public T Run(T startSolution, Func <T, double, T> mutationFunction, Func <T, double> objectiveFunction)
{
if (startSolution == null)
{
throw new ArgumentNullException("startSolution");
}
if (mutationFunction == null)
{
throw new ArgumentNullException("mutationFunction");
}
if (objectiveFunction == null)
{
throw new ArgumentNullException("objectiveFunction");
}
T bestSolution = startSolution;
double minObjective = objectiveFunction(bestSolution);
int lastUpdateIteration = 0;
int currentIteration = 0;
int iterationsFromLastReannealing = 0;
double prevObjective = minObjective;
T prevSolution = bestSolution;
while (currentIteration < this.MaxIterations && currentIteration - lastUpdateIteration < this.MaxStallingIterations)
{
double temperature = CalcTemperature(iterationsFromLastReannealing);
T currentSolution = mutationFunction(prevSolution, temperature);
double currentObjective = objectiveFunction(currentSolution);
double acceptanceProb = CalcAcceptanceProbability(prevObjective, currentObjective, temperature);
if (Random.Double() < acceptanceProb)
{
prevObjective = currentObjective;
prevSolution = currentSolution;
}
if (currentObjective < minObjective)
{
lastUpdateIteration = currentIteration;
minObjective = currentObjective;
bestSolution = currentSolution;
DebugConfiguration.WriteDebugText("Best solution update: {0:0.000}", minObjective);
}
++currentIteration;
if (currentIteration % this.reportRate == 0)
{
DebugConfiguration.WriteDebugText("Iteration {0}", currentIteration);
if (this.AnnealingProgress != null)
{
this.AnnealingProgress(this, new SimulatedAnnealingProgressEventArgs <T>(currentSolution, bestSolution));
}
}
if (iterationsFromLastReannealing >= this.ReannealingInterval)
{
iterationsFromLastReannealing = 0;
prevSolution = bestSolution;
DebugConfiguration.WriteDebugText("Reannealing");
}
else
{
++iterationsFromLastReannealing;
}
}
return(bestSolution);
}
public static Mixture <VectorGaussian> Fit(MicrosoftResearch.Infer.Maths.Vector[] data, int componentCount, int retryCount, double tolerance = 1e-4)
{
Debug.Assert(data != null);
Debug.Assert(data.Length > componentCount * 3);
Debug.Assert(componentCount > 1);
Debug.Assert(retryCount >= 0);
int dimensions = data[0].Count;
// Find point boundary
MicrosoftResearch.Infer.Maths.Vector min = data[0].Clone();
MicrosoftResearch.Infer.Maths.Vector max = min.Clone();
for (int i = 1; i < data.Length; ++i)
{
Debug.Assert(dimensions == data[i].Count);
for (int j = 0; j < dimensions; ++j)
{
min[j] = Math.Min(min[j], data[i][j]);
max[j] = Math.Max(max[j], data[i][j]);
}
}
// Initialize solution
MicrosoftResearch.Infer.Maths.Vector[] means = new MicrosoftResearch.Infer.Maths.Vector[componentCount];
PositiveDefiniteMatrix[] covariances = new PositiveDefiniteMatrix[componentCount];
for (int i = 0; i < componentCount; ++i)
{
GenerateRandomMixtureComponent(min, max, out means[i], out covariances[i]);
}
double[] weights = Enumerable.Repeat(1.0 / componentCount, componentCount).ToArray();
// EM algorithm for GMM
double[,] expectations = new double[data.Length, componentCount];
double lastEstimate;
const double negativeInfinity = -1e+20;
bool convergenceDetected;
double currentEstimate = negativeInfinity;
do
{
lastEstimate = currentEstimate;
convergenceDetected = false;
// E-step: estimate expectations on hidden variables
for (int i = 0; i < data.Length; ++i)
{
double sum = 0;
for (int j = 0; j < componentCount; ++j)
{
expectations[i, j] =
Math.Exp(VectorGaussian.GetLogProb(data[i], means[j], covariances[j])) * weights[j];
sum += expectations[i, j];
}
for (int j = 0; j < componentCount; ++j)
{
expectations[i, j] /= sum;
}
}
// M-step:
// Re-estimate means
for (int j = 0; j < componentCount; ++j)
{
means[j] = MicrosoftResearch.Infer.Maths.Vector.Zero(dimensions);
double sum = 0;
for (int i = 0; i < data.Length; ++i)
{
means[j] += data[i] * expectations[i, j];
sum += expectations[i, j];
}
means[j] *= 1.0 / sum;
}
// Re-estimate covariances
for (int j = 0; j < componentCount; ++j)
{
Matrix covariance = new Matrix(dimensions, dimensions);
double sum = 0;
for (int i = 0; i < data.Length; ++i)
{
MicrosoftResearch.Infer.Maths.Vector dataDiff = data[i] - means[j];
covariance += dataDiff.Outer(dataDiff) * expectations[i, j];
sum += expectations[i, j];
}
covariance *= 1.0 / sum;
covariances[j] = new PositiveDefiniteMatrix(covariance);
if (covariances[j].LogDeterminant() < -30)
{
DebugConfiguration.WriteDebugText("Convergence detected for component {0}", j);
if (retryCount == 0)
{
throw new InvalidOperationException("Can't fit GMM. Retry number exceeded.");
}
retryCount -= 1;
GenerateRandomMixtureComponent(min, max, out means[j], out covariances[j]);
DebugConfiguration.WriteDebugText("Component {0} regenerated", j);
convergenceDetected = true;
}
}
if (convergenceDetected)
{
currentEstimate = negativeInfinity;
continue;
}
// Re-estimate weights
double expectationSum = 0;
for (int j = 0; j < componentCount; ++j)
{
weights[j] = 0;
for (int i = 0; i < data.Length; ++i)
{
weights[j] += expectations[i, j];
expectationSum += expectations[i, j];
}
}
for (int j = 0; j < componentCount; ++j)
{
weights[j] /= expectationSum;
}
// Compute likelihood estimate
currentEstimate = 0;
for (int i = 0; i < data.Length; ++i)
{
for (int j = 0; j < componentCount; ++j)
{
currentEstimate +=
expectations[i, j] * (VectorGaussian.GetLogProb(data[i], means[j], covariances[j]) + Math.Log(weights[j]));
}
}
DebugConfiguration.WriteDebugText("L={0:0.000000}", currentEstimate);
} while (convergenceDetected || (currentEstimate - lastEstimate > tolerance));
Mixture <VectorGaussian> result = new Mixture <VectorGaussian>();
for (int j = 0; j < componentCount; ++j)
{
result.Add(VectorGaussian.FromMeanAndVariance(means[j], covariances[j]), weights[j]);
}
DebugConfiguration.WriteDebugText("GMM successfully fitted.");
return(result);
}
private SortedSet <EnergyBound> BreadthFirstBranchAndBoundTraverse(ShapeConstraints constraints)
{
SortedSet <EnergyBound> front = new SortedSet <EnergyBound> {
this.CalculateEnergyBound(constraints)
};
int currentIteration = 1;
DateTime lastOutputTime = startTime;
int processedConstraintSets = 0;
while (!front.Min.Constraints.CheckIfSatisfied(this.maxCoordFreedom, this.maxWidthFreedom) && !this.IsStopping)
{
this.WaitIfPaused();
EnergyBound parentLowerBound = front.Min;
front.Remove(parentLowerBound);
List <ShapeConstraints> expandedConstraints = parentLowerBound.Constraints.SplitMostFree(this.maxCoordFreedom, this.maxWidthFreedom);
foreach (ShapeConstraints constraintsSet in expandedConstraints)
{
EnergyBound lowerBound = this.CalculateEnergyBound(constraintsSet);
front.Add(lowerBound);
// Uncomment for strong invariants check
//ObjectBackgroundTerm[,] lowerBoundShapeTerm = new ObjectBackgroundTerm[this.segmentedImage.Width, this.segmentedImage.Height];
//for (int i = 0; i < this.segmentedImage.Width; ++i)
// for (int j = 0; j < this.segmentedImage.Height; ++j)
// lowerBoundShapeTerm[i, j] = CpuBranchAndBoundShapeTermsCalculator.CalculateShapeTerm(lowerBound.Constraints, new Point(i, j));
//ObjectBackgroundTerm[,] parentLowerBoundShapeTerm = new ObjectBackgroundTerm[this.segmentedImage.Width, this.segmentedImage.Height];
//for (int i = 0; i < this.segmentedImage.Width; ++i)
// for (int j = 0; j < this.segmentedImage.Height; ++j)
// parentLowerBoundShapeTerm[i, j] = CpuBranchAndBoundShapeTermsCalculator.CalculateShapeTerm(parentLowerBound.Constraints, new Point(i, j));
//for (int i = 0; i < this.segmentedImage.Width; ++i)
// for (int j = 0; j < this.segmentedImage.Height; ++j)
// {
// Debug.Assert(lowerBoundShapeTerm[i, j].ObjectTerm >= parentLowerBoundShapeTerm[i, j].ObjectTerm - 1e-7);
// Debug.Assert(lowerBoundShapeTerm[i, j].BackgroundTerm >= parentLowerBoundShapeTerm[i, j].BackgroundTerm - 1e-7);
// //CalculateShapeTerm(lowerBound.Constraints, new Point(0, 67));
// //CalculateShapeTerm(parentLowerBound.Constraints, new Point(0, 67));
// }
// Lower bound should not decrease (check always, it's important!)
Trace.Assert(lowerBound.SegmentationEnergy >= parentLowerBound.SegmentationEnergy - 1e-6);
Trace.Assert(lowerBound.ShapeEnergy >= parentLowerBound.ShapeEnergy - 1e-6);
//this.CalculateEnergyBound(lowerBound.Constraints);
//this.CalculateEnergyBound(parentLowerBound.Constraints);
++processedConstraintSets;
}
// Some debug output
if (currentIteration % this.ProgressReportRate == 0)
{
DateTime currentTime = DateTime.Now;
EnergyBound currentMin = front.Min;
DebugConfiguration.WriteDebugText(
"On iteration {0} front contains {1} constraint sets.", currentIteration, front.Count);
DebugConfiguration.WriteDebugText(
"Current lower bound is {0:0.0000} ({1:0.0000} + {2:0.0000}).",
currentMin.Bound,
currentMin.SegmentationEnergy,
currentMin.ShapeEnergy * this.ShapeEnergyWeight);
double processingSpeed = processedConstraintSets / (currentTime - lastOutputTime).TotalSeconds;
DebugConfiguration.WriteDebugText("Processing speed is {0:0.000} items per sec", processingSpeed);
double maxVertexConstraintsFreedom = currentMin.Constraints.VertexConstraints.Max(c => c.Freedom);
double maxEdgeConstraintsFreedom = currentMin.Constraints.EdgeConstraints.Max(c => c.Freedom);
DebugConfiguration.WriteDebugText(
"Max vertex freedom: {0:0.00}, max edge freedom: {1:0.00}",
maxVertexConstraintsFreedom,
maxEdgeConstraintsFreedom);
DebugConfiguration.WriteDebugText("Elapsed time: {0}", DateTime.Now - this.startTime);
DebugConfiguration.WriteDebugText();
this.ReportBranchAndBoundProgress(front);
lastOutputTime = currentTime;
processedConstraintSets = 0;
}
currentIteration += 1;
}
return(front);
}