scalar_t C45Tree::prune(const InputSet& inputSet,
unsigned int* indices,
unsigned int nbSamples,
bool update) {
// Get the number of labels
const unsigned int nbLabels = inputSet.nbLabels();
// Get the labels and the weights of the samples
const unsigned int* labels = inputSet.labels();
const scalar_t* weights = inputSet.weights();
// Compute the frequency of appearance of each label
std::vector<double> distr(nbLabels, 0); // Use double's for better precision
// Determine the label with the largest frequency
for(unsigned int s = 0; s < nbSamples; ++s) {
distr[labels[indices[s]]] += weights[indices[s]];
}
unsigned int label = std::max_element(distr.begin(), distr.end()) -
distr.begin();
double sumWeights = std::accumulate(distr.begin(), distr.end(), 0.0);
// Update the node if needed
if(update) {
label_ = label;
sumWeights_ = sumWeights;
}
// The error if the tree was a leaf
double leafError = sumWeights - distr[label];
// Add the uncertainty to obtain an upper bounds on the error
leafError += addErrs(sumWeights, leafError);
// If the tree is a leaf
if(!children_[0]) {
// Update the node if needed
if(update) {
distr_.assign(distr.begin(), distr.end());
}
return leafError;
}
// If the tree has children first prune them (bottom-up traversal)
else {
// Build the indices for the left and the right children by partitioning
// the indices in-place
unsigned int rightIndex = Utils::partition(indices,
inputSet.samples(feature_),
nbSamples,
split_);
// Prune the left child
scalar_t treeError = children_[0]->prune(inputSet, indices, rightIndex,
update);
// Prune the right child
treeError += children_[1]->prune(inputSet, indices + rightIndex,
nbSamples - rightIndex, update);
if(!update) {
return treeError;
}
// Compute the classification error on the biggest branch
C45Tree* biggestBranch = children_[0];
C45Tree* smallestBranch = children_[1];
if(biggestBranch->sumWeights_ < smallestBranch->sumWeights_) {
std::swap(biggestBranch, smallestBranch);
}
scalar_t branchError = biggestBranch->prune(inputSet, indices,
nbSamples, false);
// The +0.1 constant comes directly from Dr. Quilans implementation
if(leafError <= branchError + 0.1 && leafError <= treeError + 0.1) {
// Replace the tree by a leaf
// Update the node if needed
distr_.assign(distr.begin(), distr.end());
delete children_[0];
delete children_[1];
children_[0] = 0;
children_[1] = 0;
return leafError;
}
else if(branchError <= treeError + 0.1) {
// Replace the tree by it's biggest branch
delete smallestBranch;
// Recopy the biggest branch
feature_ = biggestBranch->feature_;
split_ = biggestBranch->split_;
children_[0] = biggestBranch->children_[0];
children_[1] = biggestBranch->children_[1];
// Delete the biggest branch top node
biggestBranch->children_[0] = 0;
biggestBranch->children_[1] = 0;
delete biggestBranch;
// Update the subtrees
prune(inputSet, indices, nbSamples, true);
return branchError;
}
else {
return treeError;
}
}
}
void C45Tree::make(const InputSet& inputSet,
unsigned int* indices,
unsigned int nbSamples) {
// Stop if there is only one label (the tree is a leaf), or if we have
// reached the maximum depth
assert(distr_.size() > label_);
if(Utils::geq(distr_[label_], sumWeights_) || !maxDepth_) {
return;
}
// Get the number of features and labels
const unsigned int nbFeatures = inputSet.nbFeatures();
const unsigned int nbLabels = inputSet.nbLabels();
// Get the labels and the weights of the samples
const unsigned int* labels = inputSet.labels();
const scalar_t* weights = inputSet.weights();
// Compute the node's information from the frequency of each label
scalar_t information = 0;
for(unsigned int l = 0; l < nbLabels; ++l) {
information += Utils::entropy(distr_[l]);
}
information -= Utils::entropy(sumWeights_);
// Current best split in node
scalar_t largestGain = 0;
scalar_t sumWeights0 = 0;
std::vector<scalar_t> distr0;
// Frequencies of each label before the split. The frequencies of the labels
// after the split can be directly calculated by subtracting to the total
// frequencies
std::vector<double> partialDistr(nbLabels); // Use double's for better
// precision
// Try to split on every feature
for(unsigned int f = 0; f < nbFeatures; ++f) {
// Set the partial frequencies to zero
std::fill_n(partialDistr.begin(), nbLabels, 0);
// Get the samples (the values of the current feature)
const scalar_t* samples = inputSet.samples(f);
// Sort the indices according to the current feature
Utils::sort(indices, samples, nbSamples);
// Update the weight of the samples before the split by adding the
// weight of each sample at every iteration. The weight of the samples
// after the split is just the sum of the weights minus that weight
double leftWeight = 0; // Use a double for better precision
for(unsigned int s = 0; s < nbSamples - 1; ++s) {
const unsigned int index = indices[s];
const unsigned int nextIndex = indices[s + 1];
const unsigned int label = labels[index];
const scalar_t weight = weights[index];
partialDistr[label] += weight;
leftWeight += weight;
const double rightWeight = sumWeights_ - leftWeight;
// Make sure the weights of the leaves are sufficient and try only
// to split in-between two samples with different feature
if(leftWeight >= minWeight_ && rightWeight >= minWeight_ &&
Utils::less(samples[index], samples[nextIndex])) {
scalar_t leftInfo = 0, rightInfo = 0;
for(unsigned int l = 0; l < nbLabels; ++l) {
leftInfo += Utils::entropy(partialDistr[l]);
rightInfo += Utils::entropy(distr_[l] - partialDistr[l]);
}
leftInfo -= Utils::entropy(leftWeight);
rightInfo -= Utils::entropy(rightWeight);
// Gain of the split
scalar_t gain = information - leftInfo - rightInfo;
// Gain ratio criterion
// gain /= Utils::entropy(leftWeight) +
// Utils::entropy(rightWeight) -
// Utils::entropy(sumWeights_);
// If it is the best gain so far...
if(gain > largestGain) {
largestGain = gain;
feature_ = f;
split_ = (samples[index] + samples[nextIndex]) / 2;
sumWeights0 = leftWeight;
distr0.assign(partialDistr.begin(), partialDistr.end());
}
}
}
}
// If no good split, create a leaf
if(largestGain < Utils::epsilon) {
return;
}
// Create the two children of the tree
children_[0] = new C45Tree(minWeight_, confidence_, maxDepth_ - 1);
children_[1] = new C45Tree(minWeight_, confidence_, maxDepth_ - 1);
// Assign them the correct label, sumWeights and distribution
children_[0]->label_ = std::max_element(distr0.begin(), distr0.end()) -
distr0.begin();
// Ok since the distribution is only needed for leaves
std::transform(distr_.begin(), distr_.end(), distr0.begin(), distr_.begin(),
std::minus<scalar_t>());
children_[1]->label_ = std::max_element(distr_.begin(), distr_.end()) -
distr_.begin();
children_[0]->sumWeights_ = sumWeights0;
children_[1]->sumWeights_ = sumWeights_ - sumWeights0;
children_[0]->distr_.swap(distr0);
children_[1]->distr_.swap(distr_);
// Build the indices for the left and the right children by partitioning
// the indices in-place around the pivot split0
unsigned int rightIndex = Utils::partition(indices,
inputSet.samples(feature_),
nbSamples,
split_);
// Create the two children recursively
children_[0]->make(inputSet, indices, rightIndex);
children_[1]->make(inputSet, indices + rightIndex, nbSamples - rightIndex);
}
