Exemple #1
0
  static boolean computeLogMi(
      FeatureGenerator featureGen,
      double lambda[],
      DoubleMatrix2D Mi_YY,
      DoubleMatrix1D Ri_Y,
      boolean takeExp,
      boolean reuseM,
      boolean initMDone) {

    if (reuseM && initMDone) {
      Mi_YY = null;
    } else initMDone = false;
    if (Mi_YY != null) Mi_YY.assign(0);
    Ri_Y.assign(0);
    while (featureGen.hasNext()) {
      Feature feature = featureGen.next();
      int f = feature.index();
      int yp = feature.y();
      int yprev = feature.yprev();
      float val = feature.value();
      //	    System.out.println(feature.toString());

      if (yprev < 0) {
        // this is a single state feature.
        double oldVal = Ri_Y.getQuick(yp);
        Ri_Y.setQuick(yp, oldVal + lambda[f] * val);
      } else if (Mi_YY != null) {
        Mi_YY.setQuick(yprev, yp, Mi_YY.getQuick(yprev, yp) + lambda[f] * val);
        initMDone = true;
      }
    }
    if (takeExp) {
      for (int r = Ri_Y.size() - 1; r >= 0; r--) {
        Ri_Y.setQuick(r, expE(Ri_Y.getQuick(r)));
        if (Mi_YY != null)
          for (int c = Mi_YY.columns() - 1; c >= 0; c--) {
            Mi_YY.setQuick(r, c, expE(Mi_YY.getQuick(r, c)));
          }
      }
    }
    return initMDone;
  }
  /**
   * 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;
  }