0}$. We rank order channels on such metric, and we select the top $k$ as the most salient to discriminate between the two classes of trials.

Once the top $K$ most relevant channels have been selected, ERNEST tackles the classification of new trials by exploiting the pretrained models associated to each selected channel. Indeed, at the end of the training phase, each channel is associated with an embedding function $\phi_{c}$ parametrized with supervision to maximize class separability. Given an unseen test set of (trial, target) pairs, for each trial the algorithm filters on the selected $K$ channels, and concatenates the representations obtained applying $\phi_{k}$ to the corresponding signal, with $k=(1,...,K)$. By doing that, we strongly reduce the dimensionality of the problem by transforming a high-dimensional multi-channel representation of each trial into a single vector of controlled size that is highly informative w.r.t. the task at hand. Indeed, we end up with the matrix $\textbf{A}\in\rm I\!R^{P\times(KM)}$, where $P$ is the number of new trials, $K$ is the number of selected relevant channels and $M$ is the representation dimension. As mentioned, each trial is associated to a target, that constitutes the vector $\textbf{y}_{new}\in\rm I\!R^{P}$ associated to A. The matrix A and the associated target vector can then be supplied to any classifier.

Considering that VEP are generally known to grant higher accuracies compared to other paradigms, for this proof of concept experiment we focused on a more complex classification objective by trying to classify trials (the class is determined by the subject associated to each trial) on the basis of the brain signals produced as response to the first visual stimulus (S1) only. We splitted the 122 subjects in training (102 subjects, equally divided between alcoholics and controls) and test group (20 new subjects, 50% alcoholics and 50% controls). The former group with all its trials was exploited for channel-wise 1DCNNs training and channel selection, while the latter was supplied to the algorithm to test the cross-subject classification performance. To perform the channel-wise embedding of the EEG recordings we had to train several channel-specific models. We opted for a shallow 1D-CNN and the specific architectural details are reported in Figure 2.(a). Notably, signals from each channel were reduced to the very low dimension of $M=4$. Hyperparameters were chosen by randomly sampling 10,000 training signals irrespectively of the channel - to make the tuning generalizable across electrodes - equally splitted between classes, and performing random search of the best combination. After setting hyperparameters, each channel-specific 1D-CNN was trained for 200 epochs with a batch size of 1,000 signals.

For what concerns the channel selection module, details are reported in Figure 2.(b). Each DSAE model in the Ensemble (30 components in total) was trained for 300 epochs with a batch size of 500 training trials. The whole algorithm was implemented in Python 3.7, exploiting Keras framework with Tensorflow backend and scikit-learn. The code is available upon request to allow for reproducibility of results. To evaluate the performance on test set we adopted several classifiers, namely Support Vector Machines (SVM), Random Forests (RF) and Logistic Regression (LR). We evaluated whether the channel reduction would impact the performance of the classifiers by first trying to classify trials using all 61 channels (after their embedding via 1DCNNs and transformation into trial vectors) and then with smaller subsets of $K=\{30,20,15,10,5\}$ most relevant channels. The resulting performance was measured using the Area Under the ROC curve (AUROC) and Accuracy metrics by cross-validating 10 times. Whenever possible, we will include in the following results the empirical comparison to the limited literature pursuing cross-subject channel selection on this data. However, note that those results are based on the simpler classification on S2 stimuli as well. Nonetheless, with this first case study application of ERNEST we are more interested in proving the underlying hypotheses of the algorithm, while attaining a satisfactory classification performance. Indeed, we include in our experiment an ablation study that aims at verifying the value added by the DSAEE-based CS Module. To do that, we rank order channels on the basis of the accuracy of channel-specific 1D-CNNs in classifying alcoholics and controls during Feature Extraction Module training. Then, we build the trial vectors by concatenating the top K (in terms of accuracy) channel-specific embeddings, and we feed them to the group of classifiers.

Results for this experiment are reported in Table 1. This experimental setting is lightly comparable to [13, 19] and benchmark algorithms therein, even though performance measurements and data splitting criteria are not always clear from the original papers. Our algorithm obtains a satisfactory accuracy, and a very high AUROC performance, indicating a great precision in identifying the positive class (i.e. alcoholics). Our best classifier (SVM) with only 5 electrodes surpasses the performance in [13] with 4 channels ($75.13\%$ average accuracy). However, in this work the authors exploit PCA for channel selection applied to the whole dataset, and the lack of information on splitting criteria or performance standard deviations suggest that they are reporting training accuracy measures, which are overestimated compared to our test values. The average accuracy reported more recently in [19] with 11 channels ($\sim 93\%\pm 3.3$ with the best proposed approach and SVM classifier) is therein defined as the state-of-the-art on this data. Their performance is higher compared to ours with a similar number of channels. However, note that their performance reflects the easier task including S2 stimuli, and they perform channel selection evaluating the mean-variance of each channel for all subjects in the dataset before proceeding with feature extraction and classification, therefore their selection is not comparable to our subject-agnostic approach.

In Figure 3 we plot the 2D t-SNE representations of 200 sampled trial vectors, that seem consistently separable in both training and test trials from new subjects. Finally, in Table 2 we report the results of the ablation study without the use of the AE-based CS Module. SVM remains the best classifier for this task, but the performance drop can be recognized consistently across all classifiers. Moreover, note that while in both cases the reduction in number of channels leads to a decrease in performance, when including the CS module the drop is significantly smaller: from $0.905$ mean AUROC with $K=61$ to $0.858$ mean AUROC for ERNEST with CS module and $0.778$ mean AUROC for ERNEST w/o CS module for $K=5$. This testifies for this module’s capability to effectively consider inter-channel relationships when selecting the relevant channels for classification, identifying the smallest most informative subset.