MATLAB Implementation of Support Vector Machine with SMO Algorithm

This article discusses Support Vector Machines (SVM) and their practical implementation methods. We focus specifically on implementing the Sequential Minimal Optimization (SMO) algorithm in MATLAB, accompanied by pseudocode examples. Support Vector Machines represent a powerful machine learning algorithm that demonstrates excellent performance in both classification and regression problems. The SMO algorithm provides an efficient approach for solving SVM model parameters by breaking down the large quadratic programming problem into smaller subproblems. Each iteration optimizes two Lagrange multipliers simultaneously while maintaining constraints. Key implementation aspects include: - Kernel function handling for linear and non-linear classification - Lagrange multiplier optimization through analytical solution - Bias term calculation and margin maximization - Convergence checking via KKT conditions In the following example, we demonstrate how to utilize the SMO algorithm in MATLAB to train an SVM model, including procedures for: 1. Data preprocessing and parameter initialization 2. Main optimization loop with heuristics for multiplier selection 3. Model evaluation through prediction accuracy testing 4. Visualization of decision boundaries and support vectors The implementation includes error handling for numerical stability and provides options for different kernel types (linear, polynomial, RBF) to handle various data characteristics.