Novel Two-Dimensional Visualization Approaches for Multivariate Centroids of Clustering Algorithms

Algorithm 1

K-means++.

	Input: Number of the centroids, k
	Output: Set of the final centroids, C
	Begin
	≔ Randomly selected element in I
	: Set of the initial centroids
	Y: Set of the distances between and the closest element to in
	y: Length of Y
	Add into
	Add the distance between and the closest element to in , into Y
	Repeat
	For i = 1 : y
	U ≔ U +
	u ≔ A random real number between 0 and U
	p ≔ 2
	Repeat
	U ′≔ 0
	For i = 1 : p − 1
	U ′≔ U′ +
	p ≔ p + 1
	Until U ≥ u > U′
	Add Ip−1 into
	Add the distance between Ip−1 and the closest element to Ip−1 in , into Y
	Until has k centroids
	Run the standard K-means with
	Return C returned from the standard K-means
	End