# Evaluation of Emotions from Brain Signals on 3D VAD Space via Artificial Intelligence Techniques
## 2 Materials and Methods
### Attributes  
Brief definitions of the attributes used are given below. The sample mean is the numerical average of the data. Variance can be defined as the average of the square of the differences from the mean [22]. The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of the values in the observation, while the mode is the value that occurs most frequently, and the median is the value of the variable that divides the distribution into two parts [23]. Shannon entropy is proposed to measure how the signal information can be quantified with absolute precision [24]. Skewness is a 3 rd order moment, which shows asymmetry of the data distribution about the mean, while kurtosis is a 4 th order moment indicating the major peaks in the signal's time domain [25]. If s(t) is a signal, the signal power is s\"(t), and the signal energy is [26]  
\[E=\int_{-\infty}^{\infty}s^{2}(t)dt \tag{1}\]  
The interquartile range (IQR) is a statistical distribution measure, and it is defined as the difference between the 3 rd-1 st quartiles (Q3-Q1) [27]. The mean absolute deviation (MAD) is defined as the average of absolute distances from the data mean. For n number of observations (x\({}_{1}\), x\({}_{2}\)..., x\({}_{n}\))  
\[MAD=\frac{\sum_{k=1}^{n}|x_{i}-\overset{-}{x}_{i}|}{n} \tag{2}\]  
where \(\overset{-}{x}\) is the mean of the data [28]. The mean frequency (MNF) is defined as the sum of the product of the signal power spectrum and the frequency divided by the total sum of the power spectrum. \[\text{MNF}=\sum_{j=1}^{M}f_{j}P_{j}/\sum_{j=1}^{M}P_{j} \tag{3}\]  
Pj is the power spectrum at a frequency bin j, fj is the frequency of the spectrum at a frequency bin j, and M is the total number of frequency bins [29]. The median frequency (MDF) is a frequency at which the signal power spectrum is divided into two regions with equal integrated power [29]. \[\text{MDF}=\sum_{j=1}^{M}P_{j}=\sum_{j=MDF}^{M}P_{j}=\frac{1}{2}\sum_{j=1}^{M }P_{j} \tag{4}\]  
Figure 5: Class placements on VAD space (here, a 0-midpoint on VAD space indicates 5-midpoint for the 1–9 scale, and values below and above this scale also indicate the same logical separation related to the midpoint). The correlation dimension (CD) is a method for determining the correlation of a time domain signal sampled uniformly. It is a method to determine the dimension of a nonlinear signal [30]. \[C(r)=\frac{2}{N(N-1)}{\sum_{(i\
eq j)}}\,\theta(r-|X(i)-X(j)| \tag{5}\]  
divided into two regions with an equal integrated power. Root mean square (RMS) is the square root of the mean square value, which is defined for a specific interval of time. RSSQ is the root sum of squares [31]. The power bandwidth (PBW) is defined as the measure of the frequency difference between the points where the spectrum falls at least 3 dB below the reference level [32]. The Hjorth parameters (HP), extracted by [PERSON] in 1970, are activity, mobility, and complexity. Activity can be defined as the information of the signal power; mobility is an estimation of the mean frequency; and complexity is the bandwidth, the change in frequency, or the standard deviation of the power spectrum. HPs are commonly used in biological signals and are suitable for non-stationary EEG signal analysis [25; 33]. \[Activity=Var(y(t)); \tag{6}\]  
\[Mobility=\sqrt{\frac{Var\Big{(}\frac{dy(t)}{dt}\Big{)}}{Var(y(t))}} \tag{7}\]  
\[Complexity=\frac{Mobility\Big{(}\frac{dy(t)}{dt}\Big{)}}{Mobility(y(t))} \tag{8}\]  
The Lyapunov exponent (LE) measures the exponential convergence or divergence by considering the exponent to be lower or higher than 0, respectively [24]. lyap_r indicates the largest LE, while lyap_e indicates the whole spectrum of LE, whose positive exponents indicate chaos and unpredictability. LE measures total predictability [34]. It is a strong chaos indicator if it has a positive value, and as it increases, chaos increases while predictability decreases.