The equation given below is first inequality constraint function: Thus, training SVM – maximum margin classifier – becomes a constrained optimisation problem with objective function to maximise as the following:Īnd, the following as the constraints. The left hand side of the above equation represents the length of distance / margin between the positive and negative line / hyperplane. The above equation can be normalized by dividing both the sides with the length of the vector which is the following: On another side, the line/hyperplane touching the red plus (+) satisfies the following equation:Ĭombining both of the above equations, we get the following equation: On one side, the line/hyperplane touching the blue circle satisfies the following equation On both the sides of decision boundary lies two other lines which touches the closest point representing two different classes on either sides. All the points on this hyperplane / line must satisfies the following equation: In the above line, the dashed line represents the most optimal hyperplane or decision boundary. Let’s try and understand the objective function which can be used for optimisation. These points are called as support vectors. Due to the fact that the optimisation objective is to find the optimal hyperplane with maximum margin from closest support vectors, SVM models are also called as maximum margin classifier. The red points (Class -1) and blue points (Class 1) represents the points which are closest to the hyperplane (green line). In the above diagram, the green line represents the most optimal hyperplane. SVM Optimisation objective is to maximize the margin The margin is the perpendicular distance from this line/hyperplane to the closest points on either side representing different classes. However, in case of SVMs, the optimisation objective is to maximize the margin such that the points can be classified correctly. Using the perceptron algorithm, the objective is to find the line/hyperplane which minimise misclassification errors. One of them is Perceptron and another is SVM. This problem can be solved using two different algorithms. In the above diagram, the objective is to find the most optimal line / hyperplane which separates the points correctly thereby each point correctly representing the class it belongs to. Lines/hyperplanes classifying points correctly In the diagram below, you could find multiple such lines possible. The objective is to find the most optimal line (hyperplane in case of 3 or more dimensions) which could correctly classify the points with most accuracy. Lets take a 2-dimensional problem space where a point can be classified as one or the other class based on the value of the two dimensions (independent variables, say) X1 and X2. In this post, we will understand the concepts related to SVM ( Support Vector Machine) algorithm which is one of the popular machine learning algorithm. SVM algorithm is used for solving classification problems in machine learning.
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