/// <summary>
/// Finds the converged mean for the given input.
/// </summary>
public ExpectationMaximizationResults FindConvergedMeans()
{
var emResults = new ExpectationMaximizationResults();
List <double> initialMeans = this.GetInitializationMeans();
return(this.CalculateExpectationAndMaximize(emResults, initialMeans));
}
/// <summary>
/// Recursive function to calculate the
/// </summary>
ExpectationMaximizationResults CalculateExpectationAndMaximize(
ExpectationMaximizationResults results,
List <double> currentMeans)
{
var newIterationResult = new ExpectationMaximizationIterationResult(
this.mixtureCount, this.inputs);
newIterationResult.Means.AddRange(currentMeans);
double previousLogLikeyHood = 0;
if (results.Results.Count > 0)
{
previousLogLikeyHood = results.Results.Last().LogLikelyHood;
}
var newMeans = new List <double>();
// Calculate the probability Densities
// use the last calculated mean.
for (int i = 0; i < inputs.Length; i++)
{
for (int j = 0; j < mixtureCount; j++)
{
double probabilityDensity =
probabilityRatio * (Math.Pow(
Math.E,
-Math.Pow((inputs[i] - currentMeans[j]), 2) / 2) / Math.Sqrt(2 * Math.PI));
newIterationResult.ProbabilityDensities[i, j] = probabilityDensity;
}
}
// Calculate the latent/hidden variables
for (int i = 0; i < inputs.Length; i++)
{
for (int j = 0; j < mixtureCount; j++)
{
double latentVariable = newIterationResult.ProbabilityDensities[i, j];
double sumOfLatentVariables = 0;
for (int k = 0; k < mixtureCount; k++)
{
sumOfLatentVariables = sumOfLatentVariables +
newIterationResult.ProbabilityDensities[i, k];
}
newIterationResult.LatentVariables[i, j] = latentVariable / sumOfLatentVariables;
}
}
double logLikelyHood = 0;
// Calculate the new mean Loglikely hood and BIC score
// for mixtures based on new hidden variable
for (int j = 0; j < mixtureCount; j++)
{
double sumOfProductOfInputsAndHiddenVariable = 0;
double sumOfHiddenVariable = 0;
for (int i = 0; i < inputs.Length; i++)
{
sumOfProductOfInputsAndHiddenVariable
= sumOfProductOfInputsAndHiddenVariable +
(inputs[i] * newIterationResult.LatentVariables[i, j]);
sumOfHiddenVariable
= sumOfHiddenVariable + newIterationResult.LatentVariables[i, j];
logLikelyHood = logLikelyHood + (newIterationResult.LatentVariables[i, j] *
Math.Pow(inputs[i] - currentMeans[j], 2)) / 2;
}
newMeans.Add(Math.Round(sumOfProductOfInputsAndHiddenVariable / sumOfHiddenVariable, 2));
}
newIterationResult.LogLikelyHood = Math.Round((this.inputs.Length * Math.Log(this.probabilityRatio)) -
(this.inputs.Length * 0.5 * Math.Log(2 * Math.PI)) - logLikelyHood, 4);
newIterationResult.BicScore = Math.Round((2 * newIterationResult.LogLikelyHood)
- (this.mixtureCount * Math.Log(this.inputs.Length)), 4);
results.Results.Add(newIterationResult);
if (Math.Abs(previousLogLikeyHood - newIterationResult.LogLikelyHood) > .0001)
{
this.CalculateExpectationAndMaximize(results, newMeans);
}
return(results);
}
