Support Vector Machine (SVM)

Support Vector Machine (SVM) is a classic supervised learning algorithm primarily used for classification and regression tasks. Its core concept involves identifying an optimal hyperplane that maximizes the margin between different classes of data, thereby enhancing the model's generalization capability.

Implementing Support Vector Machines in MATLAB typically involves the following key steps:

Data Preparation: Ensure the dataset is divided into training and testing sets, with necessary normalization or standardization applied. In MATLAB, preprocessing functions like `zscore` or `mapminmax` can be used for feature scaling to improve SVM performance.

Model Training: Select appropriate kernel functions (such as linear, polynomial, or Gaussian/RBF kernels) to construct classification boundaries. The kernel function choice directly impacts model performance. MATLAB's `fitcsvm` function supports various kernel types through its 'KernelFunction' parameter, where developers can specify 'linear', 'polynomial', or 'rbf' kernels with customizable parameters.

Parameter Tuning: Adjust regularization parameters (like C-value) and kernel parameters to optimize classification performance. Cross-validation is a commonly used tuning method. MATLAB provides `crossval` function and `fitcsvm`'s 'OptimizeHyperparameters' option for automated parameter optimization through grid search or Bayesian optimization techniques.

Prediction and Evaluation: Use the trained model to make predictions on test data and evaluate performance using metrics like accuracy, recall, and precision. MATLAB's `predict` function generates predictions from SVM models, while functions like `confusionmat` and `perfcurve` help calculate performance metrics and plot ROC curves respectively.

Support Vector Machines perform exceptionally well with small-sample, high-dimensional data and are particularly suitable for nonlinear classification problems. Through the kernel trick, SVM can map original feature spaces to higher dimensions, enabling the discovery of more complex decision boundaries.

Although MATLAB provides built-in SVM functions like `fitcsvm`, many researchers develop custom implementations for specific requirements, such as multi-class classification tasks (using one-vs-one or one-vs-all approaches) or custom kernel function implementations. These custom solutions often involve mathematical programming using MATLAB's optimization toolbox for quadratic programming solutions.