Support Vector Machine Classification

A Support Vector Machine (SVM) is a classification and regression technique based on statistical learning theory that has been proved very effective in solving complex classification problems in many different application domains. The success of SVMs is due to the important properties of this approach, which integrated with the effectiveness of the classification procedure and the elegance of the theoretical developments, result in a very solid classification methodology in many different remote sensing data analyses domains.

SVM focuses classification decisions on the boundary between classes and not on mean and variances of classes. The SVM attempts to divide the feature space using a hyperplane such that each class will reside entirely on its own side of the plane. Using a kernel function, SVMs map the input space of independent variables to a higher dimensional space where complex nonlinear decision boundaries between classes become linear. Popular kernel functions include linear, polynomial, radial basis, and sigmoid. SVM Regression is used to define a real-valued output function given the independent input variables. SVM Regression applies the concept of a ε-insensitive loss function that ignores point errors within a distance of ε from the true value by weighting them with zero. The solution is obtained through a small subset of training points and the support vectors (vectors from points nearest to decision boundary) contain all the required information to define the function and results in extremely efficient algorithms.

All input parameters should be scaled to have zero mean and unit variance before training.

Classification accuracy can be measured using stratified 10-fold cross-validation wherein the data are randomly split into ten different groups, or folds, each containing an approximately equal number of valid and invalid samples. The SVM is run ten times, using each fold once for testing, and the remaining nine folds for training.