nak.liblinear.SolverMCSVM_CS Maven / Gradle / Ivy
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package nak.liblinear;
import static nak.liblinear.Linear.copyOf;
import static nak.liblinear.Linear.info;
import static nak.liblinear.Linear.swap;
/**
* A coordinate descent algorithm for
* multi-class support vector machines by Crammer and Singer
*
*
* min_{\alpha} 0.5 \sum_m ||w_m(\alpha)||^2 + \sum_i \sum_m e^m_i alpha^m_i
* s.t. \alpha^m_i <= C^m_i \forall m,i , \sum_m \alpha^m_i=0 \forall i
*
* where e^m_i = 0 if y_i = m,
* e^m_i = 1 if y_i != m,
* C^m_i = C if m = y_i,
* C^m_i = 0 if m != y_i,
* and w_m(\alpha) = \sum_i \alpha^m_i x_i
*
* Given:
* x, y, C
* eps is the stopping tolerance
*
* solution will be put in w
*
* See Appendix of LIBLINEAR paper, Fan et al. (2008)
*
*/
class SolverMCSVM_CS {
private final double[] B;
private final double[] C;
private final double eps;
private final double[] G;
private final int max_iter;
private final int w_size, l;
private final int nr_class;
private final Problem prob;
public SolverMCSVM_CS( Problem prob, int nr_class, double[] C ) {
this(prob, nr_class, C, 0.1);
}
public SolverMCSVM_CS( Problem prob, int nr_class, double[] C, double eps ) {
this(prob, nr_class, C, eps, 100000);
}
public SolverMCSVM_CS( Problem prob, int nr_class, double[] weighted_C, double eps, int max_iter ) {
this.w_size = prob.n;
this.l = prob.l;
this.nr_class = nr_class;
this.eps = eps;
this.max_iter = max_iter;
this.prob = prob;
this.C = weighted_C;
this.B = new double[nr_class];
this.G = new double[nr_class];
}
private int GETI(int i) {
return (int)prob.y[i];
}
private boolean be_shrunk(int i, int m, int yi, double alpha_i, double minG) {
double bound = 0;
if (m == yi) bound = C[GETI(i)];
if (alpha_i == bound && G[m] < minG) return true;
return false;
}
public void solve(double[] w) {
int i, m, s;
int iter = 0;
double[] alpha = new double[l * nr_class];
double[] alpha_new = new double[nr_class];
int[] index = new int[l];
double[] QD = new double[l];
int[] d_ind = new int[nr_class];
double[] d_val = new double[nr_class];
int[] alpha_index = new int[nr_class * l];
int[] y_index = new int[l];
int active_size = l;
int[] active_size_i = new int[l];
double eps_shrink = Math.max(10.0 * eps, 1.0); // stopping tolerance for shrinking
boolean start_from_all = true;
// Initial alpha can be set here. Note that
// sum_m alpha[i*nr_class+m] = 0, for all i=1,...,l-1
// alpha[i*nr_class+m] <= C[GETI(i)] if prob->y[i] == m
// alpha[i*nr_class+m] <= 0 if prob->y[i] != m
// If initial alpha isn't zero, uncomment the for loop below to initialize w
for (i = 0; i < l * nr_class; i++)
alpha[i] = 0;
for (i = 0; i < w_size * nr_class; i++)
w[i] = 0;
for (i = 0; i < l; i++) {
for (m = 0; m < nr_class; m++)
alpha_index[i * nr_class + m] = m;
QD[i] = 0;
for (Feature xi : prob.x[i]) {
double val = xi.getValue();
QD[i] += val * val;
// Uncomment the for loop if initial alpha isn't zero
// for(m=0; mindex-1)*nr_class+m] += alpha[i*nr_class+m]*val;
}
active_size_i[i] = nr_class;
y_index[i] = (int)prob.y[i];
index[i] = i;
}
DoubleArrayPointer alpha_i = new DoubleArrayPointer(alpha, 0);
IntArrayPointer alpha_index_i = new IntArrayPointer(alpha_index, 0);
while (iter < max_iter) {
double stopping = Double.NEGATIVE_INFINITY;
for (i = 0; i < active_size; i++) {
// int j = i+rand()%(active_size-i);
int j = i + Linear.random.nextInt(active_size - i);
swap(index, i, j);
}
for (s = 0; s < active_size; s++) {
i = index[s];
double Ai = QD[i];
// double *alpha_i = &alpha[i*nr_class];
alpha_i.setOffset(i * nr_class);
// int *alpha_index_i = &alpha_index[i*nr_class];
alpha_index_i.setOffset(i * nr_class);
if (Ai > 0) {
for (m = 0; m < active_size_i[i]; m++)
G[m] = 1;
if (y_index[i] < active_size_i[i]) G[y_index[i]] = 0;
for (Feature xi : prob.x[i]) {
// double *w_i = &w[(xi.index-1)*nr_class];
int w_offset = (xi.getIndex() - 1) * nr_class;
for (m = 0; m < active_size_i[i]; m++)
// G[m] += w_i[alpha_index_i[m]]*(xi.value);
G[m] += w[w_offset + alpha_index_i.get(m)] * (xi.getValue());
}
double minG = Double.POSITIVE_INFINITY;
double maxG = Double.NEGATIVE_INFINITY;
for (m = 0; m < active_size_i[i]; m++) {
if (alpha_i.get(alpha_index_i.get(m)) < 0 && G[m] < minG) minG = G[m];
if (G[m] > maxG) maxG = G[m];
}
if (y_index[i] < active_size_i[i]) {
if (alpha_i.get((int)prob.y[i]) < C[GETI(i)] && G[y_index[i]] < minG) {
minG = G[y_index[i]];
}
}
for (m = 0; m < active_size_i[i]; m++) {
if (be_shrunk(i, m, y_index[i], alpha_i.get(alpha_index_i.get(m)), minG)) {
active_size_i[i]--;
while (active_size_i[i] > m) {
if (!be_shrunk(i, active_size_i[i], y_index[i], alpha_i.get(alpha_index_i.get(active_size_i[i])), minG)) {
swap(alpha_index_i, m, active_size_i[i]);
swap(G, m, active_size_i[i]);
if (y_index[i] == active_size_i[i])
y_index[i] = m;
else if (y_index[i] == m) y_index[i] = active_size_i[i];
break;
}
active_size_i[i]--;
}
}
}
if (active_size_i[i] <= 1) {
active_size--;
swap(index, s, active_size);
s--;
continue;
}
if (maxG - minG <= 1e-12)
continue;
else
stopping = Math.max(maxG - minG, stopping);
for (m = 0; m < active_size_i[i]; m++)
B[m] = G[m] - Ai * alpha_i.get(alpha_index_i.get(m));
solve_sub_problem(Ai, y_index[i], C[GETI(i)], active_size_i[i], alpha_new);
int nz_d = 0;
for (m = 0; m < active_size_i[i]; m++) {
double d = alpha_new[m] - alpha_i.get(alpha_index_i.get(m));
alpha_i.set(alpha_index_i.get(m), alpha_new[m]);
if (Math.abs(d) >= 1e-12) {
d_ind[nz_d] = alpha_index_i.get(m);
d_val[nz_d] = d;
nz_d++;
}
}
for (Feature xi : prob.x[i]) {
// double *w_i = &w[(xi->index-1)*nr_class];
int w_offset = (xi.getIndex() - 1) * nr_class;
for (m = 0; m < nz_d; m++) {
w[w_offset + d_ind[m]] += d_val[m] * xi.getValue();
}
}
}
}
iter++;
if (iter % 10 == 0) {
info(".");
}
if (stopping < eps_shrink) {
if (stopping < eps && start_from_all == true)
break;
else {
active_size = l;
for (i = 0; i < l; i++)
active_size_i[i] = nr_class;
info("*");
eps_shrink = Math.max(eps_shrink / 2, eps);
start_from_all = true;
}
} else
start_from_all = false;
}
info("%noptimization finished, #iter = %d%n", iter);
if (iter >= max_iter) info("%nWARNING: reaching max number of iterations%n");
// calculate objective value
double v = 0;
int nSV = 0;
for (i = 0; i < w_size * nr_class; i++)
v += w[i] * w[i];
v = 0.5 * v;
for (i = 0; i < l * nr_class; i++) {
v += alpha[i];
if (Math.abs(alpha[i]) > 0) nSV++;
}
for (i = 0; i < l; i++)
v -= alpha[i * nr_class + (int)prob.y[i]];
info("Objective value = %f%n", v);
info("nSV = %d%n", nSV);
}
private void solve_sub_problem(double A_i, int yi, double C_yi, int active_i, double[] alpha_new) {
int r;
assert active_i <= B.length; // no padding
double[] D = copyOf(B, active_i);
// clone(D, B, active_i);
if (yi < active_i) D[yi] += A_i * C_yi;
// qsort(D, active_i, sizeof(double), compare_double);
ArraySorter.reversedMergesort(D);
double beta = D[0] - A_i * C_yi;
for (r = 1; r < active_i && beta < r * D[r]; r++)
beta += D[r];
beta /= r;
for (r = 0; r < active_i; r++) {
if (r == yi)
alpha_new[r] = Math.min(C_yi, (beta - B[r]) / A_i);
else
alpha_new[r] = Math.min(0.0, (beta - B[r]) / A_i);
}
}
}
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