The ageing process may lead to cognitive and physical impairments, which may afect elderly everyday life. In recent years, the use of Brain Computer Interfaces (BCIs) based on Electroencephalography (EEG) has revealed to be particularly efective to promote and enhance rehabilitation procedures, especially by exploiting motor imagery experimental paradigms. Moreover, BCIs seem to increase patients' engagement and have proved to be reliable tools for elderly overall wellness improvement. However, EEG signals usually present a low signal-to-noise ratio and can be recorded for a limited time. Thus, irrelevant information and faulty samples could afect the BCI performance. Introducing a methodology that allows the extraction of informative components from the EEG signal while maintaining its intrinsic characteristics, may provide a solution to both the described issues: noisy data may be avoided by having only relevant components and combining relevant components may represent a good strategy to substitute the data without requiring long or repeated EEG recordings. Moreover, substituting faulty trials may significantly improve the classification performances of a BCI when translating imagined movement to rehabilitation systems. To this end, in this work the EEG signal decomposition by means of multivariate empirical mode decomposition is proposed to obtain its oscillatory modes, called Intrinsic Mode Functions (IMFs). Subsequently, a novel procedure for relevant IMF selection criterion based on the IMF time-frequency representation and entropy is provided. After having verified the reliability of the EEG signal reconstruction with the relevant IMFs only, the relevant IMFs are combined to produce new artificial data and provide new samples to use for BCI training.
In the last years, the global growth of the elderly population [
Among the various technological innovations, the Brain Computer Interfaces (BCIs) have
proved to be particularly apt to these tasks and found their application in cognitive and motor
rehabilitation systems [
The most popular method to allow the recording of the BCI input brain signals is
electroencephalography (EEG), which provides multivariate time series collected by placing electrodes
on the scalp of a subject. Therefore, the EEG signals have proved to be particularly eficient
in accessing brain activities and functions by bringing time, space (electrodes) and frequency
information of the neuronal signals [
Regarding the frequency information, the EEG signal is characterized by diferent frequency bands (or rhythms) that are representative of specific brain dynamics [ 12, 13]. Table 1 provides a brief overview of the EEG rhythms.
Notice that the and frequency bands can be specifically associated to diferent cognitive
and motor functions and thus their dynamic changes can be widely exploited in rehabilitation
systems based on motor imagery (MI) tasks [
However, controlling a BCI system with MI is dificult and the ability to perform this task varies
from person to person. A good control of a BCI is usually achieved when a user reaches the
70% accuracy in the MI paradigm [15]. Reaching this level of accuracy may require a long
time, however MI tasks usually enhance brain plasticity and providing a feedback to their users
could further improve the cognitive, motor and intellectual functions of elderly users, who are
particularly afected by brain dynamic changes due to the ageing process [
Even though MI-BCI systems based on EEG signals seem to be promising tools for rehabilitation purposes, there are many challenges that should be considered and that can afect the overall BCI performance.
In fact, the EEG signals, that are at the core of these systems, are extremely heterogeneous and easily afected by noise [16]. Moreover, collecting an adequate quantity of reliable data to perform the classification tasks involved in the BCI control system is dificult, due to the lack of suficient time for recording, the possible poor number of subjects and the dificulty of the experimental tasks [17]. These issues may lead to a general classification deterioration and thus afect machine learning model performances [18].
In the EEG domain, attempts to solve the problem of generating new artificial signals have been
provided by the data augmentation literature [18] [17] [
In [19], an interesting data substitution approach is proposed1. The authors exploit the recombination of the oscillatory modes, called Intrinsic Mode Functions (IMFs), obtained through 1The original code is available at https://github.com/fbear1993/DR-EMD.
Therefore, the present paper extends the work provided by Dinarès-Ferran et al. [19] and focuses on finding significant IMFs for portions of MI signals presenting tasks of interest, from now on called trials. The IMFs are computed with a multivariate extension of the EMD algorithm [21], wanting to maintain the cross-channel interdependence typical of EEG data [22]. The IMFs are then selected and recombined in order to obtain an unbiased data substitution.
Therefore, our main contributions are (i) the time-frequency representation of the IMFs, on which (ii) the entropy is computed to define the most informative (relevant) IMFs and (iii) the reconstruction of artificial trials by significant IMF combination.
These steps should provide artificial EEG signals presenting coherent brain dynamics and thus exploitable in a BCI paradigm.
The work is then organized as follows. Section 2 provides a brief literature review on EMD and its multivariate extension, when exploited for IMF selection or data substitution. Section 3 presents the datasets and literature methods employed. Section 4 describes our proposed approach for relevant IMF selection and artificial data generation. Section 5 discusses the obtained results and Section 6 concludes the work.
As introduced in Section 1 and starting from the EMD based artificial trial generation proposed by Dinarès-Ferran et al., this work will focus on the use of the Multivariate Empirical Mode Decomposition (MEMD) [21] to select relevant IMFs and recombine them to produce new trials. Therefore, in this section a brief overview of the works presenting some solutions for relevant, redundant, or noisy IMF selection will be provided.
In the EMD literature, some authors [23, 24] have focused on finding redundant IMFs by exploiting the Minkowski distance and the Jensen-Rènyi divergence [25] to track the diferences between the original signals and the IMFs. The use of a thresholding critrion is presented by Bueno et al. [26]. The authors compute the entropy of each IMF and select them if their entropy is greater than a specifically defined threshold
(max − min )/2 + min . Notice that is the vector containing the entropy of all the IMFs.
Considering instead the MEMD literature, the IMF selection has been performed (i) empirically by retaining the IMFs whose combination provides the best classification performance [ 27], (ii) by comparing through the Wasserstein distance [28] the IMFs obtained by decomposing the EEG data against the IMFs coming from reference electrodes [29], or (iii) by using a measure of similarity between IMFs and reference noise [30, 31].
In the following, we will highlight the fact that our IMF selection is also based on choosing the frequency ranges characterizing EEG rhythms of interest. In the literature, Piper et al. and Gaur et al. [32, 33] have exploited the frequency information: Piper et al. wanted to obtain consistent IMFs between subjects and selected the first 2 IMFs retaining rhythm information, while Gaur et al. found the and rhythm contributions by computing the median frequency values of each IMF.
Besides IMF selection or noise removal, EMD and some of its variations have been exploited for artificial data generation.
Considering the reference work, Dinarès-Ferran et al. [19] employed EMD and obtained IMFs for each trial. Afterwards, they generated artificial data by combining 15 IMFs of diferent trials and used them to substitute certain percentages of the data, finding that the eficacy of these substitutions varies from subject to subject.
A similar strategy has been presented by Lee et al. [34], who decomposed the signals with the ensemble variation of the EMD [35], instead of using the original EMD.
As a final remark, notice that the majority of the described methodologies set the maximum number of IMFs to combine to a specific and unchanged number (during computation) , and when producing artificial data, all the IMFs are considered.
In this section, the datasets employed to test our proposal and the Multivariate Empirical Mode Decomposition (MEMD) [21] used for the IMF decomposition of the EEG signals are described.
The following procedures have been tested on 2 datasets: (i) the EEG Simulated dataset [36, 37], and (ii) the EEG Motor Imagery BCI dataset [19].
The choice of the EEG Simulated dataset was driven by the necessity of assessing the eficacy of the proposed relevant IMF selection on controlled data. In fact, the EEG Simulated dataset presents clean and raw (noise afected with signal-to-noise ratio from -20dB to 20dB and adding ocular artifacts) simulated EEG signals on 19 electrodes, i.e., C{3, 4, }, F{3, 4, 7, 8, }, Fp{1, 2}, O{1, 2}, P{3, 4, }, T{3, 4, 5, 6}, and considering the , , and rhythms. 10 trials of 10 s each have been generated. For further details, please refer to [36, 37].
Instead, the EEG Motor Imagery BCI dataset was chosen due to the fact that it has been employed by the reference work on artificial trial substitution for a BCI paradigm [19]. 7 healthy males were asked to perform a MI task consisting of left/right wrist dorsiflexion imagined movements. Each subject participated to 2 experimental runs, during each of which 40 tasks of left and 40 tasks of right wrist MI were randomly performed. A trial consisted of 2s of resting time, an acoustic cue for task preparation and 5s of motor imagination. The recorded electrodes were C{1, 2, 3, 4, 5, 6, }, Cp{1, 2, 5, 6}, Fc{1, 2, 5, 6, }. Notice that the dataset has been pre-processed by the authors, who used a bandpass (0.5 − 30Hz) and a notch (50Hz) filter. For more details, please refer to [19].
In 1998, Huang et al. proposed the Empirical Mode Decomposition (EMD) [20], a signal processing technique that allows the decomposition of a time series into oscillatory modes (the IMFs), with a completely data-driven approach and avoiding the loss or distortion of the data [38]. In fact, considering a signal (), it (i) finds the signal local maxima and minima, (ii) defines () upper and lower envelopes, (iii) computes their mean envelope and (iv) subtracts it from (), obtaining the detail (). The computation is repeated assigning () to (), until () satisfies the IMFs conditions, i.e., its number of zero-crossings and extrema are equal or difer by a unit and its mean envelope is zero. Thus, () is considered as an IMF and () can be reconstructed by summing the obtained IMFs and a residuum (): () = ∑︀ =1 () + ().
Therefore, EMD seems to be suitable to deal with non-stationary and non-linear signals [39] [36], like the EEG ones. However, it works on multivariate signals with a channel-by-channel approach, thus ignoring the cross-channel interdependence which characterizes the EEG signals [22].
To address this issue, Rehman and Mandic proposed an EMD variation, i.e., the Multivariate Empirical Mode Decomposition (MEMD) [21]. MEMD provides IMFs with the same number of oscillations for each channel by exploiting diferent projections of the -channel signal into a -dimensional space. Thus, given a multivariate signal {()}=1 = {1(), 2(), ..., ()}, MEMD: 1. Chooses a suitable direction vector = {1, 2, ..., }, where = 1, 2, ..., and is the total number of direction vectors and = { 1, 2, ..., } are the angles on a ( − 1) sphere along which are defined the direction vectors. 2. Computes the ℎ projection of {()}=1 along , obtaining { ()}=1 for all .
3. Finds {
}=1 time instants, which correspond to the { ()}=1 maxima. 4. Interpolates [ , ( )] to obtain { ()}=1 for all .
5. Estimates the mean envelope for a set of direction vectors: () = 1 ∑︀ =1 (). 6. Extracts the detail () = () − (), where = 1, 2, ..., and is the maximum number of decomposition scales. If () meets the IMF conditions, point 1-3 are applied to () − (), otherwise to ().
In this work, MEMD is used to decompose the data of each subject and trial. Fig. 1 shows an example of the IMFs obtained by applying MEMD on the electrode C1 of a specific subject and trial. The x axis corresponds to the time (s) and the y axis to the signal amplitude ( ).
After having obtained the same number of IMFs for each electrode of a specific subject and trial, the IMFs are used as inputs to the proposed procedure, which consists of 4 main steps: (i) generation of the time-frequency images for each IMF, (ii) entropy computation on the time-frequency images, (iii) significant IMF selection criterion, and (iv) data substitution.
Firstly, the time-frequency image generation requires the choice of a frequency range of interest and its time-frequency resolution. Having as targets MI tasks, the chosen frequency range spans from 8 to 30 Hz. In fact, this range includes the (8-13 Hz) and (13-30 Hz) frequency bands, which are involved in the motor tasks [14] (Section 1). Also, a trade-of between the time and frequency resolution [40] is preferred for image reconstruction. Then, the procedure loops on the frequency range and starts with the generation of a complex Morlet wavelet [41] exploiting the described parameters. Subsequently, it proceeds with the application of the fast Fourier transform on both the wavelet and the original signal. Afterwards, the inverse fast Fourier transform is applied to the wavelet convolved on the signal. Finally, the power data of the convolution is computed and thus the time-frequency image obtained. Fig. 2 presents a colored example of the time-frequency images obtained by computing this procedure on each subject, trial, electrode and relative IMFs (presented in Fig. 1). The x axis corresponds to the time (s) and the y axis to the frequency range (Hz). From the provided example, some clear diferences in the IMFs can be observed and we can hypothesize that the IMFs containing more information are the ones which present a more complex texture. Entropy [42] can be used to characterize the texture of an image and thus is employed to find the IMFs having more variability.
Here the entropy is computed on the time-frequency gray scale image and is equal to − ∑︀( × log2()), where presents the normalized histogram counts of the time-frequency image.
Considering the entropy obtained on all the IMFs of all the electrodes of a specific trial, the IMFs having entropy greater than the mean entropy are selected as the most significant ones. A more conservative approach is preferred to the elimination of a greater number of IMFs in order to avoid the exclusion of efective neurophysiological signals. The same number of IMFs are selected for all the electrodes of the same trial.
Finally, the last step of our proposal is the artificial data generation, which is performed on each subject by randomly combining the entropy-selected IMFs of diferent trials of the same task, using a scheme similar to the one described in [19, 43]. For each subject, a specific number of artificial trials balanced between the tasks of interest are produced by: 1. Finding the maximum number of entropy-selected IMFs to have the same number of IMFs for each trial. In case a trial presents a lesser number of entropy-selected IMFs if it was decomposed in at least -IMFs, the corresponding oscillation modes discarded by the entropy selection are reintegrated until the trial reaches -IMFs, otherwise IMFs equal to a null vector are added until the trial reaches -IMFs. 2. Randomly selecting -IMFs from the IMFs of diferent original trials for each artificial trial. E.g., a new artificial trial may be composed by the first IMF of the 17ℎ original trial (of the same task), by the second IMF of the 5ℎ original trial, by the third IMF of the 1 original trial and so on until -IMFs are reached. 3. Reconstructing the artificial trials according to the IMFs obtained at point 2. Notice that the original trials were reconstructed by considering both their -IMFs to provide coherent signals to compare with the artificial trials and the entropy-selected IMFs. Also, analyses on the trial similarity are performed to ensure the absence of biased artificial trials that could be eficiently used in BCI rehabilitation systems.
To better understand the reliability of the proposed relevant IMF selection, a preliminary experiment has been conducted on the EEG Simulated dataset.
MEMD has been applied for each trial of the clean and raw data, considering all the signal-tonoise ratio realizations (from -20dB to 20dB).
Subsequently, the time-frequency images of the obtained IMFs have been generated considering the 8 − 30 Hz frequency range. Finally, the entropy selection criterion has been applied and the entropy-selected IMFs summed up to obtain the reconstructed EEG signal.
The assessment of the proposed method reliability has been performed by computing the similarity between the clean and raw/entropy-reconstructed data by means of Pearson correlation coeficient. The similarity check has been applied to each signal-to-noise ratio realization, trial, and electrode.
We find that for low signal-to-noise ratios (about -20dB to -17dB), the Pearson correlation coeficient obtained by comparing the clean data versus the entropy-reconstructed ones do not deviate from the results obtained by applying the Pearson correlation coeficient on the clean data versus the raw ones. However, a significant increase of the Pearson correlation coeficient is present for the clean versus entropy-reconstructed signal case with signal-to-noise ratio greater or equal to -12dB.
Even though the similarity between the clean and entropy-reconstructed signals increases with higher values of signal-to-noise ratio, it seems that for the electrodes that are usually afected by ocular artifacts the Pearson correlation coeficient remains generally low. For all the clean versus raw data cases, the mean similarity remains always lower than 0.9 and for the majority of the electrodes remains under 0.6.
Therefore, the proposed strategy is considered suficiently reliable for relevant IMF selection and signal reconstruction, having that its results do not deviate from the raw data or that are suficiently similar to the clean ones.
Having obtained a reliable method for relevant IMF selection, it is hypothesized that the entropy-selected IMFs could be eficiently used to reconstruct simulated trials while suficiently maintaining the intrinsic EEG brain dynamics.
As previously introduced, having that the proposed strategy is modeled on the one described by Dinarès-Ferran et al. [19] and that considers a BCI experiment, the EEG Motor Imagery BCI dataset has been used for testing.
The procedure has been computed on each subject and again the MEMD has been applied for each trial separately. Notice that the final goal is to discriminate the left (LW) from the right (RW) wrist MI, which could be applied to control a rehabilitation system.
Firstly, random trials were substituted by artificial ones. These trials were obtained by unique combinations of relevant IMFs selected through the entropy criterion and belonging to diferent original trials. Remind that corresponds to the overall maximum number of IMFs selected by the entropy criterion. The artificial trials were then reconstructed by summing the selected IMFs.
To reproduce Dinarès-Ferran et al. [19] testing, 2.50, 5.00, 7.50, 10.00, 12.50, 25.0, 37.50, 50.00% of trial substitutions were performed.
The power spectral density was extracted for each electrode through Morlet wavelet convolution [44]. This feature extraction follows the time-frequency image representation computation, but as a final step, the power data is integrated in the frequency range of interest. Two rhythms were considered separately, i.e., the and frequency bands, obtaining a total of 38 features. These rhythms have been chosen, due to the presence of MI tasks (Section 1). The feature extraction has been restricted on the signal portion during which the MI task is performed to mimic Dinarès-Ferran et al. [19] experimental setting.
Finally, a linear discriminant analysis classifier has been applied. For each subject the first run has been used as the training set and the second run as the test set.
As a first analysis, Table 2 reports the median error rates for both the RW and LW conditions after having applied linear discriminant analysis 100 times on the original and reconstructed data.
Trying to mimic the analysis given by [19], the error rate is here intended as the percentage of predicted values that have been wrongly classified for each class.
The results obtained by Dinarès-Ferran et al. [19] (row DF of Table 2) have been reported for completeness, however notice that their error rate evaluation is based on all the signal samples and that the features are extracted through common spatial pattern application. The remaining table rows present the results obtained by considering the runs in their original form (row OO), and the entropy-reconstructed data of run 1 as the training set and the original data of run 2 as the test set (row RO). This last test has been conducted trying to mimic a real-time scenario, during which previously analyzed data (e.g., BCI training phase) may be exploited to predict new unseen data (e.g., BCI translation phase).
Firstly, notice that the results obtained by the proposed strategy seem to be more balanced compared to the ones reported by Dinarès-Ferran et al. [19]. Secondly, the RO results have been used for comparison with the artificial trial substitution results, which are reported in Table 3, having that their values are comparable to the ones obtained for the OO test.
Notice that the field AT (%) refers to the percentage of trial substitutions balanced between the RW and LW conditions. Therefore, row 1 (0.00%) corresponds to the RO results presented in the last row of Table 2.
Moreover, it can be observed that the results vary from subject to subject. In fact, subject S01 may be considered a good MI task performer, having that in the RO case the error rates are 2.50 and 0.00 for the RW and LW task, respectively and thus complying with what has been stated in Section 1: a person is good in performing MI tasks when he/she can accurately imagine the movement for at least the 70% of the task repetitions.
Considering a less stringent constraint, S07 may be also considered good in the MI experiment. Instead, the remaining subjects seem to have some dificulties performing the MI tasks. Analyzing S01 and S07, besides the 37.50% and 50.00% substitutions performed on S01’s trial, it can be noticed that the error rates remain stable or improve. Concerning the remaining subjects, the error rates are generally not improved. However, these error rates become more balanced between the conditions and for S03 and S04 there seem to be a decrease in the error rate values for some substitution percentages.
Therefore, to ensure that the results obtained with the trial substitutions are coherent with the original results, a double Median Absolute Deviation (MAD) [45] has been applied to detect Median error rates (%) obtained by applying 100 times the linear discriminant analysis classifier on the right (RW) and left wrist (LW) motor imagery. if the median results obtained on the original trials could be considered outliers in respect to all the 100 results obtained for each trial substitution.
Notice that if more than the 50% of the classification results are equal, the MAD is 0. Table 4 reports the outliers detected by double MAD application, with the following interpretation: (i) if a cell contains 0 MAD, it means that the MAD is 0, (ii) if a cell contains original, it means that the result obtained on the original trial is considered an outlier in respect to the results obtained on the artificial trial substitution, and (iii) if a cell contains a non-zero number, it means that the double MAD detected that specific number of outliers.
Analyzing Table 4, the original trial result seems to appear as an outlier in a suficiently limited number of cases. The proposed strategy results unreliable for S02’s RW condition, otherwise it results eficient especially when making few substitutions (2.50 to 5.00%) or a greater number of substitutions (25.00 to 50.00%). The overall number of outliers seems also to be fairly low.
Making a final evaluation of the results achieved by the trial substitution through the proposed artificial trial generation, the observation given by Dinarès-Ferran et al. [19] is confirmed: for subjects that naturally perform better the MI tasks, the strategy is generally more efective. In fact, the reported error rates generally remain stable or slightly increase for the other subjects. This efect could be due not only to the dificulties a user may face in performing the MI task which could lead to unreliable trials for a control system, but also to the presence of noisy data.
Therefore, a further development of the trial simulation could be represented by the identification of faulty trials in respect to the experiment of interest. In fact, these trials could deteriorate the overall classification performances and by removing them the trial recombination could benefit the data generation procedure.
Moreover, a BCI system could benefit from the faulty trial detection not only intended as noisy trials but also as unreliable trials. In fact, understanding immediately if an elderly person has some dificulties in performing the MI task could provide a better BCI training phase by giving preciser feedback to the subject him/herself and thus increase the task success and decrease subjects’ possible frustration.
As a final remark, the proposed methodology seems however to be not extremely faulty when dealing with possibly unskilled subjects. Thus, the performed data substitution may represent a good solution to the EEG data dimensionality problem, providing results that do not deviate excessively from the original ones to train a BCI system.
This work has provided a brief overview of BCI systems based on motor imagery and electroencephalography to enhance elderly people rehabilitation procedures.
A novel strategy to process the EEG signals before inputting them to the BCI system has been proposed to provide more reliable data without requiring long experimental sessions. In fact, having the possibility of producing artificial trials that are coherent with the natural brain dynamics can benefit the training phase of a BCI, which usually requires a long time to have a precise subject profile and thus guarantee a correct control of the system. By decreasing the training time, the BCI tasks should also become less demanding both physically and mentally for an elderly patient, who could feel more engaged and less stressed by the training procedure.
Therefore, the EEG signal decomposition by means of MEMD and the relevant IMFs selection through a newly defined entropy criterion have been applied to 2 datasets.
The proposed approach testing revealed that the signal reconstruction by using only the relevant IMFs is reliable and that the recombination of the relevant IMFs can be eficiently used for artificial trial generation. However, we have noticed that the proposed strategy is particularly suitable for trial substitution of signals recorded from good MI performers, in line with DinarèsFerran et al. observations.
Therefore, we hypothesize that detecting faulty trials in terms of noise and unsuccessful MI performing, may benefit the artificial trial generation as well as the BCI training phase during which an elderly user may efectively improve his/her brain plasticity.
Future works will focus on these directions and on exploiting the trial generation strategy for data augmentation.
In fact, many data augmentation approaches have been proposed in the literature [
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