/**
* Constructor. Learn Fisher's linear discriminant.
*
* @param x training instances.
* @param y training labels in [0, k), where k is the number of classes.
* @param L the dimensionality of mapped space.
* @param tol a tolerance to decide if a covariance matrix is singular; it will reject variables
* whose variance is less than tol<sup>2</sup>.
*/
public FLD(double[][] x, int[] y, int L, double tol) {
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));
}
// 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 (tol < 0.0) {
throw new IllegalArgumentException("Invalid tol: " + tol);
}
if (x.length <= k) {
throw new IllegalArgumentException(
String.format("Sample size is too small: %d <= %d", x.length, k));
}
if (L >= k) {
throw new IllegalArgumentException(
String.format("The dimensionality of mapped space is too high: %d >= %d", L, k));
}
if (L <= 0) {
L = k - 1;
}
final int n = x.length;
p = x[0].length;
// The number of instances in each class.
int[] ni = new int[k];
// Common mean vector.
mean = Math.colMean(x);
// Common covariance.
double[][] T = new double[p][p];
// Class mean vectors.
mu = new double[k][p];
for (int i = 0; i < n; i++) {
int c = y[i];
ni[c]++;
for (int j = 0; j < p; j++) {
mu[c][j] += x[i][j];
}
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < p; j++) {
mu[i][j] = mu[i][j] / ni[i] - mean[j];
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < p; j++) {
for (int l = 0; l <= j; l++) {
T[j][l] += (x[i][j] - mean[j]) * (x[i][l] - mean[l]);
}
}
}
for (int j = 0; j < p; j++) {
for (int l = 0; l <= j; l++) {
T[j][l] /= n;
T[l][j] = T[j][l];
}
}
// Between class scatter
double[][] B = new double[p][p];
for (int i = 0; i < k; i++) {
for (int j = 0; j < p; j++) {
for (int l = 0; l <= j; l++) {
B[j][l] += mu[i][j] * mu[i][l];
}
}
}
for (int j = 0; j < p; j++) {
for (int l = 0; l <= j; l++) {
B[j][l] /= k;
B[l][j] = B[j][l];
}
}
EigenValueDecomposition eigen = EigenValueDecomposition.decompose(T, true);
tol = tol * tol;
double[] s = eigen.getEigenValues();
for (int i = 0; i < s.length; i++) {
if (s[i] < tol) {
throw new IllegalArgumentException("The covariance matrix is close to singular.");
}
s[i] = 1.0 / s[i];
}
double[][] U = eigen.getEigenVectors();
double[][] UB = Math.atbmm(U, B);
for (int i = 0; i < k; i++) {
for (int j = 0; j < p; j++) {
UB[i][j] *= s[j];
}
}
Math.abmm(U, UB, B);
eigen = EigenValueDecomposition.decompose(B, true);
U = eigen.getEigenVectors();
scaling = new double[p][L];
for (int i = 0; i < p; i++) {
System.arraycopy(U[i], 0, scaling[i], 0, L);
}
smean = new double[L];
Math.atx(scaling, mean, smean);
smu = Math.abmm(mu, scaling);
}
/**
* 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
}
}
