public static double WithinClusterVariance(ClusterItem[][] clusters, double[][] centroids, int numSamples, Distance distance)
{
double var = 0;
for (int i = 0; i < clusters.Length; i++)
{
for (int j = 0; j < clusters[i].Length; j++)
{
var += distance.Similarity(clusters[i][j].InputVector, centroids[clusters[i][j].Label]);
}
}
var = var / numSamples * 1.0;
return(var);
}
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="clusters"></param>
/// <param name="numOfInputs"></param>
/// <param name="distance"></param>
/// <returns></returns>
public static double ICL(double[][] centroids, ClusterItem[][] clusters, int numOfInputs, Distance distance)
{
int Q = clusters[0][0].InputVector.Length; // Number of parameters
// group by cluster label
int K = clusters.Length; // No. of clusters
double ICL = ComputeLikelihood(clusters, centroids, numOfInputs, distance) - (((((K * Q) + 1) / 2.0) * Math.Log(numOfInputs)));
double sum1 = 0, sum2 = 0;
for (int i = 0; i < numOfInputs; i++)
{
sum1 += Math.Log(i + ((K + 2.0) / 2.0));
}
for (int k = 0; k < K; k++)
{
if (clusters[k] != null)
{
for (int j = 0; j < clusters[k].Length; j++)
{
sum2 += Math.Log(j + (3.0 / 2.0));
}
}
}
return(ICL - sum1 + sum2);
}
private static double ComputeLikelihood(ClusterItem[][] clusters, double[][] centroids, int numSamples, Distance distance)
{
int N = numSamples; // No. of input vectors
// Calculate Within Cluster Variance
double variance = WithinClusterVariance(clusters, centroids, N, distance);
double[] diff = null;
double likelihood = 0;
for (int i = 0; i < clusters.Length; i++)
{
for (int j = 0; j < clusters[i].Length; j++)
{
diff = VectorSubtraction(clusters[i][j].InputVector, centroids[clusters[i][j].Label]);
likelihood += Math.Log(Math.Exp(-DotProduct(diff, diff) / (2.0 * variance)) / Math.Sqrt(2.0 * Math.PI * variance));
}
}
return(likelihood);
}
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="clusters"></param>
/// <param name="numOfInputs"></param>
/// <param name="distance"></param>
/// <returns></returns>
public static double BIC(double[][] centroids, ClusterItem[][] clusters, int numOfInputs, Distance distance)
{
int Q = clusters[0][0].InputVector.Length; // Number of parameters
// group by cluster label
int K = clusters.Length; // No. of clusters
return(ComputeLikelihood(clusters, centroids, numOfInputs, distance) - (((((K * Q) + 1) / 2.0) * Math.Log(numOfInputs))));
}
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="inputs"></param>
/// <param name="labels"></param>
/// <param name="distance"></param>
/// <returns></returns>
public static double ICL(double[][] centroids, double[][] inputs, int[] labels, Distance distance)
{
int N = inputs.Length; // No. of input vectors
int Q = inputs[0].Length;
// group by cluster label
int[] legends = null;
ClusterItem[][] clusters = GroupByCluster(inputs, labels, out legends);
int K = clusters.Length; // No. of clusters
double ICL = ComputeLikelihood(clusters, centroids, N, distance) - (((((K * Q) + 1) / 2.0) * Math.Log(N)));
double sum1 = 0, sum2 = 0;
for (int i = 0; i < N; i++)
{
sum1 += Math.Log(i + ((K + 2.0) / 2.0));
}
for (int k = 0; k < K; k++)
{
if (clusters[k] != null)
{
for (int j = 0; j < clusters[k].Length; j++)
{
sum2 += Math.Log(j + (3.0 / 2.0));
}
}
}
return(ICL - sum1 + sum2);
}
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="inputs"></param>
/// <param name="labels"></param>
/// <param name="distance"></param>
/// <returns></returns>
public static double BIC(double[][] centroids, double[][] inputs, int[] labels, Distance distance)
{
int N = inputs.Length; // No. of input vectors
int Q = inputs[0].Length;
// group by cluster label
int[] legends = null;
ClusterItem[][] clusters = GroupByCluster(inputs, labels, out legends);
int K = clusters.Length; // No. of clusters
return(ComputeLikelihood(clusters, centroids, N, distance) - (((((K * Q) + 1) / 2.0) * Math.Log(N))));
}
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="clusters"></param>
/// <param name="numOfInputs"></param>
/// <param name="distance"></param>
/// <param name="aic"></param>
/// <param name="bic"></param>
/// <param name="icl"></param>
public static void InformationCriteria(double[][] centroids, ClusterItem[][] clusters, int numOfInputs, Distance distance, out double aic, out double bic, out double icl)
{
int Q = clusters[0][0].InputVector.Length; // Number of parameters
// group by cluster label
int K = clusters.Length; // No. of clusters
double llk = ComputeLikelihood(clusters, centroids, numOfInputs, distance);
aic = llk - ((K * Q) + 1);
bic = llk - (((((K * Q) + 1) / 2.0) * Math.Log(numOfInputs)));
icl = bic;
double sum1 = 0, sum2 = 0;
for (int i = 0; i < numOfInputs; i++)
{
sum1 += Math.Log(i + ((K + 2.0) / 2.0));
}
for (int k = 0; k < K; k++)
{
if (clusters[k] != null)
{
for (int j = 0; j < clusters[k].Length; j++)
{
sum2 += Math.Log(j + (3.0 / 2.0));
}
}
}
icl = icl - sum1 + sum2;
}
// Implemented based on equations from the following publication:
// Feature-Space Clustering for fMRI Meta-Analysis
//by Cyril Goutte, Lars Kai Hansen, Matthew G. Liptrot and Egill Rostrup
// Accessed via https://www.ncbi.nlm.nih.gov/pubmed/11376501
/// <summary>
///
/// </summary>
/// <param name="centroids"></param>
/// <param name="inputs"></param>
/// <param name="labels"></param>
/// <param name="distance"></param>
/// <param name="aic"></param>
/// <param name="bic"></param>
/// <param name="icl"></param>
public static void InformationCriteria(double[][] centroids, double[][] inputs, int[] labels, Distance distance, out double aic, out double bic, out double icl)
{
int N = inputs.Length; // No. of input vectors
int Q = inputs[0].Length;
// group by cluster label
int[] legends = null;
ClusterItem[][] clusters = GroupByCluster(inputs, labels, out legends);
int K = clusters.Length; // No. of clusters
double likelihood = ComputeLikelihood(clusters, centroids, N, distance);
aic = likelihood - ((K * Q) + 1);
bic = likelihood - (((((K * Q) + 1) / 2.0) * Math.Log(N)));
icl = bic;
double sum1 = 0, sum2 = 0;
for (int i = 0; i < N; i++)
{
sum1 += Math.Log(i + ((K + 2.0) / 2.0));
}
for (int k = 0; k < K; k++)
{
if (clusters[k] != null)
{
for (int j = 0; j < clusters[k].Length; j++)
{
sum2 += Math.Log(j + (3.0 / 2.0));
}
}
}
icl = icl - sum1 + sum2;
}
private static double AverageInterDissimilar(double[] currInput, ClusterItem[] cluster, Distance distance)
{
double[] d = new double[cluster.Length];
for (int i = 0; i < d.Length; i++)
{
d[i] = distance.Similarity(currInput, cluster[i].InputVector);
}
return(d.Average());
}
private static double AverageDissimilar(double[] currInput, ClusterItem[] cluster, Distance distance)
{
double[] d = new double[cluster.Length];
for (int i = 0; i < d.Length; i++)
{
d[i] = distance.Similarity(currInput, cluster[i].InputVector);
}
return(d.Sum() / (d.Length - 1)); // remove one element => itself
}
