// to the simulation.
private double learnedFunc(Matrix k) {
double s = 0;
for (int i = 0; i < nSupportVectors; i++) {
if (alph[i] > 0) {
s += alph[i] * target[i] * kernel.eval(densePoints[i], k);
}
}
s -= b;
return s;
}
// to optimize the training.
private double learnedFunc(int k) {
double s = 0;
for (int i = 0; i < nSupportVectors; i++) {
if (alph[i] > 0) {
s +=
alph[i] * target[i] * kernel.eval(precomputedDots.position(i, k) /*densePoints[i], k*/);
}
}
s -= b;
return s;
}
private int takeStep(int i1, int i2) {
if (i1 == i2) return 0;
int y1 = 0, y2 = 0, s = 0;
double alph1 = 0, alph2 = 0; /* old_values of alpha_1, alpha_2 */
double a1 = 0, a2 = 0; /* new values of alpha_1, alpha_2 */
double E1 = 0, E2 = 0, L = 0, H = 0, k11 = 0, k22 = 0, k12 = 0, eta = 0, Lobj = 0, Hobj = 0;
alph1 = alph[i1];
y1 = target[i1];
if (alph1 > 0 && alph1 < C) {
E1 = errorCache[i1];
} else {
E1 = learnedFunc(i1) - y1;
}
alph2 = alph[i2];
y2 = target[i2];
if (alph2 > 0 && alph2 < C) {
E2 = errorCache[i2];
} else {
E2 = learnedFunc(i2) - y2;
}
s = y1 * y2;
if (y1 == y2) {
double gamma = alph1 + alph2;
if (gamma > C) {
L = gamma - C;
H = C;
} else {
L = 0;
H = gamma;
}
} else {
double gamma = alph1 - alph2;
if (gamma > 0) {
L = 0;
H = C - gamma;
} else {
L = -gamma;
H = C;
}
}
if (L == H) return 0;
k11 = kernel.eval(precomputedDots.position(i1, i1) /*densePoints[i1], densePoints[i1]*/);
k12 = kernel.eval(precomputedDots.position(i1, i2) /*densePoints[i1], densePoints[i2]*/);
k22 = kernel.eval(precomputedDots.position(i2, i2) /*densePoints[i2], densePoints[i2]*/);
eta = 2 * k12 - k11 - k22;
if (eta < 0) {
a2 = alph2 + y2 * (E2 - E1) / eta;
if (a2 < L) {
a2 = L;
} else if (a2 > H) {
a2 = H;
}
} else {
double c1 = eta / 2;
double c2 = y2 * (E1 - E2) - eta * alph2;
Lobj = c1 * L * L + c2 * L;
Hobj = c1 * H * H + c2 * H;
if (Lobj > Hobj + epsilon) {
a2 = L;
} else if (Lobj < Hobj - epsilon) {
a2 = H;
} else {
a2 = alph2;
}
}
if (Math.abs(a2 - alph2) < epsilon * (a2 + alph2 + epsilon)) return 0;
a1 = alph1 - s * (a2 - alph2);
if (a1 < 0) {
a2 += s * a1;
a1 = 0;
} else if (a1 > C) {
double t = a1 - C;
a2 += s * t;
a1 = C;
}
double b1 = 0, b2 = 0, bnew = 0;
if (a1 > 0 && a1 < C) {
bnew = b + E1 + y1 * (a1 - alph1) * k11 + y2 * (a2 - alph2) * k12;
} else {
if (a2 > 0 && a2 < C) {
bnew = b + E2 + y1 * (a1 - alph1) * k12 + y2 * (a2 - alph2) * k22;
} else {
b1 = b + E1 + y1 * (a1 - alph1) * k11 + y2 * (a2 - alph2) * k12;
b2 = b + E2 + y1 * (a1 - alph1) * k12 + y2 * (a2 - alph2) * k22;
bnew = (b1 + b2) / 2;
}
}
deltaB = bnew - b;
b = bnew;
double t1 = y1 * (a1 - alph1);
double t2 = y2 * (a2 - alph2);
for (int i = 0; i < nSupportVectors; i++) {
if (0 < alph[i] && alph[i] < C) {
double tmp = errorCache[i];
tmp +=
(t1 * kernel.eval(precomputedDots.position(i1, i) /*densePoints[i1], densePoints[i]*/))
+ (t2
* kernel.eval(
precomputedDots.position(i2, i) /*densePoints[i2], densePoints[i]*/))
- deltaB;
errorCache[i] = tmp;
}
}
errorCache[i1] = 0.0;
errorCache[i2] = 0.0;
alph[i1] = a1;
alph[i2] = a2;
return 1;
}