## 2 Related Work  
### Preliminary  
SVM algorithm is suited for extreme datasets separated by a Hyperplane. Thus, SVM can be defined as a frontier which best segregates two classes. If it does not have unoptimized decision boundary, it could result in greater misclassification on new data. Support vectors are defined as the data points that the margin pushes up against or points that are close to the opposing class. Therefore SVM algorithm implies that only these support vectors are essential, whereas other training examples are ignorable [18] as seen in Figure 2.  
Let \(x^{+}\) be the shortest distance to the closest positive point and \(x^{-}\) be the shortest distance closest to the negative point, then we have a margin \(M\) of the separating hyperplane which is the distance between \(x^{+}\) and \(x^{-}\). The line (decision boundary) that segregates the two classes is referred as the Hyperplane. SVMs are used in multidimensional dataset and the data are referred to as vectors. In LSVM, classes are linearly separable but in those cases that the data are not linearly separable, a function is used to transform the data to high dimensional space [19]. The process is computationally expensive and kernel trick is used to reduce the computational costs [20]. Therefore, such a function that takes inputs as vectors in the original space and returns the dot product of the vectors in the feature space is called a Kernel Function also referred as Kernel Trick [12]. Using a kernel function, one can apply the dot product between two vectors that every point is mapped into a high dimensional space via some transformation, and using it to transform a non-linear space into a linear space. Aforementioned, some of the popular kernel types are as follows:  
* Polynomial Kernel of degree \(d\) corresponds to a particular degree \(d\) expansion of the features \(K(a,b)=(1+\sum_{j}a_{j}b_{j})\). Data on the direction of a data point \(x>0\), the larger the values of \(x\) shows a corresponding increase on the Gram Matrix \(K(X,X^{\prime})\). Studies have shown polynomial kernels have been applied to overcome challenges in various fields, such as person re-identification problem by correctly matching person image from a set of gallery of person images in the field of machine learning [21], new malware detection in cyber-security [22], big data classification [23], facial recognition on multiple face images [24], human body movement and posture recognition in the medical field [25], facial emotion recognition [26] and classification of human brain images against mental health conditions in medical imaging [27]. * Radial Basic Function (RBF Kernel), also known as the Gaussian Similarity Kernel defined as \(K(a,b)=\exp(-(a-b)^{2}/2\sigma^{2})\). It results in high values near the point of \(x\) and falling off as a Gaussian with some spread \(\sigma\) as it moves away from point \(x\). Here, the parameter \(\sigma\) can be  
Figure 2: KLSVM—A correlation-based high-dimensional multi-category data classification model with a 3D hyperplane. The support vectors around the hyperplane are consequential training examples under SVM classification. used to control over an under-fitting for \(\sigma\) chosen very large, all the data will look similar to any particular test point. This addition to the value \(R\) in Dual Optimization (discussed later in Section 3.6.2) which effectively controls the severeness of the penalty for misclassified points.