Update support-vector-machine.md

contrib/machine-learning/support-vector-machine.md

@@ -1,12 +1,19 @@
+## Support Vector Machine
+
 Support Vector Machine or SVM is one of the most popular Supervised Learning algorithms, which is used for Classification as well as Regression problems. However, primarily, it is used for Classification problems in Machine Learning.
+
 SVM can be of two types -
 1. Linear SVM: Linear SVM is used for linearly separable data, which means if a dataset can be classified into two classes by using a single straight line, then such data is termed as linearly separable data, and classifier is used called as Linear SVM classifier.
 2. Non-linear SVM: Non-Linear SVM is used for non-linearly separated data, which means if a dataset cannot be classified by using a straight line, then such data is termed as non-linear data and classifier used is called as Non-linear SVM classifier.
 
 Working of SVM - The goal of SVM is to find a hyperplane that separates the data points into different classes. A hyperplane is a line in 2D space, a plane in 3D space, or a higher-dimensional surface in n-dimensional space. The hyperplane is chosen in such a way that it maximizes the margin, which is the distance between the hyperplane and the closest data points of each class. The closest data points are called the support vectors.
+
 The distance between the hyperplane and a data point "x" can be calculated using the formula −  
+```
 distance = (w . x + b) / ||w|| 
+```
 where "w" is the weight vector, "b" is the bias term, and "||w||" is the Euclidean norm of the weight vector. The weight vector "w" is perpendicular to the hyperplane and determines its orientation, while the bias term "b" determines its position.
+
 The optimal hyperplane is found by solving an optimization problem, which is to maximize the margin subject to the constraint that all data points are correctly classified. In other words, we want to find the hyperplane that maximizes the margin between the two classes while ensuring that no data point is misclassified. This is a convex optimization problem that can be solved using quadratic programming. If the data points are not linearly separable, we can use a technique called kernel trick to map the data points into a higher-dimensional space where they become separable. The kernel function computes the inner product between the mapped data points without computing the mapping itself. This allows us to work with the data points in the higherdimensional space without incurring the computational cost of mapping them.
 
 1. Hyperplane:
@@ -19,8 +26,9 @@ It may be defined as the gap between two lines on the closet data points of diff
 
 We will use the famous Iris dataset, which contains the sepal length, sepal width, petal length, and petal width of three species of iris flowers: Iris setosa, Iris versicolor, and Iris virginica. The goal is to classify the flowers into their respective species based on these four features. We load the iris dataset using load_iris and split the data into training and testing sets using train_test_split. We use a test size of 0.2, which means that 20% of the data will be used for testing and 80% for training. We set the random state to 42 to ensure reproducibility of the results.
 
-# Implemetation of SVM in Python 
+### Implemetation of SVM in Python 
 
+```python
 from sklearn.datasets import load_iris
 from sklearn.model_selection import train_test_split
 from sklearn.svm import SVC
@@ -45,8 +53,10 @@ y_pred = svm.predict(X_test)
 # calculate the accuracy of the classifier
 accuracy = accuracy_score(y_test, y_pred)
 print("Accuracy:", accuracy)
+```
 
-# Output
+#### Output
+```
 Accuracy: 1
-
+```