void AdaBoost<MatType, WeakLearner>::Train(
const MatType& data,
const arma::Row<size_t>& labels,
const WeakLearner& other,
const size_t iterations,
const double tolerance)
{
// Clear information from previous runs.
wl.clear();
alpha.clear();
// Count the number of classes.
classes = (arma::max(labels) - arma::min(labels)) + 1;
this->tolerance = tolerance;
// crt is the cumulative rt value for terminating the optimization when rt is
// changing by less than the tolerance.
double rt, crt, alphat = 0.0, zt;
ztProduct = 1.0;
// To be used for prediction by the weak learner.
arma::Row<size_t> predictedLabels(labels.n_cols);
// Use tempData to modify input data for incorporating weights.
MatType tempData(data);
// This matrix is a helper matrix used to calculate the final hypothesis.
arma::mat sumFinalH = arma::zeros<arma::mat>(classes, predictedLabels.n_cols);
// Load the initial weights into a 2-D matrix.
const double initWeight = 1.0 / double(data.n_cols * classes);
arma::mat D(classes, data.n_cols);
D.fill(initWeight);
// Weights are stored in this row vector.
arma::rowvec weights(predictedLabels.n_cols);
// This is the final hypothesis.
arma::Row<size_t> finalH(predictedLabels.n_cols);
// Now, start the boosting rounds.
for (size_t i = 0; i < iterations; i++)
{
// Initialized to zero in every round. rt is used for calculation of
// alphat; it is the weighted error.
// rt = (sum) D(i) y(i) ht(xi)
rt = 0.0;
// zt is used for weight normalization.
zt = 0.0;
// Build the weight vectors.
weights = arma::sum(D);
// Use the existing weak learner to train a new one with new weights.
WeakLearner w(other, tempData, labels, weights);
w.Classify(tempData, predictedLabels);
// Now from predictedLabels, build ht, the weak hypothesis
// buildClassificationMatrix(ht, predictedLabels);
// Now, calculate alpha(t) using ht.
for (size_t j = 0; j < D.n_cols; j++) // instead of D, ht
{
if (predictedLabels(j) == labels(j))
rt += arma::accu(D.col(j));
else
rt -= arma::accu(D.col(j));
}
if ((i > 0) && (std::abs(rt - crt) < tolerance))
break;
crt = rt;
// Our goal is to find alphat which mizimizes or approximately minimizes the
// value of Z as a function of alpha.
alphat = 0.5 * log((1 + rt) / (1 - rt));
alpha.push_back(alphat);
wl.push_back(w);
// Now start modifying the weights.
for (size_t j = 0; j < D.n_cols; j++)
{
const double expo = exp(alphat);
if (predictedLabels(j) == labels(j))
{
for (size_t k = 0; k < D.n_rows; k++)
{
// We calculate zt, the normalization constant.
D(k, j) /= expo;
zt += D(k, j); // * exp(-1 * alphat * yt(j,k) * ht(j,k));
// Add to the final hypothesis matrix.
// sumFinalH(k, j) += (alphat * ht(k, j));
if (k == labels(j))
sumFinalH(k, j) += (alphat); // * ht(k, j));
else
sumFinalH(k, j) -= (alphat);
}
}
else
{
for (size_t k = 0; k < D.n_rows; k++)
{
// We calculate zt, the normalization constant.
D(k, j) *= expo;
zt += D(k, j);
// Add to the final hypothesis matrix.
if (k == labels(j))
sumFinalH(k, j) += alphat; // * ht(k, j));
else
sumFinalH(k, j) -= alphat;
}
}
}
// Normalize D.
D /= zt;
// Accumulate the value of zt for the Hamming loss bound.
ztProduct *= zt;
}
// Iterations are over, now build a strong hypothesis from a weighted
// combination of these weak hypotheses.
arma::colvec tempSumFinalH;
arma::uword maxIndex;
for (size_t i = 0;i < sumFinalH.n_cols; i++)
{
tempSumFinalH = sumFinalH.unsafe_col(i);
tempSumFinalH.max(maxIndex);
finalH(i) = maxIndex;
}
finalHypothesis = finalH;
}
Adaboost<MatType, WeakLearner>::Adaboost(const MatType& data,
const arma::Row<size_t>& labels, int iterations,
size_t classes, const WeakLearner& other)
{
// note: put a fail safe for the variable 'classes' or
// remove it entirely by using unique function.
int i, j, k;
double rt, alphat = 0.0, zt;
// To be used for prediction by the Weak Learner for prediction.
arma::Row<size_t> predictedLabels(labels.n_cols);
// Use tempData to modify input Data for incorporating weights.
MatType tempData(data);
// Build the classification Matrix yt from labels
arma::mat yt(predictedLabels.n_cols, classes);
// Build a classification matrix of the form D(i,l)
// where i is the ith instance
// l is the lth class.
buildClassificationMatrix(yt, labels);
// ht(x), to be loaded after a round of prediction every time the weak
// learner is run, by using the buildClassificationMatrix function
arma::mat ht(predictedLabels.n_cols, classes);
// This matrix is a helper matrix used to calculate the final hypothesis.
arma::mat sumFinalH(predictedLabels.n_cols, classes);
sumFinalH.fill(0.0);
// load the initial weights into a 2-D matrix
const double initWeight = (double) 1 / (data.n_cols * classes);
arma::mat D(data.n_cols, classes);
D.fill(initWeight);
// D.print("The value of D after initialization.");
// Weights are to be compressed into this rowvector
// for focussing on the perceptron weights.
arma::rowvec weights(predictedLabels.n_cols);
// weights.print("This is the value of weight just after initialization.");
// This is the final hypothesis.
arma::rowvec finalH(predictedLabels.n_cols);
// now start the boosting rounds
for (i = 0; i < iterations; i++)
{
std::cout<<"Run "<<i<<" times !\n";
// Initialized to zero in every round.
rt = 0.0;
zt = 0.0;
// Build the weight vectors
D.print("The value of D in each iteration, just before going for training.");
buildWeightMatrix(D, weights);
// D.print("This is the value of D, before sending off to modify data");
// call the other weak learner and train the labels.
WeakLearner w(other, tempData, weights, labels);
w.Classify(tempData, predictedLabels);
//Now from predictedLabels, build ht, the weak hypothesis
buildClassificationMatrix(ht, predictedLabels);
// Now, start calculation of alpha(t) using ht
// begin calculation of rt
for (j = 0;j < ht.n_rows; j++)
{
for (k = 0;k < ht.n_cols; k++)
rt += (D(j,k) * yt(j,k) * ht(j,k));
}
// end calculation of rt
alphat = 0.5 * log((1 + rt) / (1 - rt));
// end calculation of alphat
// now start modifying weights
for (j = 0;j < D.n_rows; j++)
{
for (k = 0;k < D.n_cols; k++)
{
// we calculate zt, the normalization constant
zt += D(j,k) * exp(-1 * alphat * yt(j,k) * ht(j,k));
D(j,k) = D(j,k) * exp(-1 * alphat * yt(j,k) * ht(j,k));
// adding to the matrix of FinalHypothesis
sumFinalH(j,k) += (alphat * ht(j,k));
}
}
// normalization of D
D = D / zt;
}
// Iterations are over, now build a strong hypothesis
// from a weighted combination of these weak hypotheses.
// This step of storing it in a temporary row vector can be improved upon ?
arma::rowvec tempSumFinalH;
arma::uword max_index;
for (i = 0;i < sumFinalH.n_rows; i++)
{
tempSumFinalH = sumFinalH.row(i);
tempSumFinalH.max(max_index);
finalH(i) = max_index;
}
// labels.print("These are the labels.");
finalH.print("This is the final hypothesis.");
int counterror = 0;
for (i = 0; i < labels.n_cols; i++)
if(labels(i) != finalH(i))
{
std::cout<<i<<"th prediction not correct!\n";
counterror++;
}
std::cout<<"There are "<<counterror<<" number of misclassified records.\n";
std::cout<<"The error rate is: "<<(double)counterror/labels.n_cols;
//finalH is the final hypothesis.
}