public static double RBFKernel(Vector w, Vector x, double c) {
double sum = 0;
for (int i = 0; i < x.getDimension(); i++) {
sum += Math.pow(w.get(i) - x.get(i), 2);
}
return Math.exp(-sum / c);
}
/**
* Trains the classifier for Multiclass SVM, by using a label for One-vs-All training.
*
* @param examples - The examples to train on
* @param rate0 - the learning rate
* @param C - The C term
* @param epochT - The number of epochs
* @param label - The label to train for
* @return - Weight vector for the classifier.
*/
public static Vector SGD(
ArrayList<Vector> examples, double rate0, double C, int epochT, String label) {
double rate;
int t = 0;
Vector w = new Vector(examples.get(0).getDimension());
for (int epoch = 0; epoch < epochT; epoch++) {
examples = Util.shuffle(examples);
for (int i = 0; i < examples.size(); i++) {
Vector x = examples.get(i);
rate = rate0 / (1 + (rate0 * t) / C);
Vector E = w;
if (x.getLabel(label) * LinearKernel(w, x, 1) <= 1)
E = w.add(x.scale(-1 * C * x.getLabel(label)));
w = w.add(E.scale(-1 * rate));
t++;
}
}
return w;
}
public static double LinearKernel(Vector w, Vector x, int power) {
return Math.pow(w.transpose(x), power);
}