/**
  * Sets the value of <SPAN CLASS="MATH"><I>&#955;</I><SUB>i</SUB> =</SPAN><TT>lambda[<SPAN
  * CLASS="MATH"><I>i</I> - 1</SPAN>]</TT>,
  *
  * <p><SPAN CLASS="MATH"><I>i</I> = 1,&#8230;, <I>k</I></SPAN> for this object.
  */
 public void setLambda(double[] lambda) {
   testLambda(lambda);
   int k = lambda.length;
   m_lambda = new double[k];
   System.arraycopy(lambda, 0, m_lambda, 0, k);
   supportA = 0.0;
 }
  /**
   * Returns the best cut of a graph w.r.t. the degree of dissimilarity between points of different
   * partitions and the degree of similarity between points of the same partition.
   *
   * @param W the weight matrix of the graph
   * @return an array of two elements, each of these contains the points of a partition
   */
  protected static int[][] bestCut(DoubleMatrix2D W) {
    int n = W.columns();
    // Builds the diagonal matrices D and D^(-1/2) (represented as their diagonals)
    DoubleMatrix1D d = DoubleFactory1D.dense.make(n);
    DoubleMatrix1D d_minus_1_2 = DoubleFactory1D.dense.make(n);
    for (int i = 0; i < n; i++) {
      double d_i = W.viewRow(i).zSum();
      d.set(i, d_i);
      d_minus_1_2.set(i, 1 / Math.sqrt(d_i));
    }
    DoubleMatrix2D D = DoubleFactory2D.sparse.diagonal(d);

    // System.out.println("DoubleMatrix2D :\n"+D.toString());

    DoubleMatrix2D X = D.copy();

    // System.out.println("DoubleMatrix2D copy :\n"+X.toString());

    // X = D^(-1/2) * (D - W) * D^(-1/2)
    X.assign(W, Functions.minus);
    // System.out.println("DoubleMatrix2D X: (D-W) :\n"+X.toString());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++)
        X.set(i, j, X.get(i, j) * d_minus_1_2.get(i) * d_minus_1_2.get(j));

    // Computes the eigenvalues and the eigenvectors of X
    EigenvalueDecomposition e = new EigenvalueDecomposition(X);
    DoubleMatrix1D lambda = e.getRealEigenvalues();

    // Selects the eigenvector z_2 associated with the second smallest eigenvalue
    // Creates a map that contains the pairs <index, eigenvalue>
    AbstractIntDoubleMap map = new OpenIntDoubleHashMap(n);
    for (int i = 0; i < n; i++) map.put(i, Math.abs(lambda.get(i)));
    IntArrayList list = new IntArrayList();
    // Sorts the map on the value
    map.keysSortedByValue(list);
    // Gets the index of the second smallest element
    int i_2 = list.get(1);

    // y_2 = D^(-1/2) * z_2
    DoubleMatrix1D y_2 = e.getV().viewColumn(i_2).copy();
    y_2.assign(d_minus_1_2, Functions.mult);

    // Creates a map that contains the pairs <i, y_2[i]>
    map.clear();
    for (int i = 0; i < n; i++) map.put(i, y_2.get(i));
    // Sorts the map on the value
    map.keysSortedByValue(list);
    // Search the element in the map previuosly ordered that minimizes the cut
    // of the partition
    double best_cut = Double.POSITIVE_INFINITY;
    int[][] partition = new int[2][];

    // The array v contains all the elements of the graph ordered by their
    // projection on vector y_2
    int[] v = list.elements();
    // For each admissible splitting point i
    for (int i = 1; i < n; i++) {
      // The array a contains all the elements that have a projection on vector
      // y_2 less or equal to the one of i-th element
      // The array b contains the remaining elements
      int[] a = new int[i];
      int[] b = new int[n - i];
      System.arraycopy(v, 0, a, 0, i);
      System.arraycopy(v, i, b, 0, n - i);
      double cut = Ncut(W, a, b, v);
      if (cut < best_cut) {
        best_cut = cut;
        partition[0] = a;
        partition[1] = b;
      }
    }

    // System.out.println("Partition:");
    // UtilsJS.printMatrix(partition);

    return partition;
  }
 /**
  * Merges two sets of points represented as integer vectors. The sets are not overlapped.
  *
  * @param a the first set of points
  * @param b the second set of points
  * @return the union of the two sets
  */
 protected static int[] merge(int[] a, int[] b) {
   int[] v = new int[a.length + b.length];
   System.arraycopy(a, 0, v, 0, a.length);
   System.arraycopy(b, 0, v, a.length, b.length);
   return v;
 }
Beispiel #4
0
  protected double computeFunctionGradientLL(double lambda[], double grad[]) {
    double logli = 0;
    try {
      for (int f = 0; f < lambda.length; f++) {
        grad[f] = -1 * lambda[f] * params.invSigmaSquare;
        logli -= ((lambda[f] * lambda[f]) * params.invSigmaSquare) / 2;
      }
      diter.startScan();
      if (featureGenCache != null) featureGenCache.startDataScan();
      for (int numRecord = 0; diter.hasNext(); numRecord++) {
        DataSequence dataSeq = (DataSequence) diter.next();
        if (featureGenCache != null) featureGenCache.nextDataIndex();
        if (params.debugLvl > 1) {
          Util.printDbg("Read next seq: " + numRecord + " logli " + logli);
        }
        alpha_Y.assign(0);
        for (int f = 0; f < lambda.length; f++) ExpF[f] = RobustMath.LOG0;

        if ((beta_Y == null) || (beta_Y.length < dataSeq.length())) {
          beta_Y = new DenseDoubleMatrix1D[2 * dataSeq.length()];
          for (int i = 0; i < beta_Y.length; i++) beta_Y[i] = new DenseDoubleMatrix1D(numY);
        }
        // compute beta values in a backward scan.
        // also scale beta-values to 1 to avoid numerical problems.
        beta_Y[dataSeq.length() - 1].assign(0);
        for (int i = dataSeq.length() - 1; i > 0; i--) {
          if (params.debugLvl > 2) {
            /*  Util.printDbg("Features fired");
            featureGenerator.startScanFeaturesAt(dataSeq, i);
            while (featureGenerator.hasNext()) {
            Feature feature = featureGenerator.next();
            Util.printDbg(feature.toString());
            }
            */
          }

          // compute the Mi matrix
          initMDone =
              computeLogMi(
                  featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, false, reuseM, initMDone);
          tmp_Y.assign(beta_Y[i]);
          tmp_Y.assign(Ri_Y, sumFunc);
          RobustMath.logMult(Mi_YY, tmp_Y, beta_Y[i - 1], 1, 0, false, edgeGen);
        }

        double thisSeqLogli = 0;
        for (int i = 0; i < dataSeq.length(); i++) {
          // compute the Mi matrix
          initMDone =
              computeLogMi(
                  featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, false, reuseM, initMDone);
          // find features that fire at this position..
          featureGenerator.startScanFeaturesAt(dataSeq, i);

          if (i > 0) {
            tmp_Y.assign(alpha_Y);
            RobustMath.logMult(Mi_YY, tmp_Y, newAlpha_Y, 1, 0, true, edgeGen);
            newAlpha_Y.assign(Ri_Y, sumFunc);
          } else {
            newAlpha_Y.assign(Ri_Y);
          }

          while (featureGenerator.hasNext()) {
            Feature feature = featureGenerator.next();
            int f = feature.index();

            int yp = feature.y();
            int yprev = feature.yprev();
            float val = feature.value();

            if ((dataSeq.y(i) == yp)
                && (((i - 1 >= 0) && (yprev == dataSeq.y(i - 1))) || (yprev < 0))) {
              grad[f] += val;
              thisSeqLogli += val * lambda[f];
              if (params.debugLvl > 2) {
                System.out.println("Feature fired " + f + " " + feature);
              }
            }

            if (yprev < 0) {
              ExpF[f] =
                  RobustMath.logSumExp(
                      ExpF[f], newAlpha_Y.get(yp) + RobustMath.log(val) + beta_Y[i].get(yp));
            } else {
              ExpF[f] =
                  RobustMath.logSumExp(
                      ExpF[f],
                      alpha_Y.get(yprev)
                          + Ri_Y.get(yp)
                          + Mi_YY.get(yprev, yp)
                          + RobustMath.log(val)
                          + beta_Y[i].get(yp));
            }
          }
          alpha_Y.assign(newAlpha_Y);

          if (params.debugLvl > 2) {
            System.out.println("Alpha-i " + alpha_Y.toString());
            System.out.println("Ri " + Ri_Y.toString());
            System.out.println("Mi " + Mi_YY.toString());
            System.out.println("Beta-i " + beta_Y[i].toString());
          }
        }
        double lZx = RobustMath.logSumExp(alpha_Y);
        thisSeqLogli -= lZx;
        logli += thisSeqLogli;
        // update grad.
        for (int f = 0; f < grad.length; f++) {
          grad[f] -= RobustMath.exp(ExpF[f] - lZx);
        }
        if (params.debugLvl > 1) {
          System.out.println(
              "Sequence "
                  + thisSeqLogli
                  + " logli "
                  + logli
                  + " log(Zx) "
                  + lZx
                  + " Zx "
                  + Math.exp(lZx));
        }
      }
      if (params.debugLvl > 2) {
        for (int f = 0; f < lambda.length; f++) System.out.print(lambda[f] + " ");
        System.out.println(" :x");
        for (int f = 0; f < lambda.length; f++) System.out.print(grad[f] + " ");
        System.out.println(" :g");
      }

      if (params.debugLvl > 0)
        Util.printDbg(
            "Iteration "
                + icall
                + " log-likelihood "
                + logli
                + " norm(grad logli) "
                + norm(grad)
                + " norm(x) "
                + norm(lambda));

    } catch (Exception e) {
      System.out.println("Alpha-i " + alpha_Y.toString());
      System.out.println("Ri " + Ri_Y.toString());
      System.out.println("Mi " + Mi_YY.toString());

      e.printStackTrace();
      System.exit(0);
    }
    return logli;
  }
Beispiel #5
0
  protected double computeFunctionGradient(double lambda[], double grad[]) {
    initMDone = false;

    if (params.trainerType.equals("ll")) return computeFunctionGradientLL(lambda, grad);
    double logli = 0;
    try {
      for (int f = 0; f < lambda.length; f++) {
        grad[f] = -1 * lambda[f] * params.invSigmaSquare;
        logli -= ((lambda[f] * lambda[f]) * params.invSigmaSquare) / 2;
      }
      boolean doScaling = params.doScaling;

      diter.startScan();
      if (featureGenCache != null) featureGenCache.startDataScan();
      int numRecord = 0;
      for (numRecord = 0; diter.hasNext(); numRecord++) {
        DataSequence dataSeq = (DataSequence) diter.next();
        if (featureGenCache != null) featureGenCache.nextDataIndex();
        if (params.debugLvl > 1) {
          Util.printDbg("Read next seq: " + numRecord + " logli " + logli);
        }
        alpha_Y.assign(1);
        for (int f = 0; f < lambda.length; f++) ExpF[f] = 0;

        if ((beta_Y == null) || (beta_Y.length < dataSeq.length())) {
          beta_Y = new DenseDoubleMatrix1D[2 * dataSeq.length()];
          for (int i = 0; i < beta_Y.length; i++) beta_Y[i] = new DenseDoubleMatrix1D(numY);

          scale = new double[2 * dataSeq.length()];
        }
        // compute beta values in a backward scan.
        // also scale beta-values to 1 to avoid numerical problems.
        scale[dataSeq.length() - 1] = (doScaling) ? numY : 1;
        beta_Y[dataSeq.length() - 1].assign(1.0 / scale[dataSeq.length() - 1]);
        for (int i = dataSeq.length() - 1; i > 0; i--) {
          if (params.debugLvl > 2) {
            Util.printDbg("Features fired");
            // featureGenerator.startScanFeaturesAt(dataSeq, i);
            // while (featureGenerator.hasNext()) {
            // Feature feature = featureGenerator.next();
            // Util.printDbg(feature.toString());
            // }
          }

          // compute the Mi matrix
          initMDone =
              computeLogMi(
                  featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
          tmp_Y.assign(beta_Y[i]);
          tmp_Y.assign(Ri_Y, multFunc);
          RobustMath.Mult(Mi_YY, tmp_Y, beta_Y[i - 1], 1, 0, false, edgeGen);
          //		Mi_YY.zMult(tmp_Y, beta_Y[i-1]);

          // need to scale the beta-s to avoid overflow
          scale[i - 1] = doScaling ? beta_Y[i - 1].zSum() : 1;
          if ((scale[i - 1] < 1) && (scale[i - 1] > -1)) scale[i - 1] = 1;
          constMultiplier.multiplicator = 1.0 / scale[i - 1];
          beta_Y[i - 1].assign(constMultiplier);
        }

        double thisSeqLogli = 0;
        for (int i = 0; i < dataSeq.length(); i++) {
          // compute the Mi matrix
          initMDone =
              computeLogMi(
                  featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
          // find features that fire at this position..
          featureGenerator.startScanFeaturesAt(dataSeq, i);

          if (i > 0) {
            tmp_Y.assign(alpha_Y);
            RobustMath.Mult(Mi_YY, tmp_Y, newAlpha_Y, 1, 0, true, edgeGen);
            //		Mi_YY.zMult(tmp_Y, newAlpha_Y,1,0,true);
            newAlpha_Y.assign(Ri_Y, multFunc);
          } else {
            newAlpha_Y.assign(Ri_Y);
          }
          while (featureGenerator.hasNext()) {
            Feature feature = featureGenerator.next();
            int f = feature.index();

            int yp = feature.y();
            int yprev = feature.yprev();
            float val = feature.value();
            if ((dataSeq.y(i) == yp)
                && (((i - 1 >= 0) && (yprev == dataSeq.y(i - 1))) || (yprev < 0))) {
              grad[f] += val;
              thisSeqLogli += val * lambda[f];
            }
            if (yprev < 0) {
              ExpF[f] += newAlpha_Y.get(yp) * val * beta_Y[i].get(yp);
            } else {
              ExpF[f] +=
                  alpha_Y.get(yprev)
                      * Ri_Y.get(yp)
                      * Mi_YY.get(yprev, yp)
                      * val
                      * beta_Y[i].get(yp);
            }
          }

          alpha_Y.assign(newAlpha_Y);
          // now scale the alpha-s to avoid overflow problems.
          constMultiplier.multiplicator = 1.0 / scale[i];
          alpha_Y.assign(constMultiplier);

          if (params.debugLvl > 2) {
            System.out.println("Alpha-i " + alpha_Y.toString());
            System.out.println("Ri " + Ri_Y.toString());
            System.out.println("Mi " + Mi_YY.toString());
            System.out.println("Beta-i " + beta_Y[i].toString());
          }
        }
        double Zx = alpha_Y.zSum();
        thisSeqLogli -= log(Zx);
        // correct for the fact that alpha-s were scaled.
        for (int i = 0; i < dataSeq.length(); i++) {
          thisSeqLogli -= log(scale[i]);
        }

        logli += thisSeqLogli;
        // update grad.
        for (int f = 0; f < grad.length; f++) grad[f] -= ExpF[f] / Zx;

        if (params.debugLvl > 1) {
          System.out.println(
              "Sequence "
                  + thisSeqLogli
                  + " logli "
                  + logli
                  + " log(Zx) "
                  + Math.log(Zx)
                  + " Zx "
                  + Zx);
        }
      }
      if (params.debugLvl > 2) {
        for (int f = 0; f < lambda.length; f++) System.out.print(lambda[f] + " ");
        System.out.println(" :x");
        for (int f = 0; f < lambda.length; f++)
          System.out.println(featureGenerator.featureName(f) + " " + grad[f] + " ");
        System.out.println(" :g");
      }

      if (params.debugLvl > 0)
        Util.printDbg(
            "Iter "
                + icall
                + " log likelihood "
                + logli
                + " norm(grad logli) "
                + norm(grad)
                + " norm(x) "
                + norm(lambda));
      if (icall == 0) {
        System.out.println("Number of training records" + numRecord);
      }
    } catch (Exception e) {
      System.out.println("Alpha-i " + alpha_Y.toString());
      System.out.println("Ri " + Ri_Y.toString());
      System.out.println("Mi " + Mi_YY.toString());

      e.printStackTrace();
      System.exit(0);
    }
    return logli;
  }