### How To Workout SVM Algorithm

In machine learning,

**support vector machines**(**SVMs**, also**support vector networks**) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output, making it a non-probabilistic binary linear classifier. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other. An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on.
More formally, a support vector machine constructs a hyper plane or set of hyper planes in a high- or
infinite-dimensional space, which can be used for classification, regression,
or other tasks. Intuitively, a good separation is achieved by the hyper plane that has the largest distance to the nearest training data point of any class
(so-called functional margin), since in general the larger the margin the lower
the generalization
error of
the classifier.

###
**1.1 SVM Binary
Classification Algorithm**

####
**Example 1:**

Step 1:Normalize the given data by
using the equation

Step 2: Compute Augmented matrix [A
-e]. ie Augment a "-1" column matrix to A.

Step 3: Compute H = D[A -e]

Step 4 : Compute U =

*V***[I –H[I/V + H***×*^{T}H]^{-1}H^{T}]×e
Where I = Identity Matrix

V = Order of H

^{T}H with value 0.1Step 5: Find w and gamma = 0.

Step 6: Find w trans * X -gamma. Find for all features

eg: X= Column_matrix{x,y}

Step 7: Compare sign(wT*x -gama ) with the actual class label.

You can notice that 3rd , 5 th and 9 th class labels are misclassified.

ie

After Traning the dataset , the below datapoints

5 9 falls in class label -1

8 7 falls in class label -1

and

8 5 falls in class label 1.

**Misclassification in 3 datapoints 3 rd 5 th and 9 th.**

**Acurracy is 70%.**