We have re-generated the GT centroids as follows.
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Birch 1:
The centroid locations were first optimized by genetic algorihm (GA)
[Fränti, Pat.Rec.Lett.2000]. The centroids form a 10x10 grid. Their
average distance was calculated as 92247. A grid using this parameter
was then manually fit for the data, and the result locations recorded
as the ground truth centroids. Ground truth partition lables were
obtained by mapping each point to its nearest centroid.
Birch 2:
Centroid locations were first optimized by GA, and their average
distance in x-axis was calculated as 9512 from the result.
The centroids form a sine curve function:
y(x) = amplitude * sin(2*pi*frequency*x + phaseshift) + offset
It was manually fit using parameters:
Offset = 43659
Amplitude = -37819
Phaseshift = 20.8388
Frequency = 0.000004205
Ground truth centroids were then plotted in this curve and the
corresponding x and y(x) were recorded as the groung truth centroids.
Ground truth partitions were obtained by mapping each point to its
nearest centroid.
Birch 3:
Centroid locations were first optimized by GA, from which they were
manually tuned and their locations recorded as the ground truth.
Due to the overlap, ground truth partitions were not calculated.
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