Assessment of learning a new skill using nonlinear and spectral features of EEG

The goal of this paper was to assess the impact of learning a new skill on several electroencephalographic (EEG) measurements. In addition, it intended to examine the active brain regions associated with learning. To this effect, changes in brain activity during the pre- and post-learning task were investigated using EEG power spectral density (PSD) and nonlinear features. The evaluated task was learning to type using the Colemak keyboard layout in a twelve-lesson training. 10 participants with a mean age of 29.3 ± 5.7 were included in the experiment. For the first time, Fractal dimension, approximate entropy, and Lyapunov exponents were extracted from a 9-channel EEG signal to characterize brain dynamics. In addition, the PSD of various EEG rhythms was estimated. To identify statistically significant changes in the EEG characteristics, as well as to determine the prominent channels, the t-test was performed. Our results showed maximum EEG power in Beta and Gamma waves; however, the most differences in the power distribution belonged to the Beta band. Among nonlinear features, entropy showed a significant difference in 70% of the EEG channels. This has mainly occurred in the F3, Fz, C3, Cz, POz, and P4 electrodes. Taken together, the results of this study pave the way to evaluate brain dynamics and actively involved areas in pre- and post-learning tasks.

process that brings changes in the neuron's synaptic levels and leads to creating new memory formation [2]. Electroencephalography (EEG), which provides biological information, is widely used as a performance index of information processing that takes place in the brain. Therefore, Changes in the EEG occurring during various mental activities in man have been the subject of many investigations since the beginning of EEG research. So far, spectral and time-frequency analysis methods have been widely used [3][4][5][6]. The first link between the active phase of learning and the non-synchronization of EEG was made by Thompson and Obrist [7], who tried to explain the correlation between EEG and learning. They obtained significant EEG changes during verbal learning compared to non-learning control conditions, while an over-learning condition resulted in a slight return to control levels. Some studies have worked on postlearning recall [2,8]. Recently [2], memory recall has been studied, reported an increase in theta and gamma power in the frontal and temporal regions for correct recall. Furthermore, in [8], recovered memory was assessed after two months. In some studies, event-related potentials (ERP) and their changes in brain signals have been investigated during learning tasks [9,10]. Ciechanski and colleagues examined the effect of stimulating Transcranial direct-current stimulation (tDCS) during learning surgical skills [11]. Everyone in it improved their individual skills in surgery [12,13]. The literature review revealed that the application of nonlinear methods for examining brain signals during learning is rarely performed. Recently, Arab et al. [14] inquired about the dynamics of learning and the process of memory. They examined the dynamics of EEG during learning using Higuchi's fractal dimension. Their results showed that the growth of the learning rate of the subjects is proportional to the reduction in the EEG fractal dimension. Research on the effect of learning on brain changes using nonlinear features is inadequate and limited. On the other hand, one of the hallmarks of time series derived from biological systems is their nonlinearity. Therefore, we propose the use of nonlinear analysis methods for evaluating EEG dynamics in acquiring a new ability. In short, in addition to the power spectral density (PSD) of different brain rhythms, we analyze five nonlinear features as the first step in finding the relationship between learning and brain dynamics. These features include the fractal dimension (Katz, Higuchi, and Petrosian), the approximate entropy, and the Lyapunov exponent. Then, a topographic map of each feature is presented to show prominent EEG regions. Additionally, a significant difference between preand post-learning tasks is evaluated for each feature using a statistical test. In our case, the t-test is performed. Figure 1 schematically shows the process of our work in the current research.

Participants and task procedure
In the current study, the open-access EEG time series available at IEEEDataPort [15] were analyzed. Ten volunteers, including six females and four males, participated in this experiment. All of them were right-handed, with a mean age of 29.3 ± 5.7 years. The experiment was training through a series of twelve daily lessons to type in a computer using the Colemak keyboard layout, an alternative to the QWERTY and Dvorak layouts. The guideline available at "colemak.com/Typing lessons" was used for lessons. In this experiment, participants were asked to repeat each of the lessons five times (while resting intervals of two minutes were offered in between) [15]. The trials were done in a sound-proof room to separate volunteers from disruptions. All the experiments were carried out at the same hour of the day. The participants did not have any additional training. To measure participants' ability to type, repetitions were measured with a stopwatch. The measured time included the time used to spell all the words in the lesson correctly and the time it took to clear and rewrite the words due to any mistakes [15].

EEG recordings
EEG signals were recorded by the B-Alert X10 wireless system from Advanced Brain Monitoring, Inc, for four sessions. The system included nine EEG sensors with fixed gain referenced to linked mastoids and located at mid-line and lateral positions. The electrode positions were determined based on the international 10-20 reference system; at F3, Fz, F4, C3, Cz, C4, P3, POz, and P4. All data were acquired at a sampling frequency of 256 Hz. Additionally, the signals were bandpass filtered with a fifth-order Butterworth with cutoff frequencies at 0.1 and 100 Hz [15]. EEG measurements were obtained during the typing task and its repetitions in the fourth, eighth, and eleventh lessons. In the current study, we assessed the signals of the first and the last sessions as "pre-learning" and "post-learning" experiments.

EEG data analysis
The relevant information extraction from raw signals is a critical step in the EEG analysis, owing to its direct influence on the results. This study used several nonlinear and spectral-based features to analyze the data. We aimed to identify statistically significant changes in PSD of various EEG rhythms and nonlinear features at pre and post-learning stages for nine brain channels. All analyses of this article have been done using MATLAB software.

Feature extraction
This article evaluated several nonlinear features, including the fractal dimensions (FD) features using Katz, Higuchi, Petrosian, approximate entropy, and largest Lyapunov exponents. These indicators were introduced to describe the chaotic behavior of the EEG signals [16]. We also calculated the power spectrum density (PSD) of the 5 EEG frequency bands. The calculated EEG frequency bands were 1-2 Hz for δ, 3-7 Hz for θ , 8-12 Hz for α, 13-29 Hz for β, and 30-40 Hz for γ . The descriptions of the features are provided in the following subsections.
Katz Fractal Dimension: There are different methods for estimating the fractal dimension. One of the efficient algorithms is the Katz algorithm. This method was introduced in 1988 for calculating the fractal dimension. Here, the calculation of the fractal dimension (FD) is performed as follows [17]: where N + 1 is the size of the data sequence. The diameter of the data is shown by d, and the summation of the intervals between sequential points is demonstrated by L. Higuchi Fractal Dimension: Suppose a time series x(1), x(2), …, x(N) as an input. The following time series is achieved [17]: For n 1, 2, 3, …, k, where n is the first sample and demonstrates the integer part of the series. l n (k) is given by: where N is the number of samples in the time series, and Higuchi dimension slope is the best line approximated with the least square error method for log(l(k)) according to log k [14]. Petrosian Fractal Dimension: For calculating the fractal dimension, the alternative algorithm is the Petrosian algorithm. This method is offered by Petrosian [18]. In this algorithm, new time series is created by sequentially subtracting the instances of a time series. Then, value 1 is allocated to positive samples and − 1 to negative samples. Consequently, the number of tokens that change in the new time series is equal to the number of local extremes in the original time series. The value of FD in the above method is calculated as follows: D log n 10 log n 10 + log 10 (n/(n + 0.4N )) (4) where N and n are the numbers of the sign changes and the number of samples in the binary time series, respectively. It can be said that the Petrosian method is faster and more sensitive to noise because the number of sign changes is important in this algorithm. In contrast, in the Katz algorithm amplitude differences are essential to estimate the FD. Approximate Entropy (ApEn): It is a common technique for quantifying the amount of regularity and the unpredictability of variations over time series data. This algorithm is calculated as follows [19]: where d is the interval between vectors x n (i) and x n (j), and N is assumed as the number of samples. m is data length, and r f is filtering level. Parameters m and r f are positive real integers. Largest Lyapunov Exponent (LLE): It is an important quantifier for detecting and describing chaos produced by a dynamic system. If the LLE of a system is > zero, the system has a chaotic behavior. LLE of a time series is specified according to the developmental rate of the differences between consecutive samples (not necessarily being consecutive). LLE is calculated as follows [20,21]: where d 0 is the interval between consecutive samples in the primary time. And d n is the consecutive interval in nth time.
Power spectral density: The PSD was computed using the FFT method and Kaiser window. Here, it was calculated with 50% overlapping (256 points) and kept the nfft as 512 points [15].
The above-mentioned features were extracted from the data acquired by 9 sensors. The total number of computed features for each session of pre-and post-learning was 90 (9 sensors) × (10 features).

Two-sample t-test
A T-test was applied using Matlab to show a statistical difference in the features. More precisely, to investigate if the features from the measurements at the last trial are significantly different compared to those from the first, we performed paired t-tests. The statistical tests were carried out for every nine measures of EEG channels.

Results
Different nonlinear EEG measures namely Katz's fractal dimension, Higuchi fractal dimension, Petrosian fractal dimension, Approximate Entropy, and Lyapunov exponents were extracted. Additionally, the PSD of different EEG frequency bands was extracted. The results are shown in the following subsections.

Spectral features
The variation of PSD of alpha wave in different EEG electrodes for pre-and post-learning is shown in Fig. 2. To understand the changes correctly, the figures show the values of 10 log 10 (PSD). Besides, its topographic map over the scalp has been shown in the figure. Figure 2 shows that the PSDs of Alpha waves in pre-learning trials are higher than those in post-learning trials for all electrode positions. Moreover, the highest values of Alpha power were observed  in the F3 electrode for the pre-learning session. In contrast, its minimum values were concentrated in POz and P4 for post-learning trials. The greatest difference between the values of this feature between the pre-and post-learning test was observed in F3, POz, and P4. Figure 3 illustrates the variations of the PSD of Beta wave in different electrodes, as well as the distribution of the features across the scalp in pre-and post-learning tasks. Figure 3 shows higher Beta values in pre-learning compared to the post-learning test in all brain sites. The lowest Beta values were found in the POz and P4 for post-learning, and the highest Beta values were in F3 for the pre-learning task. The topographic maps also show different Beta distributions over the scalp for two tests; i.e., pre-and post-learning.
For the before and after learning task, the discrepancies of the PSD values for theta bands in different electrode positions, as well as its topographic maps are presented in Fig. 4.
Higher PSD values of the Theta wave were achieved for the  pre-learning task, where the maximum values were observed in F3. The PSD values for the Theta band were differently distributed over the scalp for the two tests. In contrast, the lowest values were detected in the POz and P4 channels for post-learning assignments. Figure 5 illustrates the PSD variations for Delta's waves and their distributions across the scalp in pre-and postlearning conditions. The results show that PSD values of the Delta band are higher in pre-learning compared to postlearning conditions. The highest/lowest amount of the feature was in the F3/ POz and P4, respectively. Figure 6 describes the variation and distribution of PSD of the Gamma frequency band over the scalp in the two tasks. As shown in Fig. 6, the PSD values of Gamma waves are different in the two classes. In some channels, the PSD of the two groups fluctuates in the same range. However, the maximum and minimum PSD values of Gamma were in the F3 for  Comparing the PSD values of different EEG frequency bands (Figs. 2, 3, 4, 5, 6) reveals that the maximum EEG power was in Beta waves, especially before learning tasks. The second highest power of EEG occurred for Gamma bands. The most active EEG electrode was F3 in all frequency bands before the learning procedure, and the lowest PSD measures were detected in POz after learning the task.

Nonlinear measures
For before and after learning sessions, the discrepancies of the Katz fractal dimensions in different electrode positions, as well as the topographic maps are offered in Fig. 7. Higher PSD values for Katz's fractal dimensions were achieved for  POz and P4 in the post-learning task. The Katz fractal dimensions were differently distributed over the scalp for the two tests. Feature values oscillate in the same range in all regions of the head before learning. However, after learning, the maximum intensity of the Katz fractal dimension is concentrated in the POz and P4 regions. Figure 8 illustrates the variations of the Higuchi fractal dimensions in different electrodes, as well as the distribution of the features across the scalp in pre-and post-learning tasks. Figure 8 reveals higher Higuchi's fractal dimensions in F3, POz, and P4 for the post-learning sessions compared to the pre-learning test. The lowest values of this feature were found in F3 for the pre-learning task. Figure 9 describes the variation and distribution of Petrosian fractal dimensions over the scalp in the two tasks. As shown in Fig. 9, the patterns of alteration in Petrosian fractal dimensions are different in the two classes. In almost all channels, the Petrosian fractal dimensions of the pre-learning  These changes were obviously perceived in C3, Cz, POz, and P4. The lowest measure was achieved for C3 and C4, and the highest values of the feature were obtained in POz and P4. Figure 10 provides the variations of approximate entropy and its distribution over the scalp in two groups of pre-and post-learning. Figure 10 reveals different values of entropy in pre-and post-learning tasks for all scalp areas. In some channels, the EEG entropy of the pre-learning class has the highest value, like C3 and Cz. In contrast, in some other electrode positions, the highest entropy measures were achieved for the post-learning groups, like F3, POz, and P4. The topographic maps reveal that the entropy was poorly distributed in frontal/central brain regions for the pre-/post-learning group.
The variation of Lyapunov exponents in different EEG electrodes for pre-and post-learning is shown in Fig. 11. Besides, the topographic maps over the scalp for the groups have been presented in the figure. The results (Fig. 11) show  Table 1 illustrates the p values of nonlinear and frequency features for pre-and post-learning styles and 9 EEG electrodes. The significant differences were confirmed by paired t-tests. The most differences in the power distribution within the five frequency bands belong to the Beta band. After that, alpha, Delta, and Theta bands showed the most significant differences. The lowest significant difference between preand post-learning was observed in the Gamma band. This was mainly seen in the channels located in the frontal, central and parietal lobes (F3, Fz, C3, Cz, POz, and P4). Significant differences were also obtained for nonlinear features. Using entropy, a significant difference was observed between the two groups in 70% of brain channels. After entropy, the most difference between the two groups was revealed using the Petrosian fractal dimensions. It is noteworthy that these nonlinear features also activated the same regions that frequency features enabled, which is clearly visible in the parietal area. Relevant sensors in the 10 features are collected in Table  2. As you can see in Table 2, the P4 and POz sensors have known as active sensors in all features.

Discussion
The main purpose of this study was to statistically analyze PSD and some nonlinear features to enhance the ability to describe the time-changing dynamics of the learning process. In our results, the highest PSD values were observed in beta rhythms (especially before learning tasks) and gamma, which had a significant decrease after learning. Our findings are consistent with previous reports of changes in frequency rhythms during learning tasks [15,22]. However, our results are not in the line with some reports. For example, in [5], in addition to decreasing gamma, an increase in the theta band was also reported. Additionally, an increase in beta and gamma in the anterior regions has been reported [4]. This difference for active areas may be due to different learning tasks. For instance, in [4], learning a sport has been used as a new ability. In [23], it has been shown that gamma and beta connectivity increased for the complex task as compared to the simple task, while theta connectivity decreased after training.
Since learning to type can be considered as a motorsensory task, it can be said that the negative reduction in EEG rhythms after the learning task is associated with an increase in motor skills [24]. In addition, in the majority of the features, sensors have enabled, which are located in the frontal, central and parietal areas cover their location in the brain areas associated with focusing and learning a new skill (See Table 2).
Usually, different factors such as emotions, motivation, anxiety, attention, and stimulation can affect brain function [25]. However, in later studies, the physiological effects of learning should be carefully considered. In addition, different learning protocols such as the environment, the number of repetitions and the subject to be learned can be effective factors in disagreements in results.
As far as the authors know, this is the first study to use five nonlinear features to analyze changes in electroencephalogram waves during learning. Our results showed that the use of nonlinear features can be used to analyze and describe EEG signals. The use of nonlinear analysis for EEG has provided useful information about complex brain approaches that cannot be evident by traditional temporal and spectral analysis. So far, most studies have used traditional features (i.e., spectral, time, spatial or time-frequency features) to analyze the data [3,6,8,26]. More recently, in one study only, Arab et al. [14] examined the dynamics of changes before and after learning using the Higuchi fractal dimension of electroencephalographic waves. They believed that increasing the learning rate was proportional to reducing the fractal dimension of the waves. Our results showed a significant change in the F3, C3, Cz, POz, and P4 electrodes, which is clearly noticeable in the POz and P4 electrodes (see Figs. 9, 10, 11). These changes also confirmed the activation of the frontal, central, and parietal areas. However, to confirm these results, further research should be performed. For future work, it is suggested that in addition to examining more nonlinear features, an intelligent algorithm be used to distinguish between pre-and post-learning modes. Basically, people's abilities to learn different tasks are different. Therefore, comparing age and gender during the learning process can be useful in the upcoming studies. In this study, a comparison of nonlinear and frequency features pre-and post-learning (first and last training session) was performed.
Exploring learning in all sessions should be investigated in future. The present study may have not provided complete results of the learning process, but it paves the way for future research.