Support Vector Machines for Binary Classification 2

Support Vector Machines (SVMs) are a powerful supervised machine learning algorithm used for binary classification. Here's a brief overview of how SVMs work for binary classification:

How SVMs Work:

1. Data Representation: SVMs classify data by finding the best hyperplane that separates data points of one class from those of another class.

2. Margin Maximization: The best hyperplane is the one with the largest margin, which is the maximal width of the slab parallel to the hyperplane that has no interior data points.

3. Support Vectors: The data points that are closest to the separating hyperplane are called support vectors. These points define the margin2.

4. Mathematical Formulation: The problem is formulated as a quadratic programming problem, where the goal is to minimize the norm of the weights subject to constraints that ensure correct classification of the data points.

Example in MATLAB:

Here's a simple example of how to use SVM for binary classification in MATLAB:

% Generate sample data
X = [1 2; 5 4; 3 6; 7 8; 2 3; 6 7; 4 5];
Y = [-1 -1 -1 -1 1 1 1]; % Labels: -1 for class 1, 1 for class 2

% Create SVM model
SVMModel = fitcsvm(X, Y);

% Plot the data points and decision boundary
figure;
plot(X(Y == -1, 1), X(Y == -1, 2), 'ko', 'MarkerSize', 10);
hold on;
plot(X(Y == 1, 1), X(Y == 1, 2), 'ro', 'MarkerSize', 10);
plot(SVMModel, X, Y);
legend('Class 1', 'Class 2', 'Decision Boundary');
xlabel('Feature 1');
ylabel('Feature 2');
title('SVM for Binary Classification');
grid on;

Explanation:

• Generate Sample Data: X contains the feature vectors, and Y contains the corresponding labels1.

• Create SVM Model: The fitcsvm function is used to create the SVM model1.

• Plot Data Points and Decision Boundary: The data points are plotted, and the decision boundary is added using the SVM model1.