// kmeans partitions datapoints into K clusters. This results in a partitioning of
// the data space into Voronoi cells. The problem is NP-hard so here we attempt
// to parallelize or make concurrent as many processes as possible to reduce the
// running time.
//
// 1. Place K points into the space represented by the objects that are being clustered.
// These points represent initial group centroids.
//
// 2. Assign each object to the group that has the closest centroid.
//
// 3. When all objects have been assigned, recalculate the positions of the K centroids
// by calculating the mean of all cooridnates in a cluster and making that
// the new centroid.
//
// 4. Repeat Steps 2 and 3 until the centroids no longer move.
//
// centroids is K x M matrix that cotains the coordinates for the centroids.
// The centroids are indexed by the 0 based rows of this matrix.
// ____ _________
// | 12.29 32.94 ... | <-- The coordinates for centroid 0
// | 4.6 29.22 ... | <-- The coordinates for centroid 1
// |_____ __________|
//
//
// CentPointDist is ax R x M matrix. The rows have a 1:1 relationship to
// the rows in datapoints. Column 0 contains the row number in centroids
// that corresponds to the centroid for the datapoint in row i of this matrix.
// Column 1 contains (x_i - mu(i))^2.
// ____ _______
// | 3 38.01 | <-- Centroid 3, squared error for the coordinates in row 0 of datapoints
// | 1 23 .21| <-- Centroid 1, squared error for the coordinates in row 1 of datapoints
// | 0 14.12 | <-- Centroid 0, squared error for the coordinates in row 2 of datapoints
// _____ _______
//
func kmeans(datapoints, centroids *matrix.DenseMatrix, measurer VectorMeasurer) Model {
/* datapoints CentPoinDist centroids
________________
____ ____ __|__ ______ | ____ ___________
| ... | | ... | V | ... |
| 3.0 5.1| <-- row i --> | 3 32.12 | row 3 | 3 38.1, ... |
|____ ___| |____ ______| |___ __________ |
*/
R, M := datapoints.GetSize()
CentPointDist := matrix.Zeros(R, 2)
k, _ := centroids.GetSize()
clusterChanged := true
var clusters []cluster
for clusterChanged == true {
clusterChanged = false
clusters = make([]cluster, 0)
jobs := make(chan PairPointCentroidJob, 1024)
results := make(chan PairPointCentroidResult, 1024)
done := make(chan int, 1024)
// Pair each point with its closest centroid.
go addPairPointCentroidJobs(jobs, datapoints, centroids, measurer, results)
for i := 0; i < numworkers; i++ {
go doPairPointCentroidJobs(done, jobs)
}
go awaitPairPointCentroidCompletion(done, results)
clusterChanged = assessClusters(CentPointDist, results) // This blocks so that all the results can be processed
// You have each data point grouped with a centroid,
for idx, cent := 0, 0; cent < k; cent++ {
// Select all the rows in CentPointDist whose first col value == cent.
// Get the corresponding row vector from datapoints and place it in pointsInCluster.
r, _ := CentPointDist.GetSize()
matches := make([]int, 0)
for i := 0; i < r; i++ {
v := CentPointDist.Get(i, 0)
if v == float64(cent) {
matches = append(matches, i)
}
}
// It is possible that some centroids may have zero points, so there
// may not be any matches.
if len(matches) == 0 {
continue
}
pointsInCluster := matrix.Zeros(len(matches), M)
i := 0
for _, rownum := range matches {
pointsInCluster.Set(i, 0, datapoints.Get(int(rownum), 0))
pointsInCluster.Set(i, 1, datapoints.Get(int(rownum), 1))
i++
}
// pointsInCluster now contains all the data points for the current
// centroid. The mean of the coordinates for this cluster becomes
// the new centroid for this cluster.
mean := pointsInCluster.MeanCols()
centroids.SetRowVector(mean, cent)
clust := cluster{pointsInCluster, mean, 0}
clust.Variance = variance(clust, measurer)
clusters = append(clusters, clust)
idx++
}
}
modelbic := calcbic(R, M, clusters)
model := Model{modelbic, clusters}
return model
}