## 3 Experiment
### Classification Features Extraction
#### 3.3.1 Statistical-Based Features  
For the statistical-based feature vectors (SFV), for each signal channel in each data sample, we calculated five types of vectors. These are mean vectors, the standard deviation vectors, variance vectors, median skewness vectors and kurtosis vectors. All SFVs were collected by the statistic feature vectors, i.e., (see Equation (3)):  
\[SFV=[\mu_{SFV},\sigma_{SFV},Var,Sk_{SFV},Kur_{SFV}] \tag{3}\]  
where \(\mu_{SFV}\) are the mean vectors, \(\sigma_{SFV}\) are the standard deviation vectors, \(Var\) are variance vectors, \(Sk_{SFV}\) are the median skewness vectors, \(Kur_{SFV}\) are kurtosis vectors. 1. Mean vectors Mean vectors are a collection of the mean of the normalized sample in each signal channel and defined as : \[\mu_{SFV}=[\bar{x}(i)_{EDA},\bar{x}(i)_{temp},\bar{x}(i)_{BVP},\bar{x}(i)_{HR} ]^{T},\ \ \ \ \ i=1,2,\ldots,N\] (4) where \(\bar{x}(i)_{EDA}\) is the mean of the EDA data for each sample, \(\bar{x}(i)_{temp}\) is the mean of body temperature data for each sample, \(\bar{x}(i)_{BVP}\) is the mean of the BVP data for each sample, \(\bar{x}(i)_{HR}\) is the mean of heart rate data for each sample, and \(N=40\) is the number of the data samples. 2. Standard deviation vectors The standard deviation vectors \(\sigma_{SFV}\) are defined in the following (see Equation (5)): \[\sigma_{SFV}=[S(i)_{EDA},S(i)_{temp},S(i)_{BVP},S(i)_{HR}]^{T},\ \ \ \ \ i=1,2,\ldots,N\] (5) where \(S(i)_{EDA}\) is the standard deviation of the EDA data for each sample, \(S(i)_{temp}\) is the standard deviation of body temperature data for each sample, \(S(i)_{BVP}\) is the standard deviation of the BVP data for each sample, \(S(i)_{HR}\) is the standard deviation of heart rate data for each sample, \(N=40\) is the number of data samples. 3. Variance vectors Variance is the average of the squared differences from the mean. It is the square of the standard deviation. In a similar manner as above, variance vectors are calculated and represented as \(Var\). It can be calculated using the following (see Equation (6)): \[Var=\sigma_{SFV}^{2}=[S(i)_{EDA}^{2},S(i)_{temp}^{2},S(i)_{BVP}^{2},S(i)_{HR} ^{2}]^{T},\ \ \ \ \ i=1,2,\ldots,N\] (6) where \(\sigma_{SFV}\) is the standard deviation of each signal for each sample defined in Equation (5). 4. Median skewness vectorsMedian skewness is also called [PERSON]'s second skewness coefficient. It is defined as [20]):  
\[Sk_{2}=\frac{3(\mu-\
u)}{\sigma} \tag{7}\]  
where \(Sk_{2}\) is the [PERSON]'s second skewness coefficient, \(\mu\) is the mean of the data, \(\
u\) is the median, and \(\sigma\) is the standard deviation of each signal in each file. This formula compares the mean to the median in a precise way and shows how many standard deviations apart they are [21]. The median skewness vectors \(Sk_{SFV}\) are the collection of median skewness of each signal channel for each sample:  
\[Sk_{SFV}=[Sk_{2}(i)_{EDA},Sk_{2}(i)_{temp},Sk_{2}(i)_{BVP},Sk_{2}(i)_{HR}]^{T},\ \ \ \ \ i=1,2,\ldots,N \tag{8}\]  
where \(Sk_{2}(i)_{EDA}\) is the median skewness of the EDA data for each sample, \(Sk_{2}(i)_{temp}\) is the median skewness of body temperature data for each sample, \(Sk_{2}(i)_{BVP}\) is the median skewness of the BVP data for each sample, \(Sk_{2}(i)_{HR}\) is the median skewness of heart rate data for each sample, \(N=40\) is the number of samples. 5. Kurtosis vectors  
Kurtosis is an important descriptive statistic of data distribution. It describes how much the tails of a distribution differ from the tails of a normal distribution. Is is defined as the fourth central moment divided by the square of the variance [22; 23]:  
\[Kurtosis(X)=E[(\frac{X-\mu}{\sigma})^{4}]=\frac{\mu_{4}}{\sigma^{4}} \tag{9}\]  
where \(X\) is the dataset, \(Kurtosis(X)\) is the kurtosis value of the normal distribution for the dataset, \(\mu_{4}\) is the fourth central moment, \(\mu\) is the mean (defined in Equation (4)), and \(\sigma\) is the standard deviation of each signal in each sample defined in Equation (5).