// variance calculates the unbiased variance based on the number of data points
// and centroids (i.e., parameters). In our case, numcentroids should always be 1
// since each data point has been paired with one centroid.
//
// The points matrix contains the coordinates of the data points.
// The centroids matrix is 1Xn that contains the centroid cooordinates.
// variance = // 1 / (numpoints - numcentroids) * sum for all points (x_i - mean_(i))^2
func variance(points, centroid *matrix.DenseMatrix, measurer matutil.VectorMeasurer) (float64, error) {
crows, _ := centroid.GetSize()
if crows > 1 {
return float64(0), errors.New(fmt.Sprintf("variance: expected centroid matrix with 1 row, received matrix with %d rows.", crows))
}
prows, _ := points.GetSize()
// Term 1
t1 := float64(1 / float64((prows - 1)))
// Mean of distance between all points and the centroid.
mean := modelMean(points, centroid)
// Term 2
// Sum over all points (point_i - mean(i))^2
t2 := float64(0)
for i := 0; i < prows; i++ {
p := points.GetRowVector(i)
dist, err := measurer.CalcDist(p, mean)
if err != nil {
return float64(-1), errors.New(fmt.Sprintf("variance: CalcDist returned: %v", err))
}
t2 += math.Pow(dist, 2)
}
variance := t1 * t2
return variance, nil
}
// addPairPointCentroidJobs adds a job to the jobs channel.
func addPairPointCentroidJobs(jobs chan<- PairPointCentroidJob, datapoints,
centroids *matrix.DenseMatrix, measurer VectorMeasurer, results chan<- PairPointCentroidResult) {
numRows, _ := datapoints.GetSize()
for i := 0; i < numRows; i++ {
point := datapoints.GetRowVector(i)
jobs <- PairPointCentroidJob{point, centroids, results, i, measurer}
}
close(jobs)
}
// modelMean calculates the mean between all points in a model and a centroid.
func modelMean(points, centroid *matrix.DenseMatrix) *matrix.DenseMatrix {
prows, pcols := points.GetSize()
pdist := matrix.Zeros(prows, pcols)
for i := 0; i < prows; i++ {
diff := matrix.Difference(centroid, points.GetRowVector(i))
pdist.SetRowVector(diff, i)
}
return pdist.MeanCols()
}
// DataCentroids picks k distinct points from the dataset. If k is > points in
// the matrix then k is set to the number of points.
func (c DataCentroids) ChooseCentroids(mat *matrix.DenseMatrix, k int) *matrix.DenseMatrix {
// first set up a map to keep track of which data points have already been chosen so we don't dupe
rows, cols := mat.GetSize()
centroids := matrix.Zeros(k, cols)
if k > rows {
k = rows
}
chosenIdxs := make(map[int]bool, k)
for len(chosenIdxs) < k {
index := rand.Intn(rows)
chosenIdxs[index] = true
}
i := 0
for idx, _ := range chosenIdxs {
centroids.SetRowVector(mat.GetRowVector(idx).Copy(), i)
i += 1
}
return centroids
}
// Kmeansbi bisects a given cluster and determines which centroids give the lowest error.
// Take the points in a cluster
// While the number of cluster < k
// for every cluster
// measure total error
// cacl kmeansp with k=2 on a given cluster
// measure total error after kmeansp split
// choose the cluster split with the lowest SSE
// commit the chosen split
//
// N.B. We are using SSE until the BIC is completed.
func Kmeansbi(datapoints *matrix.DenseMatrix, k int, cc CentroidChooser, measurer matutil.VectorMeasurer) (matCentroidlist, clusterAssignment *matrix.DenseMatrix, err error) {
numRows, numCols := datapoints.GetSize()
clusterAssignment = matrix.Zeros(numRows, numCols)
matCentroidlist = matrix.Zeros(k, numCols)
centroid0 := datapoints.MeanCols()
centroidlist := []*matrix.DenseMatrix{centroid0}
// Initially create one cluster.
for j := 0; j < numRows; j++ {
point := datapoints.GetRowVector(j)
distJ, err := measurer.CalcDist(centroid0, point)
if err != nil {
return matCentroidlist, clusterAssignment, errors.New(fmt.Sprintf("Kmeansbi: CalcDist returned err=%v", err))
}
clusterAssignment.Set(j, 1, math.Pow(distJ, 2))
}
var bestClusterAssignment, bestNewCentroids *matrix.DenseMatrix
var bestCentroidToSplit int
// Find the best centroid configuration.
for len(centroidlist) < k {
lowestSSE := math.Inf(1)
// Split cluster
for i, _ := range centroidlist {
// Get the points in this cluster
pointsCurCluster, err := clusterAssignment.FiltCol(float64(i), float64(i), 0)
if err != nil {
return matCentroidlist, clusterAssignment, err
}
centroids, splitClusterAssignment, err := Kmeansp(pointsCurCluster, 2, cc, measurer)
if err != nil {
return matCentroidlist, clusterAssignment, err
}
/* centroids is a 2X2 matrix of the best centroids found by kmeans
splitClustAssignment is a mX2 matrix where col0 is either 0 or 1 and refers to the rows in centroids
where col1 cotains the squared error between a centroid and a point. The rows here correspond to
the rows in ptsInCurrCluster. For example, if row 2 contains [1, 7.999] this means that centroid 1
has been paired with the point in row 2 of splitClustAssignment and that the squared error (distance
between centroid and point) is 7.999.
*/
// Calculate the sum of squared errors for each centroid.
// This give a statistcal measurement of how good
// the clustering is for this cluster.
sseSplit := splitClusterAssignment.SumCol(1)
// Calculate the SSE for the original cluster
sqerr, err := clusterAssignment.FiltCol(float64(0), math.Inf(1), 0)
if err != nil {
return matCentroidlist, clusterAssignment, err
}
sseNotSplit := sqerr.SumCol(1)
// TODO: Pre-BCI is this the best way to evaluate?
if sseSplit+sseNotSplit < lowestSSE {
bestCentroidToSplit = 1
bestNewCentroids = matrix.MakeDenseCopy(centroids)
bestClusterAssignment = matrix.MakeDenseCopy(splitClusterAssignment)
}
}
// Applying the split overwrites the existing cluster assginments for the
// cluster you have decided to split. Kmeansp() returned two clusters
// labeled 0 and 1. Change these cluster numbers to the cluster number
// you are splitting and the next cluster to be added.
m, err := bestClusterAssignment.FiltColMap(1, 1, 0)
if err != nil {
return matCentroidlist, clusterAssignment, err
}
for i, _ := range m {
bestClusterAssignment.Set(i, 0, float64(len(centroidlist)))
}
n, err := bestClusterAssignment.FiltColMap(0, 0, 0)
if err != nil {
return matCentroidlist, clusterAssignment, err
}
for i, _ := range n {
bestClusterAssignment.Set(i, 1, float64(bestCentroidToSplit))
}
fmt.Printf("Best centroid to split %f\n", bestCentroidToSplit)
r, _ := bestClusterAssignment.GetSize()
fmt.Printf("The length of best cluster assesment is %f\n", r)
// Replace a centroid with the two best centroids from the split.
centroidlist[bestCentroidToSplit] = bestNewCentroids.GetRowVector(0)
centroidlist = append(centroidlist, bestNewCentroids.GetRowVector(1))
// Reassign new clusters and SSE
rows, _ := clusterAssignment.GetSize()
for i, j := 0, 0; i < rows; i++ {
if clusterAssignment.Get(i, 0) == float64(bestCentroidToSplit) {
clusterAssignment.Set(i, 0, bestClusterAssignment.Get(j, 0))
clusterAssignment.Set(i, 1, bestClusterAssignment.Get(j, 1))
j++
}
}
// make centroidlist into a matrix
s := make([][]float64, len(centroidlist))
for i, mat := range centroidlist {
s[i][0] = mat.Get(0, 0)
s[i][1] = mat.Get(0, 1)
}
matCentroidlist = matrix.MakeDenseMatrixStacked(s)
}
return matCentroidlist, clusterAssignment, nil
}