1) This part has almost same timing as that of total impostors()
Timer::Start("sgd-knn");
// Perform KNN search with differently labeled points as reference
// set and same class points as query set.
knn.Train(dataset.cols(indexDiff[i]));
knn.Search(subDataset.cols(subIndexSame), k, neighbors, distances);
Timer::Stop("sgd-knn");



2) Similarly, the part below is the one which is most inefficient, it takes a lot more time than impostors()

  Timer::Start("sgd-total_computation_part");
  for (size_t i = begin; i < begin + batchSize; i++)
  {
    for (size_t j = 0; j < k ; j++)
    {
      // Calculate cost due to distance between target neighbors & data point.
      double eval = metric.Evaluate(transformedDataset.col(i),
                        transformedDataset.col(targetNeighbors(j, i)));
      cost += (1 - regularization) * eval;

      // Calculate gradient due to target neighbors.
      arma::vec diff = dataset.col(i) - dataset.col(targetNeighbors(j, i));
      cij += diff * arma::trans(diff);
    }

    for (int j = k - 1; j >= 0; j--)
    {
      // Bound constraints to avoid uneccesary computation.
      for (size_t l = 0, bp = k; l < bp ; l++)
      {
        // Calculate cost due to {data point, target neighbors, impostors}
        // triplets.
        double eval = metric.Evaluate(transformedDataset.col(i),
                          transformedDataset.col(targetNeighbors(j, i))) -
                      metric.Evaluate(transformedDataset.col(i),
                          transformedDataset.col(impostors(l, i)));

        // Check bounding condition.
        if (eval < -1)
        {
          // update bound.
          bp = l;
          break;
        }

        cost += regularization * 1 + eval;

        // Caculate gradient due to impostors.
        arma::vec diff = dataset.col(i) - dataset.col(targetNeighbors(j, i));
        cil += diff * arma::trans(diff);

        diff = dataset.col(i) - dataset.col(impostors(l, i));
        cil -= diff * arma::trans(diff);
      }
    }
  }

  gradient = 2 * coordinates * ((1 - regularization) * cij +
      regularization * cil);
  Timer::Stop("sgd-total_computation_part");