## 4 Extraction of Diverse Features  
This work extracts the following features from the input data. A brief explanation of the features is as follows:  
_Kurtosis_[20]: \"It is a measure that identifies whether the data are light-tailed or heavy-tailed and related to the normal distribution\". Datasets with smaller kurtosis offer minor outliers or tails. In addition, the datasets with high kurtosis provide heavy outliers or tails. The arithmetic formulation of kurtosis KS for univariate data such as \(Y_{1}\),\(Y_{2}\),... \(Y_{k}\), is articulated in Equation (1).  
\[KS=\frac{\sum_{i=1}^{k}\Bigl{(}Y_{i}-Y\Bigr{)}^{4}/k}{\Gamma^{4}}. \tag{1}\]  
The standard deviation is calculated by \(k\) value available in the denominator whilst computing the kurtosis.  
_Variance_[21]: It is defined as the mean squared disparity amongst every data point and the center of distribution computed by mean.  
_Moment_[22]: It is the instant probability distribution along with arbitrary variables in probability theory and statistics. It is the ordinary value of a specified integer power difference of the arbitrary variable from the mean. The moments with higher order are related to the shape and spread distribution of the location. The \(m^{th}\) the moment linked to the central moment of a real-valued arbitrary variable \(Q\) is the quantity \(Q_{m}=eo[(Q-eo[Q]^{m})]\), in which, \(eo\) stands for the expectation operator. The \(m^{th}\) moment regarding the mean \(Q\) is portrayed for a continuous UPD with \(f(y)\) PDF. The moment is given in Equation (2).  
\[Moment=Q_{m}=eo\biggl{[}\biggl{(}Q-eo[Q]^{m}=\int_{+\infty}^{-\infty}\Bigl{(} y-Q\Bigr{)}^{m}f(y)dy^{\prime}\biggr{)}\biggr{]}. \tag{2}\]  
_MI Features:_ It is defined as the calculation of exchanged information among two ensembles of random variables \(N\) and \(Z\) It is formulated as revealed in Equation (3), in which, \(\rho\) signifies probability.  
\[MI=\sum\rho(N,Z)log_{2}\frac{\rho(N,Z)}{\rho(N).\rho(Z)}. \tag{3}\]  
_Symmetrical uncertainty:_ SU computes the features depending upon evaluated SU correlation metrics amongst the class and feature. The MI is calculated as in Equation (4), wherein, MI implies MI, \(fe\) stands for features, \(cl\) stands for class, and \(P\) implies probability function. Further, SU is formulated as in Equation (5), in which \(En\) refers to the entropy function.  
\[MI(fe,cl)=\sum P(fe,cl)log_{2}\frac{P(fe,cl)}{P(fe).P(cl)} \tag{4}\]  
\[SU(fe,cl)=2(MI(fe,cl))/(En(fe).En(cl)). \tag{5}\]  
_IGR [23]:_ It is the ratio between information gain \((IG)\) and split information \((SI)\) value as shown in Equation (6), where \(K\) refers to a random variable, \(b\) refers to an attribute and in equation (7) \(U(ti)\) refers to the number of times \(ti\) occurs, \(U(t)\) refers to entire event counts and \(t\) refers to event sets.  
\[IGR(K,b)=\frac{IG(K,b)}{SI(K)} \tag{6}\]  
\[IGR(K,b)=\frac{\sum_{i=1}^{n}P(K)\log P(K)-\biggl{(}-\sum_{i=1}^{n}P(K|b)\log P (K|b)\biggr{)}}{-\sum_{i=1}^{n}\frac{U(ti)}{U(t)}*\log_{2}\frac{U(ti)}{U(t)}}. \tag{7}\]Relief Features:It was modeled for application to binary classification issues with discrete or numerical features. It is modeled as in Equation (8), where \(E_{i}\) points out the feature vector, the closer same class instance is termed \"\(nearHit\)\", and the closer different class instance is termed \"\(nearMiss\)\".  
\[R_{i}=R_{i}-(E_{i}-nearHit_{i})^{2}+(E_{i}-nearMiss_{i})^{2}. \tag{8}\]  
The derived features are signified by \(Fe\), which are then subjected to hybrid classification.