func TestComputeCentroid(t *testing.T) {
empty := matrix.Zeros(0, 0)
_, err := ComputeCentroid(empty)
if err == nil {
t.Errorf("Did not raise error on empty matrix")
}
twoByTwo := matrix.Ones(2, 2)
centr, err := ComputeCentroid(twoByTwo)
if err != nil {
t.Errorf("Could not compute centroid, err=%v", err)
}
expected := matrix.MakeDenseMatrix([]float64{1.0, 1.0}, 1, 2)
if !matrix.Equals(centr, expected) {
t.Errorf("Incorrect centroid: was %v, should have been %v", expected, centr)
}
twoByTwo.Set(0, 0, 3.0)
expected.Set(0, 0, 2.0)
centr, err = ComputeCentroid(twoByTwo)
if err != nil {
t.Errorf("Could not compute centroid, err=%v", err)
}
if !matrix.Equals(centr, expected) {
t.Errorf("Incorrect centroid: was %v, should have been %v", expected, centr)
}
}
// variance is the maximum likelihood estimate (MLE) for the variance, under
// the identical spherical Gaussian assumption.
//
// points = an R x M matrix of all point coordinates.
//
// CentPointDist = R x M+1 matrix. Column 0 contains the index {0...K-1} of
// a centroid. Column 1 contains (datapoint_i - mu(i))^2
//
// centroids = K x M+1 matrix. Column 0 continas the centroid index {0...K}.
// Columns 1...M contain the centroid coordinates. (See kmeans() for an example.)
//
// 1 __ 2
// ------ * \ (x - mu )
// R - K /__ i i (i)
//
// where i indexes the individual points.
//
// N.B. mu_(i) denotes the coordinates of the centroid closest to the i-th data point. Not
// the mean of the entire cluster.
//
// TODO would it be more efficient to calculate it in one pass instead of pre-calculating the
// mean? Or will we always have to pre-calc to fill the cluster?
//
// 1 __ 2 1 / __ \2
// ----- \ x - -------- |\ x |
// R - K /__ i 2 \/__ i /
// (R - K)
//
func variance(c cluster, measurer VectorMeasurer) float64 {
if matrix.Equals(c.Points, c.Centroid) == true {
return 0.0
}
sum := float64(0)
denom := float64(c.Numpoints() - c.Numcentroids())
for i := 0; i < c.Numpoints(); i++ {
p := c.Points.GetRowVector(i)
mu_i := c.Centroid.GetRowVector(0)
dist := measurer.CalcDist(mu_i, p)
sum += dist * dist
}
v := (1.0 / denom) * sum
return v
}