MATLAB Code Implementation of Support Vector Machines

Implementing Support Vector Machines (SVM) in MATLAB can be achieved using the built-in Statistics and Machine Learning Toolbox, which provides comprehensive SVM classification capabilities supporting both linear and nonlinear classification tasks.

### 1. Linear SVM Implementation Linear SVM is used for linearly separable data, with the core objective of finding an optimal hyperplane that maximizes the classification margin. In MATLAB, you can train a linear SVM model using the `fitcsvm` function by setting the `KernelFunction` parameter to `'linear'`. The function implements the sequential minimal optimization (SMO) algorithm for efficient training.

After training, use the `predict` function for classification of new data points, and evaluate model performance using `confusionmat` to generate confusion matrices and calculate accuracy metrics.

### 2. Nonlinear SVM Implementation For nonlinearly separable data, SVM utilizes kernel functions to map data to higher-dimensional spaces where linear separation becomes possible. MATLAB supports various kernel functions including Gaussian radial basis function (`'rbf'`), polynomial kernel (`'polynomial'`), and sigmoid kernel.

During training, appropriate kernel selection and parameter tuning are crucial. Key parameters include `BoxConstraint` (controlling misclassification penalty) and `KernelScale` (affecting kernel function width). The `fitcsvm` function automatically scales numeric predictors unless specified otherwise.

### 3. Usage Guidelines and Optimization Data Preprocessing: Normalize data using `normalize` or `zscore` functions to improve SVM performance and convergence. Cross-Validation: Implement model validation using `crossval` or `cvpartition` functions to prevent overfitting and assess generalization capability. Parameter Tuning: Utilize the `OptimizeHyperparameters` option in `fitcsvm` for automated optimization of key parameters through Bayesian optimization techniques.

MATLAB's SVM implementation not only handles binary classification problems but can be extended to multi-class classification using `fitcecoc` (error-correcting output codes), making it suitable for diverse machine learning applications including pattern recognition and predictive modeling.