## 3 Proposed Model
### Feature Extraction
#### 3.4.1 Statistical Features  
Statistics is an effective mathematical technique to perform technical data analysis. Statistics help us to get deeper and meaningful information along with the graphical visualization of data. Every person has unique feature values. Sometimes some feature values are very close but not exactly the same to each other. These features are genuine and unique to identify a writer. Here, we consider both time domain and frequency domain statistical parameters. For this, some statistical feature has been extracted from the sensor signal of handwriting dataset. Table 2 shows total of 20 features along with their corresponding statistical formulas. A brief explanation of these statistical features is given below:  
The mean is commonly known as the average which is the total of all the data values divided by the number of data points. We can understand the standard level of attributes from the mean value. Here, mean represents average value for writing attributes such as angle, pressure, axis value, etc. When the data is sorted in ascending or descending order then the middle value is known as median. The median is sometimes used as opposite to the mean when there are outliers in the sequence that might skew the average value. Standard deviation (SD) is a measure of how a set of data is spread out. A low SD states that the data is closely clustered around the mean or average while a high SD indicates that the data is dispersed over a wider range of values. Standard deviation is used to realize whether a specific data point is standard or unusual. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Features** & **Equation** & **Features** & **Equation** \\ \hline Mean & \(\mu=\frac{1}{N}\sum\limits_{i=1}^{N}x_{i}\) & Cross-Correlation & \(\rho_{ij}=\frac{X_{ij}}{\sqrt{c_{i}^{2}c_{j}^{2}}}\) \\ \hline Median & M = \(\left(\frac{2}{f}-f\right)\)(\(w\)) + \(L_{m}\) & Absolute Mean value & \(A_{m}=\mu(abs_{x})\) \\ \hline Maximum & MAX(M) & Shape Factor & SF = \(\frac{X_{mn}}{A_{m}}\) \\ \hline Minimum & Minimum MIN(M) & Energy & \(E=\sum\limits_{i=1}^{N}|x_{i}|^{2}\) \\ \hline Standard Deviation of & \(P_{sl}=\frac{\sqrt{\sum_{i=1}^{N}(P_{x}-P_{max})}}{N}\) & RMS Frequency & \(RMS_{fr}=\mu\Big{(}\sqrt{\big{(}frx_{1}^{2}\big{)}\ +\ frx_{2}^{2}\ +\ \cdots\ +\ frx_{n}^{2}\Big{)}}\) \\ \hline Skewness & \(P_{skw}=\frac{\sum_{i=1}^{N}(P_{x}-\overline{P})^{3}/N}{P_{sl}^{2}}\) & Peak to Peak & \(PPV=MAX(M)\ -\ MN(M)\) \\ \hline Kurtosis & \(P_{k}=\frac{\sum_{i=1}^{N}(P_{x}-\overline{P})^{4}/N}{(P_{sl}^{2})^{4}}\) & SRA & \(SF=\mu\Big{(}\sqrt[3]{abs}X\Big{)}\) \\ \hline Variance & \(\sigma^{2}=\frac{\sum_{i=1}^{N}(x-\overline{P})^{2}}{N}\) & Impulse Factor & \(i=\frac{x_{peak}}{x_{max}}\) \\ \hline Correlation Coefficient & \(\frac{n(\Sigma,x)}{\overline{n}\ \ \ }\) & Margin Factor & \(MF=x_{peak}/x_{sra}\) \\ \hline Root mean Square & \(\frac{X_{rms}=}{\sqrt{\frac{1}{N}(x_{1}^{2}\ +\ x_{2}^{2}\ +\ \cdots\ +\ x_{n} ^{2})}}\) & Energy Center & \(FC=\sqrt{f_{1}f_{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical Features from Pen-Tablet Sensor Data. Skewness is a measure of the degree of asymmetry of a frequency distribution. In our research, its value of skewness became as negative, positive or zero. A positive value indicates right-skewed, a negative value indicates left-skewed and zero-skewed indicates symmetric distribution. It helps to understand on which side of the data we need to work. Skewness is measured by using the average of attributes, and their standard deviation. Kurtosis is a measure of the peakedness of a distribution. Kurtosis generally represents a positive value. It is used as a measure of error or risk. A large kurtosis is represented with a high error and low indicates low error. Variance is used to determine how well the mean represents an entire set of data. In our research, the variances of several attributes are measured such as for pressure, angle, time, etc. Standard deviation and variance are related to each other.