/// <summary>
/// Performs the K-Means clustering algorithm on the data set using the provided parameters.
/// </summary>
/// <param name="matrix">Input matrix</param>
/// <param name="similarityMethod">Similarity measure used to compare instances</param>
/// <param name="distanceMethod">Distance measure used to compare instances</param>
/// <param name="clusters">Number of desired clusters</param>
/// <returns>Result set that includes cluster centroids, cluster assignments, and total distortion</returns>
private IClusteringResults PerformKMeansClustering(InsightMatrix matrix,
DistanceMethod? distanceMethod, int? clusters)
{
if (distanceMethod == null)
{
// Default to sum of squared error (equivalent to Euclidean distance)
distanceMethod = DistanceMethod.EuclideanDistance;
}
if (clusters == null)
{
// Need to add some type of intelligent way to figure out a good number
// of clusters to use based on an analysis of the data
clusters = 3;
}
var assignments = new InsightVector(matrix.RowCount);
var centroids = new InsightMatrix(clusters.Value, matrix.ColumnCount);
var random = new Random();
double distortion = -1;
// Initialize means via random selection
for (int i = 0; i < clusters; i++)
{
var samples = new List<int>();
int sample = random.Next(0, matrix.RowCount - 1);
// Make sure we don't use the same instance more than once
while (samples.Exists(x => x == sample))
{
sample = random.Next(0, matrix.RowCount - 1);
}
samples.Add(sample);
centroids.SetRow(i, matrix.Row(sample));
}
// Keep going until convergence point is reached
while (true)
{
// Re-initialize the distortion (total error)
distortion = 0;
// Assign each point to the nearest mean
for (int i = 0; i < matrix.RowCount; i++)
{
// Compute the proximity to each centroid to find the closest match
double closestProximity = -1;
for (int j = 0; j < clusters; j++)
{
double proximity = matrix.Row(i).DistanceFrom(centroids.Row(j), distanceMethod.Value);
if (j == 0)
{
closestProximity = proximity;
assignments[i] = j;
}
else if (proximity < closestProximity)
{
closestProximity = proximity;
assignments[i] = j;
}
}
// Add the proximity value to the total distortion for this solution
distortion += closestProximity;
}
// Calculate the new means for each centroid
var newCentroids = new InsightMatrix(clusters.Value, matrix.ColumnCount);
bool converged = true;
for (int i = 0; i < clusters; i++)
{
int instanceCount = assignments.Where(x => x == i).Count();
// Compute the means for each instance assigned to the current cluster
for (int j = 0; j < newCentroids.ColumnCount; j++)
{
double sum = 0;
for (int k = 0; k < matrix.RowCount; k++)
{
if (assignments[k] == i) sum += matrix[k, j];
}
if (instanceCount > 0)
newCentroids[i, j] = Math.Round(sum / instanceCount, 2);
else
newCentroids[i, j] = centroids[i, j];
if (newCentroids[i, j] != centroids[i, j])
converged = false;
}
centroids.SetRow(i, newCentroids.Row(i));
}
// If the new centroid means did not change then we've reached the final result
if (converged) break;
}
return new ClusteringResults(centroids, assignments, distortion);
}
