/**
* Constructor. Learns a classification tree for AdaBoost and Random Forest.
*
* @param attributes the attribute properties.
* @param x the training instances.
* @param y the response variable.
* @param nodeSize the minimum size of leaf nodes.
* @param maxNodes the maximum number of leaf nodes in the tree.
* @param mtry the number of input variables to pick to split on at each node. It seems that
* sqrt(p) give generally good performance, where p is the number of variables.
* @param rule the splitting rule.
* @param order the index of training values in ascending order. Note that only numeric attributes
* need be sorted.
* @param samples the sample set of instances for stochastic learning. samples[i] is the number of
* sampling for instance i.
*/
public DecisionTree(
Attribute[] attributes,
double[][] x,
int[] y,
int maxNodes,
int nodeSize,
int mtry,
SplitRule rule,
int[] samples,
int[][] order) {
if (x.length != y.length) {
throw new IllegalArgumentException(
String.format("The sizes of X and Y don't match: %d != %d", x.length, y.length));
}
if (mtry < 1 || mtry > x[0].length) {
throw new IllegalArgumentException(
"Invalid number of variables to split on at a node of the tree: " + mtry);
}
if (maxNodes < 2) {
throw new IllegalArgumentException("Invalid maximum leaves: " + maxNodes);
}
if (nodeSize < 1) {
throw new IllegalArgumentException("Invalid minimum size of leaf nodes: " + nodeSize);
}
// class label set.
int[] labels = Math.unique(y);
Arrays.sort(labels);
for (int i = 0; i < labels.length; i++) {
if (labels[i] < 0) {
throw new IllegalArgumentException("Negative class label: " + labels[i]);
}
if (i > 0 && labels[i] - labels[i - 1] > 1) {
throw new IllegalArgumentException("Missing class: " + labels[i] + 1);
}
}
k = labels.length;
if (k < 2) {
throw new IllegalArgumentException("Only one class.");
}
if (attributes == null) {
int p = x[0].length;
attributes = new Attribute[p];
for (int i = 0; i < p; i++) {
attributes[i] = new NumericAttribute("V" + (i + 1));
}
}
this.attributes = attributes;
this.mtry = mtry;
this.nodeSize = nodeSize;
this.maxNodes = maxNodes;
this.rule = rule;
importance = new double[attributes.length];
if (order != null) {
this.order = order;
} else {
int n = x.length;
int p = x[0].length;
double[] a = new double[n];
this.order = new int[p][];
for (int j = 0; j < p; j++) {
if (attributes[j] instanceof NumericAttribute) {
for (int i = 0; i < n; i++) {
a[i] = x[i][j];
}
this.order[j] = QuickSort.sort(a);
}
}
}
// Priority queue for best-first tree growing.
PriorityQueue<TrainNode> nextSplits = new PriorityQueue<>();
int n = y.length;
int[] count = new int[k];
if (samples == null) {
samples = new int[n];
for (int i = 0; i < n; i++) {
samples[i] = 1;
count[y[i]]++;
}
} else {
for (int i = 0; i < n; i++) {
count[y[i]] += samples[i];
}
}
double[] posteriori = new double[k];
for (int i = 0; i < k; i++) {
posteriori[i] = (double) count[i] / n;
}
root = new Node(Math.whichMax(count), posteriori);
TrainNode trainRoot = new TrainNode(root, x, y, samples);
// Now add splits to the tree until max tree size is reached
if (trainRoot.findBestSplit()) {
nextSplits.add(trainRoot);
}
// Pop best leaf from priority queue, split it, and push
// children nodes into the queue if possible.
for (int leaves = 1; leaves < this.maxNodes; leaves++) {
// parent is the leaf to split
TrainNode node = nextSplits.poll();
if (node == null) {
break;
}
node.split(nextSplits); // Split the parent node into two children nodes
}
}
/** Split the node into two children nodes. Returns true if split success. */
public boolean split(PriorityQueue<TrainNode> nextSplits) {
if (node.splitFeature < 0) {
throw new IllegalStateException("Split a node with invalid feature.");
}
int n = x.length;
int tc = 0;
int fc = 0;
int[] trueSamples = new int[n];
int[] falseSamples = new int[n];
if (attributes[node.splitFeature].getType() == Attribute.Type.NOMINAL) {
for (int i = 0; i < n; i++) {
if (samples[i] > 0) {
if (x[i][node.splitFeature] == node.splitValue) {
trueSamples[i] = samples[i];
tc += samples[i];
} else {
falseSamples[i] = samples[i];
fc += samples[i];
}
}
}
} else if (attributes[node.splitFeature].getType() == Attribute.Type.NUMERIC) {
for (int i = 0; i < n; i++) {
if (samples[i] > 0) {
if (x[i][node.splitFeature] <= node.splitValue) {
trueSamples[i] = samples[i];
tc += samples[i];
} else {
falseSamples[i] = samples[i];
fc += samples[i];
}
}
}
} else {
throw new IllegalStateException(
"Unsupported attribute type: " + attributes[node.splitFeature].getType());
}
if (tc < nodeSize || fc < nodeSize) {
node.splitFeature = -1;
node.splitValue = Double.NaN;
node.splitScore = 0.0;
return false;
}
double[] trueChildPosteriori = new double[k];
double[] falseChildPosteriori = new double[k];
for (int i = 0; i < n; i++) {
int yi = y[i];
trueChildPosteriori[yi] += trueSamples[i];
falseChildPosteriori[yi] += falseSamples[i];
}
// add-k smoothing of posteriori probability
for (int i = 0; i < k; i++) {
trueChildPosteriori[i] = (trueChildPosteriori[i] + 1) / (tc + k);
falseChildPosteriori[i] = (falseChildPosteriori[i] + 1) / (fc + k);
}
node.trueChild = new Node(node.trueChildOutput, trueChildPosteriori);
node.falseChild = new Node(node.falseChildOutput, falseChildPosteriori);
TrainNode trueChild = new TrainNode(node.trueChild, x, y, trueSamples);
if (tc > nodeSize && trueChild.findBestSplit()) {
if (nextSplits != null) {
nextSplits.add(trueChild);
} else {
trueChild.split(null);
}
}
TrainNode falseChild = new TrainNode(node.falseChild, x, y, falseSamples);
if (fc > nodeSize && falseChild.findBestSplit()) {
if (nextSplits != null) {
nextSplits.add(falseChild);
} else {
falseChild.split(null);
}
}
importance[node.splitFeature] += node.splitScore;
return true;
}