We have re-generated the GT centroids as follows. ----------------------------------------------------------------------- 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. -----------------------------------------------------------------------