static void ComputeNormalizationFactorsRecurse(
Tree <AxisAlignedFeatureResponse, GaussianAggregator2d> t,
int nodeIndex,
int nTrainingPoints,
Bounds bounds,
double[] normalizationFactors)
{
GaussianPdf2d g = t.GetNode(nodeIndex).TrainingDataStatistics.GetPdf();
// Evaluate integral of bivariate normal distribution within this node's bounds
double u = CumulativeNormalDistribution2d.M(
(bounds.Upper[0] - g.MeanX) / Math.Sqrt(g.VarianceX),
(bounds.Upper[1] - g.MeanY) / Math.Sqrt(g.VarianceY),
g.CovarianceXY / Math.Sqrt(g.VarianceX * g.VarianceY));
double l = CumulativeNormalDistribution2d.M(
(bounds.Lower[0] - g.MeanX) / Math.Sqrt(g.VarianceX),
(bounds.Lower[1] - g.MeanY) / Math.Sqrt(g.VarianceY),
g.CovarianceXY / Math.Sqrt(g.VarianceX * g.VarianceY));
normalizationFactors[nodeIndex] = (double)(t.GetNode(nodeIndex).TrainingDataStatistics.SampleCount) / nTrainingPoints * 1.0 / (u - l);
if (!t.GetNode(nodeIndex).IsLeaf)
{
Bounds leftChildBounds = bounds.Clone();
leftChildBounds.Upper[t.GetNode(nodeIndex).Feature.Axis] = t.GetNode(nodeIndex).Threshold;
ComputeNormalizationFactorsRecurse(t, nodeIndex * 2 + 1, nTrainingPoints, leftChildBounds, normalizationFactors);
Bounds rightChildBounds = bounds.Clone();
rightChildBounds.Lower[t.GetNode(nodeIndex).Feature.Axis] = t.GetNode(nodeIndex).Threshold;
ComputeNormalizationFactorsRecurse(t, nodeIndex * 2 + 2, nTrainingPoints, rightChildBounds, normalizationFactors);
}
}
public static Bitmap VisualizeLabels(Forest <LinearFeatureResponse2d, SemiSupervisedClassificationStatisticsAggregator> forest, DataPointCollection trainingData, Size PlotSize, PointF PlotDilation)
{
// Generate some test samples in a grid pattern (a useful basis for creating visualization images)
PlotCanvas plotCanvas = new PlotCanvas(trainingData.GetRange(0), trainingData.GetRange(1), PlotSize, PlotDilation);
// Apply the trained forest to the test data
Console.WriteLine("\nApplying the forest to test data...");
DataPointCollection testData = DataPointCollection.Generate2dGrid(plotCanvas.plotRangeX, PlotSize.Width, plotCanvas.plotRangeY, PlotSize.Height);
int[][] leafNodeIndices = forest.Apply(testData);
Bitmap result = new Bitmap(PlotSize.Width, PlotSize.Height);
// Paint the test data
GaussianPdf2d[][] leafDistributions = new GaussianPdf2d[forest.TreeCount][];
for (int t = 0; t < forest.TreeCount; t++)
{
leafDistributions[t] = new GaussianPdf2d[forest.GetTree(t).NodeCount];
for (int i = 0; i < forest.GetTree(t).NodeCount; i++)
{
Node <LinearFeatureResponse2d, SemiSupervisedClassificationStatisticsAggregator> nodeCopy = forest.GetTree(t).GetNode(i);
if (nodeCopy.IsLeaf)
{
leafDistributions[t][i] = nodeCopy.TrainingDataStatistics.GaussianAggregator2d.GetPdf();
}
}
}
// Form a palette of random colors, one per class
Color[] colors = new Color[Math.Max(trainingData.CountClasses(), 4)];
// First few colours are same as those in the book, remainder are random.
colors[0] = Color.FromArgb(183, 170, 8);
colors[1] = Color.FromArgb(194, 32, 14);
colors[2] = Color.FromArgb(4, 154, 10);
colors[3] = Color.FromArgb(13, 26, 188);
Color grey = Color.FromArgb(255, 127, 127, 127);
System.Random r = new Random(0); // same seed every time so colours will be consistent
for (int c = 4; c < colors.Length; c++)
{
colors[c] = Color.FromArgb(255, r.Next(0, 255), r.Next(0, 255), r.Next(0, 255));
}
int index = 0;
for (int j = 0; j < PlotSize.Height; j++)
{
for (int i = 0; i < PlotSize.Width; i++)
{
// Aggregate statistics for this sample over all leaf nodes reached
HistogramAggregator h = new HistogramAggregator(trainingData.CountClasses());
for (int t = 0; t < forest.TreeCount; t++)
{
int leafIndex = leafNodeIndices[t][index];
SemiSupervisedClassificationStatisticsAggregator a = forest.GetTree(t).GetNode(leafIndex).TrainingDataStatistics;
h.Aggregate(a.HistogramAggregator);
}
// Let's muddy the colors with a little grey where entropy is high.
float mudiness = 0.5f * (float)(h.Entropy());
float R = 0.0f, G = 0.0f, B = 0.0f;
for (int b = 0; b < trainingData.CountClasses(); b++)
{
float p = (1.0f - mudiness) * h.GetProbability(b); // NB probabilities sum to 1.0 over the classes
R += colors[b].R * p;
G += colors[b].G * p;
B += colors[b].B * p;
}
R += grey.R * mudiness;
G += grey.G * mudiness;
B += grey.B * mudiness;
Color c = Color.FromArgb(255, (byte)(R), (byte)(G), (byte)(B));
result.SetPixel(i, j, c);
index++;
}
}
PaintTrainingData(trainingData, plotCanvas, result);
return(result);
}
public static Forest <LinearFeatureResponse2d, SemiSupervisedClassificationStatisticsAggregator> Train(
DataPointCollection trainingData,
TrainingParameters parameters,
double a_,
double b_)
{
// Train the forest
Console.WriteLine("Training the forest...");
Random random = new Random();
ITrainingContext <LinearFeatureResponse2d, SemiSupervisedClassificationStatisticsAggregator> classificationContext
= new SemiSupervisedClassificationTrainingContext(trainingData.CountClasses(), random, a_, b_);
var forest = ForestTrainer <LinearFeatureResponse2d, SemiSupervisedClassificationStatisticsAggregator> .TrainForest(
random,
parameters,
classificationContext,
trainingData);
// Label transduction to unlabelled leaves from nearest labelled leaf
List <int> unlabelledLeafIndices = null;
List <int> labelledLeafIndices = null;
int[] closestLabelledLeafIndices = null;
List <int> leafIndices = null;
for (int t = 0; t < forest.TreeCount; t++)
{
var tree = forest.GetTree(t);
leafIndices = new List <int>();
unlabelledLeafIndices = new List <int>();
labelledLeafIndices = new List <int>();
for (int n = 0; n < tree.NodeCount; n++)
{
if (tree.GetNode(n).IsLeaf)
{
if (tree.GetNode(n).TrainingDataStatistics.HistogramAggregator.SampleCount == 0)
{
unlabelledLeafIndices.Add(leafIndices.Count);
}
else
{
labelledLeafIndices.Add(leafIndices.Count);
}
leafIndices.Add(n);
}
}
// Build an upper triangular matrix of inter-leaf distances
float[,] interLeafDistances = new float[leafIndices.Count, leafIndices.Count];
for (int i = 0; i < leafIndices.Count; i++)
{
for (int j = i + 1; j < leafIndices.Count; j++)
{
SemiSupervisedClassificationStatisticsAggregator a = tree.GetNode(leafIndices[i]).TrainingDataStatistics;
SemiSupervisedClassificationStatisticsAggregator b = tree.GetNode(leafIndices[j]).TrainingDataStatistics;
GaussianPdf2d x = a.GaussianAggregator2d.GetPdf();
GaussianPdf2d y = b.GaussianAggregator2d.GetPdf();
interLeafDistances[i, j] = (float)(Math.Max(
x.GetNegativeLogProbability((float)(y.MeanX), (float)(y.MeanY)),
+y.GetNegativeLogProbability((float)(x.MeanX), (float)(x.MeanY))));
}
}
// Find shortest paths between all pairs of nodes in the graph of leaf nodes
FloydWarshall pathFinder = new FloydWarshall(interLeafDistances);
// Find the closest labelled leaf to each unlabelled leaf
float[] minDistances = new float[unlabelledLeafIndices.Count];
closestLabelledLeafIndices = new int[unlabelledLeafIndices.Count];
for (int i = 0; i < minDistances.Length; i++)
{
minDistances[i] = float.PositiveInfinity;
closestLabelledLeafIndices[i] = -1; // unused so deliberately invalid
}
for (int l = 0; l < labelledLeafIndices.Count; l++)
{
for (int u = 0; u < unlabelledLeafIndices.Count; u++)
{
if (pathFinder.GetMinimumDistance(unlabelledLeafIndices[u], labelledLeafIndices[l]) < minDistances[u])
{
minDistances[u] = pathFinder.GetMinimumDistance(unlabelledLeafIndices[u], labelledLeafIndices[l]);
closestLabelledLeafIndices[u] = leafIndices[labelledLeafIndices[l]];
}
}
}
// Propagate class probability distributions to each unlabelled
// leaf from its nearest labelled leaf.
for (int u = 0; u < unlabelledLeafIndices.Count; u++)
{
// Unhelpfully, C# only allows us to pass value types by value
// so Tree.GetNode() returns only a COPY of the Node. We update
// this copy and then copy it back over the top of the
// original via Tree.SetNode().
// The C++ version is a lot better!
var unlabelledLeafCopy = tree.GetNode(leafIndices[unlabelledLeafIndices[u]]);
var labelledLeafCopy = tree.GetNode(closestLabelledLeafIndices[u]);
unlabelledLeafCopy.TrainingDataStatistics.HistogramAggregator
= (HistogramAggregator)(labelledLeafCopy.TrainingDataStatistics.HistogramAggregator.DeepClone());
tree.SetNode(leafIndices[unlabelledLeafIndices[u]], unlabelledLeafCopy);
}
}
return(forest);
}
