The data used for this study is an open-source dataset from Child Mind Institute (Alexander et al., 2017). It contains a large high-density EEG (129 electrodes) dataset from the age distribution 5–21 years, including male and female subjects, with varied brain pathologies. The objective of the DL models was to classify the sex of a subject, given the EEG data. After removing samples which did not fulfill the inclusion criteria for data quality (see Section 2.1.1), the dataset was balanced by down sampling the class in abundance, resulting in a final dataset with 1,788 subjects. Only the resting-state EEG data files were extracted. The first 30 s of the recordings were skipped as the first parts of the EEG are more likely to contain unwanted artifacts. The proceeding 10 s was used as input for the models. Only a single 10 s window was used per subject, and the splitting of data was thus made on subject level. The sampling frequency was kept at 500 Hz as in the original dataset.

The Inception network is a convolutional neural network (CNN) based architecture, which is the main building block of InceptionTime. Here, the Inception network is briefly described, and for further details on the architecture, the reader is referred to the original study (Ismail Fawaz et al., 2020).

An Inception network is composed of multiple Inception modules, with linear shortcut connections for every third Inception module. A key component of the Inception module is the bottleneck layer, which effectively computes linear combinations of the input time series. Furthermore, the Inception module applies filters of different lengths simultaneously on the same input time series, and resulting feature maps are aggregated by concatenation. After passing the data through all Inception modules, global average pooling is performed in the temporal dimension. Finally, while the original Inception network used a fully connected layer with softmax activation, this was changed to a single fully connected layer with sigmoid activation (Ismail Fawaz et al., 2020).

The hyperparameters of our Inception network was set as described in the original study. This includes a depth of six Inception modules, and 32 number of filters for all convolutional kernels in all Inception modules (Ismail Fawaz et al., 2020).

Three methods for handling a varied number of channels were tested on a binary classification problem, sex prediction. The three methods were (1) zero-filling, (2) spherical spline interpolation (Perrin et al., 1989), and our suggested new method (3) Region Based Pooling (RBP). Inception network (Ismail Fawaz et al., 2020) was the DL model used after zero-filling, interpolation, or applying RBP, with the exception that the final layer used scalar output and sigmoid as activation function for predictions.

RBP splits the topology of the EEG montage into regions, as illustrated in Figure 2. The channels within a single region are pooled into one or more region representations, and hence the name Region Based Pooling. To minimize the loss of information, multiple splits with different region formations are performed. RBP introduces three new optimization problems; (1) how to split the EEG montage into regions (both the number of montage splits and the algorithm separating the regions), (2) how to pool the channels within the same region, and (3) how to merge the outputs of the different montage splits. The proceeding two subsections intend to illustrate how the first two problems can be addressed and are meant as examples of implementation.

All RBP models in the experiments of this study merged the outputs of the montage splits by concatenation. Furthermore, all channels within the same region were merged to a single region representation. Finally, all region representations were normalized by subtracting the mean and dividing by the standard deviation in the temporal dimension.

All models were implemented using PyTorch (Paszke et al., 2019), version 1.10.1+cu113. The hardware used was a computer equipped with an NVIDIA GeForce RTX 3060 12GB GPU. The code is publicly available on GitHub.²

All models were run with learning rate set to 0.0001. The maximum number of epochs was set to 50, except for RBP with continuous channel attention, which used 20 epochs due to high time consumption. The batch size was mainly set to 16 although some models required smaller batch size due to memory constraints. The exceptions are listed in Table 1. Experiments using zero-filling and spherical spline interpolation were run with batch size set to 4, 8, 16, and 32, to ensure that potential improvements were not due to differences in batch size. Adam (Kingma and Ba, 2015) and binary crossentropy (with logits loss for improved numerical stability) were used as optimization technique and loss function, respectively.

For all experiments, a 5-fold cross validation strategy was carried out. For every fold, the 4 folds not used for testing were split into training and validation 75/25. The training data was used to optimize the trainable parameters of the DL models, whereas the validation data was used to estimate what epoch to stop at. During a single fold, only the model parameters which obtained the highest area under the receiver operating characteristics curve (AUC) on the validation set (computed as the mean performance on the 32, 65, and 129-channel versions of the channel system) was used when testing on the test data fold.

To evaluate the sensitivity with respect to two new hyperparameters introduced by RBP, a grid search was made for all pooling mechanisms. The first hyperparameter was min_nodes, which is the smallest number of channels allowed in the 32-channel version of the channel system. The smaller the min_nodes, the smaller the regions are allowed to be when splitting the montage. The second hyperparameter was num_montage_splits, which is the number of montage splits performed. The grid search was carried out with min_nodes∈{1, 2, 3} and num_montage_splits∈{5, 10, 25, 50}, with the exception of RBP using continuous channel attention, which was restricted to num_montage_splits∈{5, 10, 25} due to memory limitations.

RBP shows highly similar performance to spherical spline interpolation for all channel systems, as seen in Figure 10. Both RBP and spherical spline interpolation demonstrate robustness in handling a varied number of channels, as indicated by the minor performance degradation observed on the down-sampled channel systems. A potential decrease in performance when reducing the number of channels is not necessarily to be evaluated as weaknesses in these methods but may be due to a loss of information when removing channels. The objective of the methods is to handle the channel down-sampling with the smallest reduction in performance as possible although no method can restore the fully lost information. In contrast to RBP and spherical spline interpolation, zero-filling missing channels vastly reduce the performance on the lower resolution channel systems. Zero-filling is therefore not a recommended approach for handling missing channels, despite its use in, e.g., the official preprocessed version of the EEG data of the Child Mind Institute (Alexander et al., 2017).

The results from the grid searches on the different pooling mechanisms indicate that the selection of pooling mechanism was unimportant for the selected task and dataset, except for continuous channel attention for 25 number of montage splits. However, the batch size was set to 1 due to memory constraints, which is not optimal for training, and thus a strong confounder. More research is therefore needed to assess if a high number of montage splits failed in continuous channel attention due to inadequacy of the pooling mechanism or if it is solely due to the batch size. No pooling mechanism was superior to the others for all hyperparameters. A consistent trend appears to be that RBP benefits from smaller regions, as the performance on especially the channel systems with 32 and 65 channels seem to increase when the stopping criteria min_nodes decrease. This is not an unexpected finding as using smaller regions increases the spatial resolution per montage split. The current results further suggest that solely increasing the number of montage splits is insufficient when the regions are excessively large. However, as future work may include even smaller channel systems, larger regions may be beneficial from a practical point of view. Finding the optimal balance between low resolution channel systems compatibility and model performance may therefore be important for future research. However, as the model was trained only on 129 channels, the performance on the low-resolution channel systems may be increased by including them in the training data as well. For extension to the large-scale setting with multiple datasets, this is likely to be a feasible approach. Furthermore, it may be used as a data augmentation technique, in particular when the high-resolution channel system has low-resolution equivalents.

This study proposed an algorithm for splitting the EEG montage into regions although no optimization of montage splits was performed. It is likely that different EEG related problems may benefit from different montage splits. This is because the important spatial features may be task related and require higher or lower resolution of some areas. Furthermore, as only one algorithm for splitting the EEG montage into regions was tested, future work could benefit from exploring and evaluating alternative methods. Note that with the current use of regions having defined boundaries, where an electrode is either inside or not inside a region, optimizing montage splits by gradient based methods cannot work directly. This is because an infinitely small change to the boundaries of the region will either cause zero change in output or an output change of fixed size (not infinitely small, as required). The gradients would thus be either zero or infinite, making gradient based learning infeasible. Two potential solutions are further discussed in Section 4.4.2.

As discussed in Wei et al. (2022), limited studies has focused on generalizing DL models to handle the cross-dataset setting and a varied number of channels. A desired outcome of the BEETL competition was to develop transfer learning techniques in the cross-dataset setting (Wei et al., 2022). However, the top three entries selected simple methods to handle a varied number of channels and the difference in channel locations; channel removal, dataset removal, or both. Furthermore, to handle a varied number of channels in the pre-training and downstream training, Kostas et al. (2021) mapped all datasets to 19 channels, and in that process, sacrificed a considerable part of the data for several of the datasets used for downstream training. However, research from clinical neurology suggests that certain characteristics require high-density EEG with an increased number of channels (Kuhnke et al., 2018; Hatlestad-Hall et al., 2023). The feasibility of downsampling the spatial resolution may therefore be limited to only a subset of EEG-related tasks.

Li and Metsis (2022) developed SPP-EEGNET, an architecture designed for inter-dataset transfer learning, and is compatible with a varied number of channels. However, SPP-EEGNET pools the feature maps by spatial pyramid pooling (SPP) (He et al., 2014) after convolutions have been applied channel-wise. Cross-channel patterns can therefore not be extracted by the convolutional module of SPP-EEGNET as the receptive field of the feature maps are bounded to their respective single channel. Such cross-channel patterns may only be extracted by the fully connected module, after applying the SPP layer. As the success of signal processing is mostly attributed to the convolutional module, this approach may be sub-optimal. Furthermore, many existing DL architectures for EEG data apply 1D convolutions across channels, hindering its application to many of the currently existing architectures. This contrasts with RBP, which is compatible with any DL model for multivariate time series classification/regression.³ This is beneficial, as the current high-performing models from literature may apply RBP with ease (simply use RBP as the initial layer), meaning the accumulated research and development on DL architectures over time is respected. Furthermore, it offers a simple solution for working on the cross-dataset and cross-channel system setting in the future. Note also that although this study represented the EEG data as time series, using other representations such as power spectral density or operating on wavelet transformed images are popular choices of input to DL models. RBP is indeed compatible with such representations although the pooling mechanisms must be tailored to fit the input domain. Finally, the pooling in RBP is performed based on the spatial positions of the electrodes, whereas SPP-EEGNET does not precisely specify how the feature maps of the different channels were merged. If the pooling is made only by the data matrix X [as if it was an image, following the original SPP-net (He et al., 2014)], then inconsistency in which channels end up in which spatial region will occur.

A limitation of this study is its reliance on a single dataset and classification problem, which may restrict the generalizability of the findings. In particular, the size of the dataset was larger than what is commonly available for EEG datasets with more clinically relevant labels. When the total number of region representations exceeds the number of channels in a given channel system, RBP effectively expands the dimensionality of the data. This is especially the case when the regions are small, and the number of montage splits are many. For smaller datasets in particular, this may lead to an increased risk of overfitting. The generalizability of the results to smaller datasets, and in particular, the effect of the hyperparameters min_nodes and num_montage_splits is therefore poorly investigated. While testing the methods on sex classification allowed for a large dataset with low chance of false labeling, its clinical utility is low. Thus, classification/regression problems with higher clinical relevance should be considered in the future. Furthermore, only a single model (Inception network) was used in combination with the three different methods for handling a varied number of electrodes. Although Inception network is an effective DL model for multivariate time series analysis, generalization to other models was not assessed. This is needed due to the high number of DL models used for EEG analysis. Finally, hardware limitations constrained the training of all RBP models using the same batch size, potentially reducing the performance of the models with smaller batch size. By testing with more models, datasets, and classification/regression problems, the relevance of the methods will thus be better addressed. In particular, to fully explore the potential and relevance of the investigated methods, experiments including datasets with even smaller numbers of EEG channels, such as 19 or 25, are required.