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/**
* *******************************************************************************
* Copyright (c) 2011, Monnet Project All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met: *
* Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer. * Redistributions in binary
* form must reproduce the above copyright notice, this list of conditions and
* the following disclaimer in the documentation and/or other materials provided
* with the distribution. * Neither the name of the Monnet Project nor the names
* of its contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE MONNET PROJECT BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
package eu.monnetproject.translation.jmert;
import java.util.Arrays;
import org.apache.commons.math.linear.Array2DRowRealMatrix;
import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.stat.regression.OLSMultipleLinearRegression;
/**
* Derived from Olivier Chappelle's Matlab implementation. Based on "Efficient
* algorithms for Ranking with SVMs", Chappelle & Keerthi (2009).
*
* @author John McCrae
*/
public class SVMRank {
// Configuration variables
public int maxNewtonIterations = 10;
public double prec = 1e-4;
public double minresPrecision = 1e-3;
public int minResIterations = 20;
// Problem space variables
double[] w; // d
double C; // p
double[] out; // p
double[] step; // d
double[][] A; // pxn
int[][] spA; // px2
double[][] X; // nxd
int d;
int p;
int n;
int[] sv; // p
int svN; // < p
double[] grad; // d
double obj;
/**
* Create a Ranking SVM problem
* @param X The vectors
* @param A The matrix where {@code A[i][j] = 1} iff {@code rank(i) > rank(j)} and
* {@code A[i][j] = -1} iff {@code rank(i) < rank(j)}
* @param C The loss parameter
*/
public SVMRank(double[][] X, double[][] A, double C) {
this.X = X;
this.A = A;
this.C = C;
}
/**
* Create a Ranking SVM problem
* @param X The vectors
* @param A A set of vectors where {@code spA[_] = { i, j } } iff {@code rank(i) > rank(j) }
* @param C The loss parameter
*/
public SVMRank(double[][] X, int[][] spA, double C) {
this.X = X;
this.spA = spA;
this.C = C;
}
public double[] solve() {
if (X.length == 0) {
return new double[0];
}
d = X[0].length;
n = X.length;
final int k = Math.min(d, minResIterations);
// Min Residual method has complexity O(k^2nd + pd)
// LU method has complexity O(d^3 + pd)
return solve(k * k * n < d * d);
}
public double[] solve(boolean minResidualMethod) {
d = X[0].length;
n = X.length;
if (spA != null) {
p = spA.length;
} else {
p = A.length;
}
if (p == 0) {
return new double[d];
}
w = new double[d];
Arrays.fill(w, 1.0);
sv = new int[p];
svN = 0;
grad = new double[d];
x0 = new double[d];
step = new double[d];
int iter = 0;
out = new double[p];
// out = 1 - A*(X*w)
for (int i = 0; i < p; i++) {
out[i] = 1;
for (int j = 0; j < d; j++) {
if (spA != null) {
out[i] -= (X[spA[i][0]][j] - X[spA[i][1]][j]) * w[j];
} else {
for (int k = 0; k < n; k++) {
out[i] -= A[i][k] * X[k][j] * w[j];
}
}
}
}
//while 1
while (true) {
// iter = iter + 1;
iter++;
if (iter > maxNewtonIterations) {
System.err.println("Maximum number of Newton steps reached.Try larger lambda");
break;
}
//[obj, grad, sv] = obj_fun_linear(w,C,out);
objFunLinear();
if (minResidualMethod) {
// [step, foo, relres] = minres(@hess_vect_mult, -grad,...
// opt.cg_prec,opt.cg_it,[],[],[],sv,C);
// minres(A,b,tolerance,itMax,...)
gmresHessMult();
} else {
luHessSolve();
}
if(allZero(step)) {
break;
}
// [t,out] = line_search_linear(w,step,out,C);
double t = lineSearchLinear();
// w = w + t*step;
for (int i = 0; i < d; i++) {
w[i] = w[i] + t * step[i];
}
// if -step'*grad < opt.prec * obj
// % Stop when the Newton decrement is small enough
// break;
if (-1.0 * innerProduct(step, grad) < prec * obj) {
break;
}
}
return w;
}
private void luHessSolve() {
// Xsv = A(sv,:)*X;
double[][] Xsv = new double[svN][d];
for (int i = 0; i < svN; i++) {
Xsv[i] = new double[d];
if (spA != null) {
for (int k = 0; k < d; k++) {
Xsv[i][k] += X[spA[sv[i]][0]][k] - X[spA[sv[i]][1]][k];
}
} else {
for (int j = 0; j < n; j++) {
for (int k = 0; k < d; k++) {
Xsv[i][k] += A[sv[i]][j] * X[j][k];
}
}
}
}
double[][] hess = new double[d][d];
//hess = eye(d) + Xsv'*(Xsv.*repmat(C(sv),1,d)); % Hessian
for (int i = 0; i < d; i++) {
hess[i][i] = 1;
for (int j = 0; j < svN; j++) {
for (int k = 0; k < d; k++) {
hess[i][k] += Xsv[j][i] * Xsv[j][k] * C;
}
}
}
//step = - hess \ grad; % Newton direction NB -1 * inv(A) * grad
Arrays.fill(step, 0);
final double[][] invHess = new LUDecompositionImpl(new Array2DRowRealMatrix(hess)).getSolver().getInverse().getData();
for (int i = 0; i < d; i++) {
for (int j = 0; j < d; j++) {
step[i] += -1.0 * invHess[i][j] * grad[j];
}
}
}
private void objFunLinear() {
//out = max(0,out);
for (int i = 0; i < out.length; i++) {
out[i] = Math.max(0, out[i]);
}
//obj = sum(C.*out.^2)/2 + w'*w/2; % L2 penalization of the errors
obj = 0.0;
for (int i = 0; i < p; i++) {
obj += (C * out[i] * out[i]) / 2.0;
}
for (int i = 0; i < d; i++) {
obj += w[i] * w[i] / 2.0;
}
//grad = w - (((C.*out)'*A)*X)'; % Gradient
for (int i = 0; i < d; i++) {
grad[i] = w[i];
for (int j = 0; j < p; j++) {
if (spA != null) {
grad[i] -= C * out[j] * (X[spA[j][0]][i] - X[spA[j][1]][i]);
} else {
for (int k = 0; k < n; k++) {
grad[i] -= C * out[j] * A[j][k] * X[k][i];
}
}
}
}
//sv = out>0;
svN = 0;
for (int i = 0; i < p; i++) {
if (out[i] > 0) {
sv[svN++] = i;
}
}
}
private double lineSearchLinear() {
int[] lsv = new int[p];
int lsvN;
// t = 0;
double t = 0;
// Precompute some dots products
// Xd = A*(X*step);
double[] Xd = new double[p];
for (int i = 0; i < p; i++) {
for (int k = 0; k < d; k++) {
if (spA != null) {
Xd[i] += (X[spA[i][0]][k] - X[spA[i][1]][k]) * step[k];
} else {
for (int j = 0; j < n; j++) {
Xd[i] += A[i][j] * X[j][k] * step[k];
}
}
}
}
// wd = w'*step;
double wd = 0.0;
for (int i = 0; i < d; i++) {
wd += w[i] * step[i];
}
// dd = step'*step;
double dd = 0.0;
for (int i = 0; i < d; i++) {
dd += step[i] * step[i];
}
// while 1
while (true) {
// out2 = out - t*Xd; % The new outputs after a step of length t
double[] out2 = new double[p];
System.arraycopy(out, 0, out2, 0, p);
for (int i = 0; i < p; i++) {
out2[i] = out[i] - t * Xd[i];
}
// sv = find(out2>0);
lsvN = 0;
for (int i = 0; i < p; i++) {
if (out2[i] > 0) {
lsv[lsvN++] = i;
}
}
// g = wd + t*dd - (C(sv).*out2(sv))'*Xd(sv); % The gradient (along the line)
double g = wd + t * dd;
for (int i = 0; i < lsvN; i++) {
g -= C * out2[lsv[i]] * Xd[lsv[i]];
}
// h = dd + Xd(sv)'*(Xd(sv).*C(sv)); % The second derivative (along the line)
double h = dd;
for (int i = 0; i < lsvN; i++) {
h += Xd[lsv[i]] * Xd[lsv[i]] * C;
}
// t = t - g/h; % Take the 1D Newton step. Note that if d was an exact Newton
t = t - g / h;
// % direction, t is 1 after the first iteration.
// if g^2/h < 1e-10, break; end;
if (g * g / h < 1e-10) {
// out = out2;
out = out2;
return t;
}
// end;
}
}
public static double[] hessVectMult(double[][] X, int[][] spA, double[] w, int[] sv, int svN, double C) {
int d = w.length;
//int n = X.length;
// y = w
double[] y = new double[d];
System.arraycopy(w, 0, y, 0, d);
// z = (C.*sv).*(A*(X*w)); % Computing X(sv,:)*x takes more time in Matlab :-(
double[] z = new double[svN];
for (int i2 = 0; i2 < svN; i2++) {
int i = sv[i2];
for (int j = 0; j < d; j++) {
//if (spA != null) {
z[i2] += (X[spA[i][0]][j] - X[spA[i][1]][j]) * w[j];
//} else {
// for (int k = 0; k < n; k++) {
// z[i2] += A[i][k] * X[k][j] * w[j];
// }
//}
}
z[i2] *= C;
}
// y = y + ((z'*A)*X)';
for (int i = 0; i < d; i++) {
for (int j2 = 0; j2 < svN; j2++) {
int j = sv[j2];
//if(spA != null) {
y[i] += 2 * (X[spA[j][0]][i] - X[spA[j][1]][i]) * z[j2];
//} else {
// for (int k = 0; k < n; k++) {
// y[i] += A[j][k] * X[k][i] * z[j2];
// }
//}
}
}
return y;
}
public static double[] hessVectMult(double[][] X, double[][] A, double[] w, int[] sv, int svN, double C) {
int d = w.length;
int n = X.length;
// y = w
double[] y = new double[d];
System.arraycopy(w, 0, y, 0, d);
// z = (C.*sv).*(A*(X*w)); % Computing X(sv,:)*x takes more time in Matlab :-(
double[] z = new double[svN];
for (int i2 = 0; i2 < svN; i2++) {
int i = sv[i2];
for (int j = 0; j < d; j++) {
for (int k = 0; k < n; k++) {
z[i2] += A[i][k] * X[k][j] * w[j];
}
}
z[i2] *= C;
}
// y = y + ((z'*A)*X)';
for (int i = 0; i < d; i++) {
for (int j2 = 0; j2 < svN; j2++) {
int j = sv[j2];
for (int k = 0; k < n; k++) {
y[i] += 2 * A[j][k] * X[k][i] * z[j2];
}
}
}
return y;
}
private double innerProduct(double[] step, double[] grad) {
double ip = 0.0;
for (int i = 0; i < step.length; i++) {
ip += step[i] * grad[i];
}
return ip;
}
public static double[] gmres(double[][] A, double[] f, double[] x0, int k) {
// r0 <- f - A %*% x0
int n = f.length;
int m = x0.length;
double[] r0 = new double[n];
for (int i = 0; i < n; i++) {
r0[i] = f[i];
for (int j = 0; j < m; j++) {
r0[i] -= A[i][j] * x0[j];
}
}
// v <- matrix(0,k+1,ncol(A))
double[][] v = new double[k + 1][n];
// v[1,] <- r0 / sqrt(sum(r0*r0))
v[0] = r0;
double sumSqR0 = 0.0;
for (int i = 0; i < n; i++) {
sumSqR0 += r0[i] * r0[i];
}
sumSqR0 = Math.sqrt(sumSqR0);
for (int i = 0; i < n; i++) {
v[0][i] /= sumSqR0;
}
// h <- matrix(0,k+1,k)
double[][] h = new double[k + 1][k];
// for(j in 1:k) {
for (int j = 0; j < k; j++) {
// for(i in 1:j) {
for (int i = 0; i <= j; i++) {
// h[i,j] <- t(A %*% v[j,]) %*% v[i,]
h[i][j] = 0;
for (int l = 0; l < n; l++) {
for (int l2 = 0; l2 < n; l2++) {
h[i][j] += v[j][l] * A[l2][l] * v[l2][i];
}
}
// }
}
// v[j+1,] <- A %*% v[j,]
for (int i = 0; i < n; i++) {
for (int l = 0; l < n; l++) {
v[j + 1][i] += A[i][l] * v[j][l];
}
}
// for(i in 1:j) {
for (int i = 0; i <= j; i++) {
// v[j+1,] <- v[j+1,] - h[i,j] * v[i,]
for (int l = 0; l < n; l++) {
v[j + 1][l] -= h[i][j] * v[i][l];
}
// }
}
// h[j+1,j] <- sqrt(sum(v[j+1,]*v[j+1,]))
h[j + 1][j] = 0;
for (int i = 0; i < n; i++) {
h[j + 1][j] += v[j + 1][i] * v[j + 1][i];
}
h[j + 1][j] = Math.sqrt(h[j + 1][j]);
// v[j+1,] <- v[j+1,] / h[j+1,j]
for (int i = 0; i < n; i++) {
v[j + 1][i] /= h[j + 1][j];
}
// }
}
// beta <- c(sqrt(sum(r0*r0)),rep(0,k-1))
double[] beta = new double[k + 1];
beta[0] = sumSqR0;
// y is least squares solution to ||beta - Hy||
final OLSMultipleLinearRegression lr = new OLSMultipleLinearRegression();
lr.newSampleData(beta, h);
final double[] y = lr.estimateRegressionParameters();
// NB y = [intercept,x0,x1,...,xn]
// x0 + v[1:k,] %*% y
double[] answer = new double[n];
for (int i = 0; i < n; i++) {
answer[i] = x0[i];
for (int j = 0; j < k; j++) {
answer[i] += v[j][i] * y[j + 1];
}
}
return answer;
}
double[] x0;
public void gmresHessMult() {
// r0 <- f - A %*% x0
double[] r0 = new double[d];
double[] r0Tmp = spA != null ? hessVectMult(X, spA, x0, sv, svN, C) : hessVectMult(X, A, x0, sv, svN, C);
for (int i = 0; i < d; i++) {
r0[i] = -grad[i] - r0Tmp[i];
}
final int k = Math.min(d, minResIterations);
// v <- matrix(0,k+1,ncol(A))
double[][] v = new double[k + 1][d];
// v[1,] <- r0 / sqrt(sum(r0*r0))
v[0] = r0;
double sumSqR0 = 0.0;
for (int i = 0; i < d; i++) {
sumSqR0 += r0[i] * r0[i];
}
sumSqR0 = Math.sqrt(sumSqR0);
for (int i = 0; i < d; i++) {
v[0][i] /= sumSqR0;
}
// h <- matrix(0,k+1,k)
double[][] h = new double[k + 1][k];
// for(j in 1:k) {
for (int j = 0; j < k; j++) {
// for(i in 1:j) {
for (int i = 0; i <= j; i++) {
// h[i,j] <- t(A %*% v[j,]) %*% v[i,]
final double[] Avi = spA != null ? hessVectMult(X, spA, v[i], sv, svN, C) : hessVectMult(X, A, v[i], sv, svN, C);
for (int l = 0; l < d; l++) {
h[i][j] += v[j][l] * Avi[l];
}
// }
}
// v[j+1,] <- A %*% v[j,]
v[j + 1] = spA != null ? hessVectMult(X, spA, v[j], sv, svN, C) : hessVectMult(X,A,v[j],sv,svN,C);
// for(i in 1:j) {
for (int i = 0; i <= j; i++) {
// v[j+1,] <- v[j+1,] - h[i,j] * v[i,]
for (int l = 0; l < d; l++) {
v[j + 1][l] -= h[i][j] * v[i][l];
}
// }
}
// h[j+1,j] <- sqrt(sum(v[j+1,]*v[j+1,]))
h[j + 1][j] = 0;
for (int i = 0; i < d; i++) {
h[j + 1][j] += v[j + 1][i] * v[j + 1][i];
}
h[j + 1][j] = Math.sqrt(h[j + 1][j]);
// v[j+1,] <- v[j+1,] / h[j+1,j]
for (int i = 0; i < d; i++) {
v[j + 1][i] /= h[j + 1][j];
}
// }
}
// beta <- c(sqrt(sum(r0*r0)),rep(0,k-1))
double[] beta = new double[k + 1];
beta[0] = sumSqR0;
// y is least squares solution to ||beta - Hy||
final OLSMultipleLinearRegression lr = new OLSMultipleLinearRegression();
lr.newSampleData(beta, h);
final double[] y = lr.estimateRegressionParameters();
// NB y = [intercept,x0,x1,...,xn]
// x0 + v[1:k,] %*% y
for (int i = 0; i < d; i++) {
step[i] = x0[i];
for (int j = 0; j < k; j++) {
step[i] += v[j][i] * y[j + 1];
}
}
}
private boolean allZero(double[] step) {
for(int i = 0; i < step.length; i++) {
if(step[i] != 0.0) {
return false;
}
}
return true;
}
}
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