/**
* Compute and store statistics required for generating artificial data.
*
* @param data training instances
* @exception Exception if statistics could not be calculated successfully
*/
protected void computeStats(Instances data) throws Exception {
int numAttributes = data.numAttributes();
m_AttributeStats = new Vector(numAttributes); // use to map attributes to their stats
for (int j = 0; j < numAttributes; j++) {
if (data.attribute(j).isNominal()) {
// Compute the probability of occurence of each distinct value
int[] nomCounts = (data.attributeStats(j)).nominalCounts;
double[] counts = new double[nomCounts.length];
if (counts.length < 2)
throw new Exception("Nominal attribute has less than two distinct values!");
// Perform Laplace smoothing
for (int i = 0; i < counts.length; i++) counts[i] = nomCounts[i] + 1;
Utils.normalize(counts);
double[] stats = new double[counts.length - 1];
stats[0] = counts[0];
// Calculate cumulative probabilities
for (int i = 1; i < stats.length; i++) stats[i] = stats[i - 1] + counts[i];
m_AttributeStats.add(j, stats);
} else if (data.attribute(j).isNumeric()) {
// Get mean and standard deviation from the training data
double[] stats = new double[2];
stats[0] = data.meanOrMode(j);
stats[1] = Math.sqrt(data.variance(j));
m_AttributeStats.add(j, stats);
} else System.err.println("Decorate can only handle numeric and nominal values.");
}
}
/**
* Calculates the distance between two instances
*
* @param test the first instance
* @param train the second instance
* @return the distance between the two given instances, between 0 and 1
*/
protected double distance(Instance first, Instance second) {
double distance = 0;
int firstI, secondI;
for (int p1 = 0, p2 = 0; p1 < first.numValues() || p2 < second.numValues(); ) {
if (p1 >= first.numValues()) {
firstI = m_instances.numAttributes();
} else {
firstI = first.index(p1);
}
if (p2 >= second.numValues()) {
secondI = m_instances.numAttributes();
} else {
secondI = second.index(p2);
}
if (firstI == m_instances.classIndex()) {
p1++;
continue;
}
if (secondI == m_instances.classIndex()) {
p2++;
continue;
}
double diff;
if (firstI == secondI) {
diff = difference(firstI, first.valueSparse(p1), second.valueSparse(p2));
p1++;
p2++;
} else if (firstI > secondI) {
diff = difference(secondI, 0, second.valueSparse(p2));
p2++;
} else {
diff = difference(firstI, first.valueSparse(p1), 0);
p1++;
}
distance += diff * diff;
}
return Math.sqrt(distance / m_instances.numAttributes());
}
/**
* Returns the best cut of a graph w.r.t. the degree of dissimilarity between points of different
* partitions and the degree of similarity between points of the same partition.
*
* @param W the weight matrix of the graph
* @return an array of two elements, each of these contains the points of a partition
*/
protected static int[][] bestCut(DoubleMatrix2D W) {
int n = W.columns();
// Builds the diagonal matrices D and D^(-1/2) (represented as their diagonals)
DoubleMatrix1D d = DoubleFactory1D.dense.make(n);
DoubleMatrix1D d_minus_1_2 = DoubleFactory1D.dense.make(n);
for (int i = 0; i < n; i++) {
double d_i = W.viewRow(i).zSum();
d.set(i, d_i);
d_minus_1_2.set(i, 1 / Math.sqrt(d_i));
}
DoubleMatrix2D D = DoubleFactory2D.sparse.diagonal(d);
// System.out.println("DoubleMatrix2D :\n"+D.toString());
DoubleMatrix2D X = D.copy();
// System.out.println("DoubleMatrix2D copy :\n"+X.toString());
// X = D^(-1/2) * (D - W) * D^(-1/2)
X.assign(W, Functions.minus);
// System.out.println("DoubleMatrix2D X: (D-W) :\n"+X.toString());
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
X.set(i, j, X.get(i, j) * d_minus_1_2.get(i) * d_minus_1_2.get(j));
// Computes the eigenvalues and the eigenvectors of X
EigenvalueDecomposition e = new EigenvalueDecomposition(X);
DoubleMatrix1D lambda = e.getRealEigenvalues();
// Selects the eigenvector z_2 associated with the second smallest eigenvalue
// Creates a map that contains the pairs <index, eigenvalue>
AbstractIntDoubleMap map = new OpenIntDoubleHashMap(n);
for (int i = 0; i < n; i++) map.put(i, Math.abs(lambda.get(i)));
IntArrayList list = new IntArrayList();
// Sorts the map on the value
map.keysSortedByValue(list);
// Gets the index of the second smallest element
int i_2 = list.get(1);
// y_2 = D^(-1/2) * z_2
DoubleMatrix1D y_2 = e.getV().viewColumn(i_2).copy();
y_2.assign(d_minus_1_2, Functions.mult);
// Creates a map that contains the pairs <i, y_2[i]>
map.clear();
for (int i = 0; i < n; i++) map.put(i, y_2.get(i));
// Sorts the map on the value
map.keysSortedByValue(list);
// Search the element in the map previuosly ordered that minimizes the cut
// of the partition
double best_cut = Double.POSITIVE_INFINITY;
int[][] partition = new int[2][];
// The array v contains all the elements of the graph ordered by their
// projection on vector y_2
int[] v = list.elements();
// For each admissible splitting point i
for (int i = 1; i < n; i++) {
// The array a contains all the elements that have a projection on vector
// y_2 less or equal to the one of i-th element
// The array b contains the remaining elements
int[] a = new int[i];
int[] b = new int[n - i];
System.arraycopy(v, 0, a, 0, i);
System.arraycopy(v, i, b, 0, n - i);
double cut = Ncut(W, a, b, v);
if (cut < best_cut) {
best_cut = cut;
partition[0] = a;
partition[1] = b;
}
}
// System.out.println("Partition:");
// UtilsJS.printMatrix(partition);
return partition;
}
/** if clusterIdx is -1, all instances are used (a single metric for all clusters is used) */
public boolean trainMetric(int clusterIdx) throws Exception {
Init(clusterIdx);
double[] weights = new double[m_numAttributes];
int violatedConstraints = 0;
int numInstances = 0;
for (int instIdx = 0; instIdx < m_instances.numInstances(); instIdx++) {
int assignment = m_clusterAssignments[instIdx];
// only instances assigned to this cluster are of importance
if (assignment == clusterIdx || clusterIdx == -1) {
numInstances++;
if (clusterIdx < 0) {
m_centroid = m_kmeans.getClusterCentroids().instance(assignment);
}
// accumulate variance
Instance instance = m_instances.instance(instIdx);
Instance diffInstance = m_metric.createDiffInstance(instance, m_centroid);
for (int attr = 0; attr < m_numAttributes; attr++) {
weights[attr] += diffInstance.value(attr);
}
// check all constraints for this instance
Object list = m_instanceConstraintMap.get(new Integer(instIdx));
if (list != null) { // there are constraints associated with this instance
ArrayList constraintList = (ArrayList) list;
for (int i = 0; i < constraintList.size(); i++) {
InstancePair pair = (InstancePair) constraintList.get(i);
int linkType = pair.linkType;
int firstIdx = pair.first;
int secondIdx = pair.second;
Instance instance1 = m_instances.instance(firstIdx);
Instance instance2 = m_instances.instance(secondIdx);
int otherIdx =
(firstIdx == instIdx)
? m_clusterAssignments[secondIdx]
: m_clusterAssignments[firstIdx];
if (otherIdx != -1) { // check whether the constraint is violated
if (otherIdx != assignment && linkType == InstancePair.MUST_LINK) {
diffInstance = m_metric.createDiffInstance(instance1, instance2);
for (int attr = 0; attr < m_numAttributes; attr++) {
weights[attr] += 0.5 * m_MLweight * diffInstance.value(attr);
}
} else if (otherIdx == assignment && linkType == InstancePair.CANNOT_LINK) {
diffInstance = m_metric.createDiffInstance(instance1, instance2);
for (int attr = 0; attr < m_numAttributes; attr++) {
// this constraint will be counted twice, hence 0.5
weights[attr] += 0.5 * m_CLweight * m_maxCLDiffInstance.value(attr);
weights[attr] -= 0.5 * m_CLweight * diffInstance.value(attr);
}
}
}
}
}
}
}
// System.out.println("Updating cluster " + clusterIdx
// + " containing " + numInstances);
// check the weights
double[] newWeights = new double[m_numAttributes];
double[] currentWeights = m_metric.getWeights();
boolean needNewtonRaphson = false;
for (int attr = 0; attr < m_numAttributes; attr++) {
if (weights[attr] <= 0) { // check to avoid divide by 0 - TODO!
System.out.println(
"Negative weight "
+ weights[attr]
+ " for clusterIdx="
+ clusterIdx
+ "; using prev value="
+ currentWeights[attr]);
newWeights[attr] = currentWeights[attr];
// needNewtonRaphson = true;
// break;
} else {
if (m_regularize) { // solution of quadratic equation - TODO!
int n = m_instances.numInstances();
double ratio = (m_logTermWeight * n) / (2 * weights[attr]);
newWeights[attr] =
ratio + Math.sqrt(ratio * ratio + (m_regularizerTermWeight * n) / weights[attr]);
} else {
newWeights[attr] = m_logTermWeight * numInstances / weights[attr];
}
}
}
// do NR if needed
if (needNewtonRaphson) {
System.out.println("GOING TO NEWTON-RAPHSON!!!\n");
newWeights = updateWeightsUsingNewtonRaphson(currentWeights, weights);
}
// PRINT routine
// System.out.println("Total constraints violated: " + violatedConstraints/2 + "; weights
// are:");
// for (int attr=0; attr<numAttributes; attr++) {
// System.out.print(newWeights[attr] + "\t");
// }
// System.out.println();
// end PRINT routine
m_metric.setWeights(newWeights);
return true;
}
